{"id":77041,"date":"2026-02-23T22:10:46","date_gmt":"2026-02-23T14:10:46","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/77041.html"},"modified":"2026-02-23T22:10:46","modified_gmt":"2026-02-23T14:10:46","slug":"agent-%e5%b7%a5%e4%bd%9c%e6%b5%81%e8%87%aa%e6%88%91%e8%bf%9b%e5%8c%96%ef%bc%9a%e5%bc%ba%e5%8c%96%e5%ad%a6%e4%b9%a0%e5%a6%82%e4%bd%95%e8%ae%a9%e6%99%ba%e8%83%bd%e4%bd%93%e8%87%aa%e5%8a%a8%e5%af%bb","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/77041.html","title":{"rendered":"Agent \u5de5\u4f5c\u6d41\u81ea\u6211\u8fdb\u5316\uff1a\u5f3a\u5316\u5b66\u4e60\u5982\u4f55\u8ba9\u667a\u80fd\u4f53\u81ea\u52a8\u5bfb\u627e\u6700\u4f18 SOP"},"content":{"rendered":"

1 \u5f15\u8a00：\u4ece\u9759\u6001\u7f16\u6392\u5230\u52a8\u6001\u6f14\u5316\u7684\u8303\u5f0f\u8dc3\u8fc1<\/h2>\n

1.1 \u667a\u80fd\u4f53\u5de5\u4f5c\u6d41\u7684\u6f14\u8fdb\u8109\u7edc<\/h3>\n

\u4eba\u5de5\u667a\u80fd\u9886\u57df\u6b63\u7ecf\u5386\u7740\u4ece\u5355\u4e00\u6a21\u578b\u5230\u590d\u5408\u667a\u80fd\u7cfb\u7edf\u7684\u6df1\u523b\u53d8\u9769\u3002\u5927\u578b\u8bed\u8a00\u6a21\u578b（Large Language Models, LLMs）\u7684\u7a81\u7834\u6027\u8fdb\u5c55\u4e3a\u6784\u5efa\u901a\u7528\u667a\u80fd\u4f53（Agent）\u5960\u5b9a\u4e86\u575a\u5b9e\u57fa\u7840，\u7136\u800c，\u5982\u4f55\u4f7f\u8fd9\u4e9b\u667a\u80fd\u4f53\u5728\u590d\u6742\u591a\u53d8\u7684\u73af\u5883\u4e2d\u6301\u7eed\u4f18\u5316\u5176\u884c\u4e3a\u7b56\u7565，\u6210\u4e3a\u5f53\u524d\u7814\u7a76\u7684\u6838\u5fc3\u6311\u6218\u3002\u4f20\u7edf\u7684\u624b\u52a8\u8bbe\u8ba1\u5de5\u4f5c\u6d41（Workflow）\u548c\u6807\u51c6\u64cd\u4f5c\u7a0b\u5e8f（Standard Operating Procedures, SOP）\u867d\u7136\u5728\u7279\u5b9a\u573a\u666f\u4e0b\u8868\u73b0\u7a33\u5b9a，\u4f46\u9762\u5bf9\u5f00\u653e\u57df\u4efb\u52a1\u7684\u591a\u6837\u6027\u4e0e\u52a8\u6001\u6027\u65f6，\u5176\u5c40\u9650\u6027\u65e5\u76ca\u51f8\u663e[1]\u3002<\/p>\n

\u667a\u80fd\u4f53\u5de5\u4f5c\u6d41\u7684\u7814\u7a76\u7ecf\u5386\u4e86\u4e09\u4e2a\u4e3b\u8981\u53d1\u5c55\u9636\u6bb5\u3002\u7b2c\u4e00\u9636\u6bb5\u4ee5\u89c4\u5219\u9a71\u52a8\u4e3a\u6838\u5fc3，\u7814\u7a76\u8005\u901a\u8fc7\u9884\u5b9a\u4e49\u7684\u6761\u4ef6-\u52a8\u4f5c\u89c4\u5219（If-Then Rules）\u6784\u5efa\u786e\u5b9a\u6027\u6d41\u7a0b\u3002\u8fd9\u79cd\u65b9\u6cd5\u7684\u53ef\u89e3\u91ca\u6027\u5f3a，\u4f46\u7f3a\u4e4f\u9002\u5e94\u6027，\u96be\u4ee5\u5904\u7406\u8fb9\u754c\u60c5\u51b5\u3002\u7b2c\u4e8c\u9636\u6bb5\u5f15\u5165\u4e86\u57fa\u4e8e\u68c0\u7d22\u7684\u589e\u5f3a\u751f\u6210（Retrieval-Augmented Generation, RAG）\u6280\u672f，\u4f7f\u667a\u80fd\u4f53\u80fd\u591f\u5229\u7528\u5916\u90e8\u77e5\u8bc6\u5e93\u52a8\u6001\u8c03\u6574\u54cd\u5e94，\u4f46\u5de5\u4f5c\u6d41\u7ed3\u6784\u672c\u8eab\u4ecd\u4fdd\u6301\u9759\u6001[2]\u3002\u5f53\u524d\u6b63\u5904\u4e8e\u7b2c\u4e09\u9636\u6bb5，\u5373\u81ea\u6211\u8fdb\u5316（Self-Evolution）\u9636\u6bb5，\u667a\u80fd\u4f53\u901a\u8fc7\u4e0e\u73af\u5883\u7684\u6301\u7eed\u4ea4\u4e92，\u5229\u7528\u5f3a\u5316\u5b66\u4e60（Reinforcement Learning, RL）\u7b97\u6cd5\u81ea\u52a8\u4f18\u5316\u5176\u5de5\u4f5c\u6d41\u7ed3\u6784，\u4ece\u800c\u5b9e\u73b0\u4ece"\u88ab\u52a8\u6267\u884c"\u5230"\u4e3b\u52a8\u5b66\u4e60"\u7684\u8d28\u53d8[3]\u3002<\/p>\n

\u81ea\u6211\u8fdb\u5316\u667a\u80fd\u4f53\u7684\u6838\u5fc3\u7279\u5f81\u5728\u4e8e\u5176\u5177\u5907\u5143\u8ba4\u77e5\u80fd\u529b（Metacognitive Capability），\u80fd\u591f\u53cd\u601d\u81ea\u8eab\u51b3\u7b56\u8fc7\u7a0b\u3001\u8bc6\u522b\u5931\u8d25\u6a21\u5f0f，\u5e76\u636e\u6b64\u8c03\u6574\u672a\u6765\u884c\u4e3a\u7b56\u7565\u3002\u8fd9\u79cd\u80fd\u529b\u4f7f\u5f97\u667a\u80fd\u4f53\u4e0d\u518d\u4f9d\u8d56\u4eba\u5de5\u9884\u8bbe\u7684\u56fa\u5b9aSOP，\u800c\u662f\u80fd\u591f\u5728\u4efb\u52a1\u6267\u884c\u8fc7\u7a0b\u4e2d\u52a8\u6001\u53d1\u73b0\u3001\u9a8c\u8bc1\u5e76\u56fa\u5316\u6700\u4f18\u64cd\u4f5c\u5e8f\u5217\u3002\u7814\u7a76\u8868\u660e，\u7ecf\u8fc7\u591a\u8f6e\u8fed\u4ee3\u81ea\u6211\u8fdb\u5316\u7684\u667a\u80fd\u4f53，\u5728\u590d\u6742\u63a8\u7406\u4efb\u52a1\u4e0a\u7684\u6210\u529f\u7387\u53ef\u63d0\u534740%\u4ee5\u4e0a[4]\u3002<\/p>\n

1.2 \u5f3a\u5316\u5b66\u4e60\u8d4b\u80fd\u5de5\u4f5c\u6d41\u4f18\u5316\u7684\u6838\u5fc3\u673a\u5236<\/h3>\n

\u5f3a\u5316\u5b66\u4e60\u4e3a\u667a\u80fd\u4f53\u5de5\u4f5c\u6d41\u7684\u81ea\u6211\u8fdb\u5316\u63d0\u4f9b\u4e86\u7406\u8bba\u6846\u67b6\u548c\u7b97\u6cd5\u5de5\u5177\u3002\u4e0e\u4f20\u7edf\u76d1\u7763\u5b66\u4e60\u4e0d\u540c，\u5f3a\u5316\u5b66\u4e60\u901a\u8fc7\u4e0e\u73af\u5883\u7684\u4ea4\u4e92\u5b66\u4e60\u6700\u4f18\u7b56\u7565，\u65e0\u9700\u5927\u91cf\u6807\u6ce8\u6570\u636e，\u8fd9\u4e00\u7279\u6027\u4f7f\u5176\u7279\u522b\u9002\u5408\u5f00\u653e\u57df\u4efb\u52a1\u573a\u666f\u3002\u5728Agent\u5de5\u4f5c\u6d41\u4f18\u5316\u95ee\u9898\u4e2d，\u72b6\u6001\u7a7a\u95f4\u5bf9\u5e94\u4e8e\u4efb\u52a1\u6267\u884c\u7684\u4e2d\u95f4\u72b6\u6001，\u52a8\u4f5c\u7a7a\u95f4\u5bf9\u5e94\u4e8e\u53ef\u6267\u884c\u7684\u64cd\u4f5c（\u5982\u5de5\u5177\u8c03\u7528\u3001\u63a8\u7406\u6b65\u9aa4\u3001\u4fe1\u606f\u68c0\u7d22\u7b49），\u800c\u5956\u52b1\u4fe1\u53f7\u5219\u6765\u6e90\u4e8e\u4efb\u52a1\u5b8c\u6210\u8d28\u91cf\u3001\u6267\u884c\u6548\u7387\u7b49\u591a\u7ef4\u5ea6\u53cd\u9988[5]\u3002<\/p>\n

\u5c06\u5de5\u4f5c\u6d41\u4f18\u5316\u5f62\u5f0f\u5316\u4e3a\u5f3a\u5316\u5b66\u4e60\u95ee\u9898\u9762\u4e34\u4e09\u4e2a\u6838\u5fc3\u6311\u6218\u3002\u9996\u5148\u662f\u957f\u7a0b\u4fe1\u7528\u5206\u914d（Long-Term Credit Assignment）\u95ee\u9898：\u5de5\u4f5c\u6d41\u901a\u5e38\u5305\u542b\u6570\u5341\u751a\u81f3\u4e0a\u767e\u4e2a\u6b65\u9aa4，\u5982\u4f55\u51c6\u786e\u8bc4\u4f30\u6bcf\u4e2a\u4e2d\u95f4\u6b65\u9aa4\u5bf9\u6700\u7ec8\u7ed3\u679c\u7684\u8d21\u732e\u81f3\u5173\u91cd\u8981\u3002\u5176\u6b21\u662f\u7a00\u758f\u5956\u52b1（Sparse Reward）\u95ee\u9898：\u53ea\u6709\u5728\u4efb\u52a1\u5b8c\u6210\u65f6\u624d\u80fd\u83b7\u5f97\u660e\u786e\u7684\u5956\u52b1\u4fe1\u53f7，\u4e2d\u95f4\u6b65\u9aa4\u7f3a\u4e4f\u5373\u65f6\u53cd\u9988\u3002\u7b2c\u4e09\u662f\u7ec4\u5408\u7206\u70b8（Combinatorial Explosion）\u95ee\u9898：\u968f\u7740\u5de5\u4f5c\u6d41\u590d\u6742\u5ea6\u7684\u589e\u52a0，\u53ef\u80fd\u7684\u64cd\u4f5c\u5e8f\u5217\u5448\u6307\u6570\u7ea7\u589e\u957f，\u6709\u6548\u63a2\u7d22\u53d8\u5f97\u6781\u4e3a\u56f0\u96be[6]\u3002<\/p>\n

\u9488\u5bf9\u8fd9\u4e9b\u6311\u6218，\u7814\u7a76\u8005\u63d0\u51fa\u4e86\u591a\u79cd\u521b\u65b0\u89e3\u51b3\u65b9\u6848\u3002\u8fc7\u7a0b\u5956\u52b1\u6a21\u578b（Process Reward Model, PRM）\u901a\u8fc7\u5728\u6bcf\u4e00\u6b65\u63d0\u4f9b\u7ec6\u7c92\u5ea6\u7684\u8bc4\u4f30\u4fe1\u53f7，\u6709\u6548\u7f13\u89e3\u4e86\u4fe1\u7528\u5206\u914d\u95ee\u9898[7]\u3002Group Relative Policy Optimization（GRPO）\u7b49\u7b97\u6cd5\u901a\u8fc7\u7ec4\u5185\u76f8\u5bf9\u4f18\u52bf\u4f30\u8ba1，\u964d\u4f4e\u4e86\u5bf9\u4ef7\u503c\u51fd\u6570\u7684\u4f9d\u8d56，\u63d0\u5347\u4e86\u8bad\u7ec3\u7a33\u5b9a\u6027[8]\u3002\u5c42\u6b21\u5316\u5f3a\u5316\u5b66\u4e60（Hierarchical Reinforcement Learning）\u5219\u901a\u8fc7\u5c06\u590d\u6742\u4efb\u52a1\u5206\u89e3\u4e3a\u5b50\u76ee\u6807\u5e8f\u5217，\u6709\u6548\u5e94\u5bf9\u4e86\u7ec4\u5408\u7206\u70b8\u6311\u6218[9]\u3002<\/p>\n

1.3 \u7814\u7a76\u610f\u4e49\u4e0e\u5e94\u7528\u524d\u666f<\/h3>\n

Agent\u5de5\u4f5c\u6d41\u7684\u81ea\u6211\u8fdb\u5316\u6280\u672f\u5177\u6709\u6df1\u8fdc\u7684\u7406\u8bba\u610f\u4e49\u548c\u5e7f\u9614\u7684\u5e94\u7528\u524d\u666f\u3002\u4ece\u7406\u8bba\u5c42\u9762\u770b，\u8fd9\u4e00\u7814\u7a76\u65b9\u5411\u67b6\u8d77\u4e86\u8ba4\u77e5\u79d1\u5b66\u3001\u63a7\u5236\u8bba\u4e0e\u4eba\u5de5\u667a\u80fd\u4e4b\u95f4\u7684\u6865\u6881\u3002\u667a\u80fd\u4f53\u901a\u8fc7\u8bd5\u9519\u5b66\u4e60\u4f18\u5316\u884c\u4e3a\u7b56\u7565\u7684\u8fc7\u7a0b，\u4e0e\u4eba\u7c7b\u6280\u80fd\u4e60\u5f97\u7684\u673a\u5236\u9ad8\u5ea6\u76f8\u4f3c，\u4e3a\u7406\u89e3\u667a\u80fd\u7684\u672c\u8d28\u63d0\u4f9b\u4e86\u65b0\u7684\u89c6\u89d2[10]\u3002\u4ece\u5e94\u7528\u5c42\u9762\u770b，\u81ea\u6211\u8fdb\u5316Agent\u80fd\u591f\u663e\u8457\u964d\u4f4e\u4eba\u5de5\u8bbe\u8ba1\u5de5\u4f5c\u6d41\u7684\u6210\u672c，\u63d0\u5347\u7cfb\u7edf\u5728\u52a8\u6001\u73af\u5883\u4e2d\u7684\u9002\u5e94\u80fd\u529b\u3002<\/p>\n

\u5728\u5b9e\u9645\u5e94\u7528\u573a\u666f\u4e2d，\u81ea\u6211\u8fdb\u5316Agent\u5df2\u5c55\u73b0\u51fa\u5de8\u5927\u6f5c\u529b\u3002\u5728\u8f6f\u4ef6\u5f00\u53d1\u9886\u57df，\u80fd\u591f\u81ea\u4e3b\u89c4\u5212\u3001\u7f16\u7801\u3001\u6d4b\u8bd5\u5e76\u4fee\u590d\u7f3a\u9677\u7684Agent\u6b63\u5728\u6539\u53d8\u4f20\u7edf\u7684\u5f00\u53d1\u6a21\u5f0f[11]\u3002\u5728\u79d1\u5b66\u7814\u7a76\u4e2d，\u5177\u5907\u81ea\u4e3b\u5047\u8bbe\u751f\u6210\u3001\u5b9e\u9a8c\u8bbe\u8ba1\u548c\u6570\u636e\u5206\u6790\u80fd\u529b\u7684Agent\u52a0\u901f\u4e86\u53d1\u73b0\u8fdb\u7a0b[12]\u3002\u5728\u5ba2\u6237\u670d\u52a1\u9886\u57df，\u80fd\u591f\u6839\u636e\u5bf9\u8bdd\u4e0a\u4e0b\u6587\u52a8\u6001\u8c03\u6574\u5e94\u7b54\u7b56\u7565\u7684Agent\u63d0\u4f9b\u4e86\u66f4\u4f18\u8d28\u7684\u7528\u6237\u4f53\u9a8c[13]\u3002<\/p>\n

\u672c\u6587\u5c06\u7cfb\u7edf\u6027\u5730\u9610\u8ff0Agent\u5de5\u4f5c\u6d41\u81ea\u6211\u8fdb\u5316\u7684\u7406\u8bba\u57fa\u7840\u3001\u6838\u5fc3\u7b97\u6cd5\u548c\u5b9e\u73b0\u673a\u5236\u3002\u6211\u4eec\u5c06\u4ece\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b（Markov Decision Process, MDP）\u7684\u5f62\u5f0f\u5316\u6846\u67b6\u51fa\u53d1，\u6df1\u5165\u5206\u6790\u8fc7\u7a0b\u5956\u52b1\u6a21\u578b\u3001\u7b56\u7565\u4f18\u5316\u7b97\u6cd5\u3001\u591a\u667a\u80fd\u4f53\u534f\u4f5c\u673a\u5236\u7b49\u5173\u952e\u6280\u672f，\u5e76\u901a\u8fc7\u6570\u5b66\u63a8\u5bfc\u548c\u7b97\u6cd5\u63cf\u8ff0\u63ed\u793a\u5176\u5185\u5728\u539f\u7406\u3002\u6700\u540e，\u6211\u4eec\u5c06\u8ba8\u8bba\u5f53\u524d\u9762\u4e34\u7684\u6311\u6218\u548c\u672a\u6765\u7814\u7a76\u65b9\u5411，\u4e3a\u8fd9\u4e00\u9886\u57df\u7684\u6301\u7eed\u63a2\u7d22\u63d0\u4f9b\u53c2\u8003\u3002<\/p>\n

#mermaid-svg-fqWc3iOPbHF99o8f{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-fqWc3iOPbHF99o8f .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-fqWc3iOPbHF99o8f .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-fqWc3iOPbHF99o8f .error-icon{fill:#552222;}#mermaid-svg-fqWc3iOPbHF99o8f .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-fqWc3iOPbHF99o8f .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-fqWc3iOPbHF99o8f .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-fqWc3iOPbHF99o8f .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-fqWc3iOPbHF99o8f .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-fqWc3iOPbHF99o8f .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-fqWc3iOPbHF99o8f .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-fqWc3iOPbHF99o8f .marker{fill:#333333;stroke:#333333;}#mermaid-svg-fqWc3iOPbHF99o8f .marker.cross{stroke:#333333;}#mermaid-svg-fqWc3iOPbHF99o8f svg{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-fqWc3iOPbHF99o8f p{margin:0;}#mermaid-svg-fqWc3iOPbHF99o8f .label{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;color:#333;}#mermaid-svg-fqWc3iOPbHF99o8f .cluster-label text{fill:#333;}#mermaid-svg-fqWc3iOPbHF99o8f .cluster-label span{color:#333;}#mermaid-svg-fqWc3iOPbHF99o8f .cluster-label span p{background-color:transparent;}#mermaid-svg-fqWc3iOPbHF99o8f .label text,#mermaid-svg-fqWc3iOPbHF99o8f span{fill:#333;color:#333;}#mermaid-svg-fqWc3iOPbHF99o8f .node rect,#mermaid-svg-fqWc3iOPbHF99o8f .node circle,#mermaid-svg-fqWc3iOPbHF99o8f .node ellipse,#mermaid-svg-fqWc3iOPbHF99o8f .node polygon,#mermaid-svg-fqWc3iOPbHF99o8f .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-fqWc3iOPbHF99o8f .rough-node .label text,#mermaid-svg-fqWc3iOPbHF99o8f .node .label text,#mermaid-svg-fqWc3iOPbHF99o8f .image-shape .label,#mermaid-svg-fqWc3iOPbHF99o8f .icon-shape .label{text-anchor:middle;}#mermaid-svg-fqWc3iOPbHF99o8f .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-fqWc3iOPbHF99o8f .rough-node .label,#mermaid-svg-fqWc3iOPbHF99o8f .node .label,#mermaid-svg-fqWc3iOPbHF99o8f .image-shape .label,#mermaid-svg-fqWc3iOPbHF99o8f .icon-shape .label{text-align:center;}#mermaid-svg-fqWc3iOPbHF99o8f .node.clickable{cursor:pointer;}#mermaid-svg-fqWc3iOPbHF99o8f .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-fqWc3iOPbHF99o8f .arrowheadPath{fill:#333333;}#mermaid-svg-fqWc3iOPbHF99o8f .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-fqWc3iOPbHF99o8f .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-fqWc3iOPbHF99o8f .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-fqWc3iOPbHF99o8f .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-fqWc3iOPbHF99o8f .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-fqWc3iOPbHF99o8f .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-fqWc3iOPbHF99o8f .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-fqWc3iOPbHF99o8f .cluster text{fill:#333;}#mermaid-svg-fqWc3iOPbHF99o8f .cluster span{color:#333;}#mermaid-svg-fqWc3iOPbHF99o8f div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-fqWc3iOPbHF99o8f .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-fqWc3iOPbHF99o8f rect.text{fill:none;stroke-width:0;}#mermaid-svg-fqWc3iOPbHF99o8f .icon-shape,#mermaid-svg-fqWc3iOPbHF99o8f .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-fqWc3iOPbHF99o8f .icon-shape p,#mermaid-svg-fqWc3iOPbHF99o8f .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-fqWc3iOPbHF99o8f .icon-shape rect,#mermaid-svg-fqWc3iOPbHF99o8f .image-shape rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-fqWc3iOPbHF99o8f .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-fqWc3iOPbHF99o8f .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-fqWc3iOPbHF99o8f :root{–mermaid-font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;}<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Agent\u5de5\u4f5c\u6d41\u6f14\u8fdb<\/p>\n

<\/span><\/p>\n

\u89c4\u5219\u9a71\u52a8\u9636\u6bb5<\/p>\n

<\/span><\/p>\n

RAG\u589e\u5f3a\u9636\u6bb5<\/p>\n

<\/span><\/p>\n

\u81ea\u6211\u8fdb\u5316\u9636\u6bb5<\/p>\n

<\/span><\/p>\n

If-Then\u89c4\u5219<\/p>\n

<\/span><\/p>\n

\u786e\u5b9a\u6027\u6d41\u7a0b<\/p>\n

<\/span><\/p>\n

\u77e5\u8bc6\u68c0\u7d22<\/p>\n

<\/span><\/p>\n

\u9759\u6001\u7ed3\u6784<\/p>\n

<\/span><\/p>\n

\u5f3a\u5316\u5b66\u4e60\u4f18\u5316<\/p>\n

<\/span><\/p>\n

\u52a8\u6001SOP\u53d1\u73b0<\/p>\n

<\/span><\/p>\n

\u6301\u7eed\u81ea\u6211\u6539\u8fdb<\/p>\n

<\/span><\/p>\n

2 \u5f3a\u5316\u5b66\u4e60\u7406\u8bba\u57fa\u7840：\u4eceMDP\u5230\u7b56\u7565\u4f18\u5316<\/h2>\n

2.1 \u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\u7684\u5f62\u5f0f\u5316\u6846\u67b6<\/h3>\n

2.1.1 MDP\u7684\u57fa\u672c\u5b9a\u4e49\u4e0e\u8981\u7d20<\/h4>\n

\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\u662f\u63cf\u8ff0\u5e8f\u8d2f\u51b3\u7b56\u95ee\u9898\u7684\u6807\u51c6\u6570\u5b66\u6846\u67b6，\u4e3aAgent\u5de5\u4f5c\u6d41\u4f18\u5316\u63d0\u4f9b\u4e86\u4e25\u8c28\u7684\u7406\u8bba\u57fa\u7840\u3002\u4e00\u4e2a\u6807\u51c6\u7684MDP\u7531\u4e94\u5143\u7ec4 M=(S,A,P,R,\u03b3)\\\\mathcal{M} = (\\\\mathcal{S}, \\\\mathcal{A}, \\\\mathcal{P}, \\\\mathcal{R}, \\\\gamma)<\/span><\/span>M<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>S<\/span>,<\/span><\/span>A<\/span>,<\/span><\/span>P<\/span>,<\/span><\/span>R<\/span>,<\/span><\/span>\u03b3<\/span>)<\/span><\/span><\/span><\/span><\/span> \u5b9a\u4e49，\u5176\u4e2d\u5404\u8981\u7d20\u7684\u7269\u7406\u610f\u4e49\u548c\u5de5\u4f5c\u6d41\u573a\u666f\u4e2d\u7684\u5bf9\u5e94\u5173\u7cfb\u5982\u88681\u6240\u793a[14]\u3002<\/p>\n

\u88681 MDP\u8981\u7d20\u4e0eAgent\u5de5\u4f5c\u6d41\u573a\u666f\u7684\u5bf9\u5e94\u5173\u7cfb<\/p>\n\nMDP\u8981\u7d20\u6570\u5b66\u7b26\u53f7\u5de5\u4f5c\u6d41\u573a\u666f\u5bf9\u5e94\u5177\u4f53\u793a\u4f8b<\/tr>\n\n\n\n\n\n\n
\u72b6\u6001\u7a7a\u95f4<\/td>\nS\\\\mathcal{S}<\/span><\/span>S<\/span><\/span><\/span><\/span><\/span><\/td>\n\u4efb\u52a1\u6267\u884c\u7684\u4e2d\u95f4\u72b6\u6001<\/td>\n\u5f53\u524d\u5df2\u5b8c\u6210\u7684\u63a8\u7406\u6b65\u9aa4\u3001\u6536\u96c6\u7684\u4fe1\u606f\u3001\u4e2d\u95f4\u7ed3\u679c<\/td>\n<\/tr>\n
\u52a8\u4f5c\u7a7a\u95f4<\/td>\nA\\\\mathcal{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span><\/td>\n\u53ef\u6267\u884c\u7684\u64cd\u4f5c\u96c6\u5408<\/td>\n\u5de5\u5177\u8c03\u7528\u3001\u4fe1\u606f\u68c0\u7d22\u3001\u63a8\u7406\u751f\u6210\u3001\u7ed3\u679c\u8f93\u51fa<\/td>\n<\/tr>\n
\u72b6\u6001\u8f6c\u79fb<\/td>\nP\\\\mathcal{P}<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span><\/td>\n\u64cd\u4f5c\u6267\u884c\u540e\u7684\u72b6\u6001\u53d8\u5316<\/td>\n\u6267\u884c\u67d0\u5de5\u5177\u540e\u83b7\u5f97\u65b0\u4fe1\u606f，\u72b6\u6001\u76f8\u5e94\u66f4\u65b0<\/td>\n<\/tr>\n
\u5956\u52b1\u51fd\u6570<\/td>\nR\\\\mathcal{R}<\/span><\/span>R<\/span><\/span><\/span><\/span><\/span><\/td>\n\u4efb\u52a1\u5b8c\u6210\u8d28\u91cf\u7684\u91cf\u5316\u8bc4\u4f30<\/td>\n\u6b63\u786e\u7b54\u6848\u5f97\u6b63\u5956\u52b1，\u9519\u8bef\u7b54\u6848\u5f97\u8d1f\u5956\u52b1<\/td>\n<\/tr>\n
\u6298\u6263\u56e0\u5b50<\/td>\n\u03b3\\\\gamma<\/span><\/span>\u03b3<\/span><\/span><\/span><\/span><\/span><\/td>\n\u672a\u6765\u5956\u52b1\u7684\u6298\u73b0\u7a0b\u5ea6<\/td>\n\u901a\u5e38\u53d60.99，\u5e73\u8861\u5373\u65f6\u4e0e\u957f\u671f\u6536\u76ca<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u72b6\u6001\u7a7a\u95f4 S\\\\mathcal{S}<\/span><\/span>S<\/span><\/span><\/span><\/span><\/span> \u5728\u5de5\u4f5c\u6d41\u573a\u666f\u4e2d\u901a\u5e38\u5177\u6709\u9ad8\u7ef4\u6027\u548c\u7ed3\u6784\u6027\u3002\u4ee5\u95ee\u7b54Agent\u4e3a\u4f8b，\u72b6\u6001\u53ef\u80fd\u5305\u542b：\u5f53\u524d\u95ee\u9898\u7684\u6587\u672c\u8868\u793a\u3001\u5df2\u68c0\u7d22\u7684\u76f8\u5173\u6587\u6863\u96c6\u5408\u3001\u5df2\u751f\u6210\u7684\u63a8\u7406\u6b65\u9aa4\u5e8f\u5217\u3001\u4e2d\u95f4\u7ed3\u8bba\u7684\u7f6e\u4fe1\u5ea6\u5206\u6570\u7b49\u3002\u8fd9\u79cd\u590d\u5408\u72b6\u6001\u7ed3\u6784\u8981\u6c42\u7b97\u6cd5\u80fd\u591f\u6709\u6548\u5904\u7406\u5f02\u6784\u4fe1\u606f\u6e90[15]\u3002<\/p>\n

\u52a8\u4f5c\u7a7a\u95f4 A\\\\mathcal{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u7684\u8bbe\u8ba1\u76f4\u63a5\u5f71\u54cdAgent\u7684\u80fd\u529b\u8fb9\u754c\u3002\u5728ReAct（Reasoning and Acting）\u6846\u67b6\u4e2d，\u52a8\u4f5c\u88ab\u5206\u4e3a\u63a8\u7406\u52a8\u4f5c（Thought）\u548c\u6267\u884c\u52a8\u4f5c（Action）\u4e24\u7c7b[1]\u3002\u63a8\u7406\u52a8\u4f5c\u8d1f\u8d23\u5206\u6790\u5f53\u524d\u72b6\u6001\u5e76\u89c4\u5212\u4e0b\u4e00\u6b65，\u6267\u884c\u52a8\u4f5c\u5219\u4e0e\u5916\u90e8\u73af\u5883\u4ea4\u4e92（\u5982\u8c03\u7528\u641c\u7d22\u5f15\u64ce\u3001\u6267\u884c\u4ee3\u7801）\u3002\u8fd9\u79cd\u5206\u5c42\u52a8\u4f5c\u8bbe\u8ba1\u4f7f\u5f97Agent\u80fd\u591f\u8fdb\u884c\u6df1\u5ea6\u63a8\u7406\u4e0e\u6709\u6548\u884c\u52a8\u7684\u6709\u673a\u7ed3\u5408\u3002<\/p>\n

\u72b6\u6001\u8f6c\u79fb\u6982\u7387 P(s\u2032\u2223s,a)\\\\mathcal{P}(s'|s,a)<\/span><\/span>P<\/span>(<\/span>s<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span> \u63cf\u8ff0\u4e86\u5728\u72b6\u6001 ss<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span> \u6267\u884c\u52a8\u4f5c aa<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span> \u540e\u8f6c\u79fb\u5230\u72b6\u6001 s\u2032s'<\/span><\/span>s<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u6982\u7387\u3002\u5728\u786e\u5b9a\u6027\u73af\u5883（\u5982\u4ee3\u7801\u6267\u884c\u73af\u5883）\u4e2d，\u8f6c\u79fb\u662f\u786e\u5b9a\u6027\u7684；\u800c\u5728\u6d89\u53ca\u5916\u90e8API\u8c03\u7528\u6216\u4eba\u7c7b\u4ea4\u4e92\u7684\u573a\u666f\u4e2d，\u8f6c\u79fb\u5177\u6709\u968f\u673a\u6027\u3002\u7406\u89e3\u8f6c\u79fb\u7684\u968f\u673a\u7279\u6027\u5bf9\u4e8e\u8bbe\u8ba1\u9c81\u68d2\u7684\u7b56\u7565\u81f3\u5173\u91cd\u8981[16]\u3002<\/p>\n

2.1.2 \u8d1d\u5c14\u66fc\u65b9\u7a0b\u4e0e\u6700\u4f18\u6027\u539f\u7406<\/h4>\n

\u8d1d\u5c14\u66fc\u65b9\u7a0b（Bellman Equation）\u662f\u5f3a\u5316\u5b66\u4e60\u7406\u8bba\u7684\u6838\u5fc3，\u5b83\u5efa\u7acb\u4e86\u503c\u51fd\u6570\u4e0e\u7b56\u7565\u4e4b\u95f4\u7684\u9012\u5f52\u5173\u7cfb\u3002\u5bf9\u4e8e\u7ed9\u5b9a\u7b56\u7565 \u03c0\\\\pi<\/span><\/span>\u03c0<\/span><\/span><\/span><\/span><\/span>，\u5176\u72b6\u6001\u503c\u51fd\u6570 V\u03c0(s)V^\\\\pi(s)<\/span><\/span>V<\/span><\/span>\u03c0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>)<\/span><\/span><\/span><\/span><\/span> \u6ee1\u8db3[16]：<\/p>\n

V\u03c0(s)=Ea\u223c\u03c0(\u22c5\u2223s)[R(s,a)+\u03b3Es\u2032\u223cP(\u22c5\u2223s,a)[V\u03c0(s\u2032)]]V^\\\\pi(s) = \\\\mathbb{E}_{a \\\\sim \\\\pi(\\\\cdot|s)} \\\\left[ \\\\mathcal{R}(s,a) + \\\\gamma \\\\mathbb{E}_{s' \\\\sim \\\\mathcal{P}(\\\\cdot|s,a)} [V^\\\\pi(s')] \\\\right]<\/span><\/span>V<\/span><\/span>\u03c0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>E<\/span><\/span>a<\/span>\u223c<\/span>\u03c0<\/span>(<\/span>\u22c5<\/span>\u2223<\/span>s<\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span>R<\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span><\/span>+<\/span><\/span>\u03b3<\/span>E<\/span><\/span>s<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u223c<\/span>P<\/span>(<\/span>\u22c5<\/span>\u2223<\/span>s<\/span>,<\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>V<\/span><\/span>\u03c0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)]<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8be5\u65b9\u7a0b\u8868\u660e，\u72b6\u6001 ss<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span> \u7684\u503c\u7b49\u4e8e\u5373\u65f6\u5956\u52b1\u52a0\u4e0a\u6298\u6263\u540e\u7684\u671f\u671b\u672a\u6765\u503c\u3002\u5bf9\u4e8e\u52a8\u4f5c\u503c\u51fd\u6570 Q\u03c0(s,a)Q^\\\\pi(s,a)<\/span><\/span>Q<\/span><\/span>\u03c0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u8d1d\u5c14\u66fc\u65b9\u7a0b\u5f62\u5f0f\u4e3a：<\/p>\n

Q\u03c0(s,a)=R(s,a)+\u03b3Es\u2032\u223cP(\u22c5\u2223s,a)[Ea\u2032\u223c\u03c0(\u22c5\u2223s\u2032)[Q\u03c0(s\u2032,a\u2032)]]Q^\\\\pi(s,a) = \\\\mathcal{R}(s,a) + \\\\gamma \\\\mathbb{E}_{s' \\\\sim \\\\mathcal{P}(\\\\cdot|s,a)} \\\\left[ \\\\mathbb{E}_{a' \\\\sim \\\\pi(\\\\cdot|s')} [Q^\\\\pi(s',a')] \\\\right]<\/span><\/span>Q<\/span><\/span>\u03c0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>R<\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b3<\/span>E<\/span><\/span>s<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u223c<\/span>P<\/span>(<\/span>\u22c5<\/span>\u2223<\/span>s<\/span>,<\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span>E<\/span><\/span>a<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u223c<\/span>\u03c0<\/span>(<\/span>\u22c5<\/span>\u2223<\/span>s<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>Q<\/span><\/span>\u03c0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)]<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6700\u4f18\u503c\u51fd\u6570 V\u2217(s)=max\u2061\u03c0V\u03c0(s)V^*(s) = \\\\max_\\\\pi V^\\\\pi(s)<\/span><\/span>V<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>max<\/span><\/span>\u03c0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>V<\/span><\/span>\u03c0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>)<\/span><\/span><\/span><\/span><\/span> \u6ee1\u8db3\u8d1d\u5c14\u66fc\u6700\u4f18\u65b9\u7a0b：<\/p>\n

V\u2217(s)=max\u2061a\u2208A[R(s,a)+\u03b3Es\u2032\u223cP(\u22c5\u2223s,a)[V\u2217(s\u2032)]]V^*(s) = \\\\max_{a \\\\in \\\\mathcal{A}} \\\\left[ \\\\mathcal{R}(s,a) + \\\\gamma \\\\mathbb{E}_{s' \\\\sim \\\\mathcal{P}(\\\\cdot|s,a)} [V^*(s')] \\\\right]<\/span><\/span>V<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>a<\/span>\u2208<\/span>A<\/span><\/span><\/span><\/span><\/span>max<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span>R<\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span><\/span>+<\/span><\/span>\u03b3<\/span>E<\/span><\/span>s<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u223c<\/span>P<\/span>(<\/span>\u22c5<\/span>\u2223<\/span>s<\/span>,<\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>V<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)]<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6700\u4f18\u7b56\u7565 \u03c0\u2217\\\\pi^*<\/span><\/span>\u03c0<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u53ef\u901a\u8fc7\u8d2a\u5a6a\u5730\u9009\u62e9\u6700\u5927\u5316Q\u503c\u7684\u52a8\u4f5c\u83b7\u5f97：<\/p>\n

\u03c0\u2217(a\u2223s)={1if\u00a0a=arg\u2061max\u2061a\u2032Q\u2217(s,a\u2032)0otherwise\\\\pi^*(a|s) = \\\\begin{cases} 1 & \\\\text{if } a = \\\\arg\\\\max_{a'} Q^*(s,a') \\\\\\\\ 0 & \\\\text{otherwise} \\\\end{cases}<\/span><\/span>\u03c0<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span>\u2223<\/span>s<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>{<\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>if\u00a0<\/span><\/span>a<\/span><\/span>=<\/span><\/span>arg<\/span><\/span><\/span>max<\/span><\/span>a<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>Q<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>otherwise<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5728Agent\u5de5\u4f5c\u6d41\u4f18\u5316\u4e2d，\u8d1d\u5c14\u66fc\u65b9\u7a0b\u4e3a\u4fe1\u7528\u5206\u914d\u63d0\u4f9b\u4e86\u7406\u8bba\u57fa\u7840\u3002\u5f53Agent\u5b8c\u6210\u4e00\u4e2a\u957f\u7a0b\u4efb\u52a1\u5e76\u83b7\u5f97\u6700\u7ec8\u5956\u52b1\u65f6，\u901a\u8fc7\u53cd\u5411\u4f20\u64ad\u8d1d\u5c14\u66fc\u65b9\u7a0b，\u53ef\u4ee5\u5c06\u5956\u52b1\u4fe1\u53f7\u9010\u5c42\u5206\u89e3\u5230\u5404\u4e2a\u4e2d\u95f4\u6b65\u9aa4，\u4ece\u800c\u8bc4\u4f30\u6bcf\u4e2a\u52a8\u4f5c\u7684\u8d21\u732e\u5ea6[16]\u3002<\/p>\n

2.1.3 \u90e8\u5206\u53ef\u89c2\u6d4bMDP\u4e0e\u5de5\u4f5c\u6d41\u573a\u666f<\/h4>\n

\u5b9e\u9645\u5de5\u4f5c\u6d41\u573a\u666f\u5f80\u5f80\u4e0d\u6ee1\u8db3\u5b8c\u5168\u53ef\u89c2\u6d4b\u5047\u8bbe，\u667a\u80fd\u4f53\u53ea\u80fd\u83b7\u53d6\u90e8\u5206\u72b6\u6001\u4fe1\u606f\u3002\u8fd9\u7c7b\u95ee\u9898\u9700\u8981\u7528\u90e8\u5206\u53ef\u89c2\u6d4b\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b（Partially Observable MDP, POMDP）\u5efa\u6a21，\u5176\u5b9a\u4e49\u4e3a\u516d\u5143\u7ec4 MPO=(S,A,O,P,Z,R,\u03b3)\\\\mathcal{M}_{PO} = (\\\\mathcal{S}, \\\\mathcal{A}, \\\\mathcal{O}, \\\\mathcal{P}, \\\\mathcal{Z}, \\\\mathcal{R}, \\\\gamma)<\/span><\/span>M<\/span><\/span>PO<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>S<\/span>,<\/span><\/span>A<\/span>,<\/span><\/span>O<\/span>,<\/span><\/span>P<\/span>,<\/span><\/span>Z<\/span>,<\/span><\/span>R<\/span>,<\/span><\/span>\u03b3<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u5176\u4e2d O\\\\mathcal{O}<\/span><\/span>O<\/span><\/span><\/span><\/span><\/span> \u4e3a\u89c2\u6d4b\u7a7a\u95f4，Z(o\u2223s,a)\\\\mathcal{Z}(o|s,a)<\/span><\/span>Z<\/span>(<\/span>o<\/span>\u2223<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u89c2\u6d4b\u6982\u7387\u5206\u5e03[16]\u3002<\/p>\n

POMDP\u7684\u6838\u5fc3\u6311\u6218\u5728\u4e8e\u72b6\u6001\u7684\u4e0d\u786e\u5b9a\u6027\u3002Agent\u9700\u8981\u7ef4\u62a4\u4fe1\u5ff5\u72b6\u6001（Belief State）b(s)=P(s\u2223ht)b(s) = P(s|h_t)<\/span><\/span>b<\/span>(<\/span>s<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>P<\/span>(<\/span>s<\/span>\u2223<\/span>h<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>，\u5373\u57fa\u4e8e\u5386\u53f2\u4ea4\u4e92 ht=(o1,a1,…,ot)h_t = (o_1, a_1, …, o_t)<\/span><\/span>h<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>o<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>o<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u5bf9\u5f53\u524d\u72b6\u6001\u7684\u540e\u9a8c\u5206\u5e03\u3002\u4fe1\u5ff5\u72b6\u6001\u7684\u66f4\u65b0\u9075\u5faa\u8d1d\u53f6\u65af\u89c4\u5219：<\/p>\n

b\u2032(s\u2032)=\u03b7\u22c5Z(o\u2032\u2223s\u2032)\u2211s\u2208SP(s\u2032\u2223s,a)b(s)b'(s') = \\\\eta \\\\cdot \\\\mathcal{Z}(o'|s') \\\\sum_{s \\\\in \\\\mathcal{S}} \\\\mathcal{P}(s'|s,a) b(s)<\/span><\/span>b<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03b7<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>Z<\/span>(<\/span>o<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>s<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>s<\/span>\u2208<\/span>S<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>P<\/span>(<\/span>s<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span>b<\/span>(<\/span>s<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d \u03b7\\\\eta<\/span><\/span>\u03b7<\/span><\/span><\/span><\/span><\/span> \u4e3a\u5f52\u4e00\u5316\u5e38\u6570\u3002\u5728Agent\u5de5\u4f5c\u6d41\u4e2d，\u8fd9\u79cd\u4e0d\u786e\u5b9a\u6027\u6765\u6e90\u4e8e\u591a\u4e2a\u65b9\u9762：\u4fe1\u606f\u68c0\u7d22\u53ef\u80fd\u8fd4\u56de\u4e0d\u76f8\u5173\u7ed3\u679c\u3001\u5de5\u5177\u6267\u884c\u53ef\u80fd\u4ea7\u751f\u610f\u5916\u8f93\u51fa\u3001\u7528\u6237\u610f\u56fe\u53ef\u80fd\u5b58\u5728\u6b67\u4e49\u3002\u6709\u6548\u7684Agent\u9700\u8981\u5177\u5907\u4ece\u4e0d\u5b8c\u6574\u4fe1\u606f\u4e2d\u63a8\u65ad\u771f\u5b9e\u72b6\u6001\u7684\u80fd\u529b[16]\u3002<\/p>\n

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Agent\u5de5\u4f5c\u6d41\u6620\u5c04<\/p>\n

<\/span><\/p>\n

\u7f16\u7801<\/p>\n

<\/span><\/p>\n

\u7b56\u7565\u03c0<\/p>\n

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\u6267\u884c<\/p>\n

<\/span><\/p>\n

\u89c2\u5bdf<\/p>\n

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\u8bc4\u4f30<\/p>\n

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\u4efb\u52a1\u63cf\u8ff0<\/p>\n

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\u72b6\u6001\u8868\u5f81<\/p>\n

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\u64cd\u4f5c\u9009\u62e9<\/p>\n

<\/span><\/p>\n

\u73af\u5883\u4ea4\u4e92<\/p>\n

<\/span><\/p>\n

\u65b0\u72b6\u6001<\/p>\n

<\/span><\/p>\n

\u5956\u52b1\u8ba1\u7b97<\/p>\n

<\/span><\/p>\n

MDP\u6846\u67b6<\/p>\n

<\/span><\/p>\n

\u6267\u884c\u52a8\u4f5ca<\/p>\n

<\/span><\/p>\n

\u72b6\u6001\u8f6c\u79fbP<\/p>\n

<\/span><\/p>\n

\u5956\u52b1R<\/p>\n

<\/span><\/p>\n

\u72b6\u6001s<\/p>\n

<\/span><\/p>\n

\u52a8\u4f5c\u7a7a\u95f4<\/p>\n

<\/span><\/p>\n

\u72b6\u6001s'<\/p>\n

<\/span><\/p>\n

\u5956\u52b1\u4fe1\u53f7<\/p>\n

<\/span><\/p>\n

2.2 \u7b56\u7565\u68af\u5ea6\u65b9\u6cd5\u4e0eActor-Critic\u67b6\u6784<\/h3>\n

2.2.1 \u7b56\u7565\u68af\u5ea6\u5b9a\u7406\u7684\u7406\u8bba\u63a8\u5bfc<\/h4>\n

\u7b56\u7565\u68af\u5ea6\u65b9\u6cd5\u76f4\u63a5\u53c2\u6570\u5316\u7b56\u7565 \u03c0\u03b8(a\u2223s)\\\\pi_\\\\theta(a|s)<\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span>\u2223<\/span>s<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u901a\u8fc7\u68af\u5ea6\u4e0a\u5347\u4f18\u5316\u7b56\u7565\u53c2\u6570 \u03b8\\\\theta<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span><\/span>\u3002\u7b56\u7565\u68af\u5ea6\u5b9a\u7406（Policy Gradient Theorem）\u7ed9\u51fa\u4e86\u671f\u671b\u7d2f\u79ef\u5956\u52b1 J(\u03b8)=E\u03c4\u223c\u03c0\u03b8[R(\u03c4)]J(\\\\theta) = \\\\mathbb{E}_{\\\\tau \\\\sim \\\\pi_\\\\theta}[R(\\\\tau)]<\/span><\/span>J<\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>E<\/span><\/span>\u03c4<\/span>\u223c<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>R<\/span>(<\/span>\u03c4<\/span>)]<\/span><\/span><\/span><\/span><\/span> \u5173\u4e8e\u7b56\u7565\u53c2\u6570\u7684\u68af\u5ea6\u8868\u8fbe\u5f0f[16]：<\/p>\n

\u2207\u03b8J(\u03b8)=E\u03c4\u223c\u03c0\u03b8[\u2211t=0T\u2207\u03b8log\u2061\u03c0\u03b8(at\u2223st)\u22c5Q\u03c0\u03b8(st,at)]\\\\nabla_\\\\theta J(\\\\theta) = \\\\mathbb{E}_{\\\\tau \\\\sim \\\\pi_\\\\theta} \\\\left[ \\\\sum_{t=0}^{T} \\\\nabla_\\\\theta \\\\log \\\\pi_\\\\theta(a_t|s_t) \\\\cdot Q^{\\\\pi_\\\\theta}(s_t, a_t) \\\\right]<\/span><\/span>\u2207<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>J<\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>E<\/span><\/span>\u03c4<\/span>\u223c<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>t<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>T<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2207<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>log<\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u22c5<\/span><\/span>Q<\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8be5\u5b9a\u7406\u7684\u76f4\u89c2\u89e3\u91ca\u662f：\u589e\u52a0\u90a3\u4e9b\u5bfc\u81f4\u9ad8Q\u503c\u52a8\u4f5c\u7684\u8f68\u8ff9\u6982\u7387，\u964d\u4f4e\u5bfc\u81f4\u4f4eQ\u503c\u52a8\u4f5c\u7684\u8f68\u8ff9\u6982\u7387\u3002\u2207\u03b8log\u2061\u03c0\u03b8(at\u2223st)\\\\nabla_\\\\theta \\\\log \\\\pi_\\\\theta(a_t|s_t)<\/span><\/span>\u2207<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>log<\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u88ab\u79f0\u4e3a\u5f97\u5206\u51fd\u6570（Score Function），\u5b83\u6307\u793a\u4e86\u5982\u4f55\u8c03\u6574\u53c2\u6570\u4ee5\u589e\u52a0\u7279\u5b9a\u52a8\u4f5c\u7684\u6982\u7387\u3002<\/p>\n

REINFORCE\u7b97\u6cd5\u662f\u57fa\u4e8e\u7b56\u7565\u68af\u5ea6\u5b9a\u7406\u7684\u57fa\u7840\u7b97\u6cd5，\u5176\u53c2\u6570\u66f4\u65b0\u89c4\u5219\u4e3a[16]：<\/p>\n

\u03b8\u2190\u03b8+\u03b1\u2211t=0T\u2207\u03b8log\u2061\u03c0\u03b8(at\u2223st)\u22c5Rt\\\\theta \\\\leftarrow \\\\theta + \\\\alpha \\\\sum_{t=0}^{T} \\\\nabla_\\\\theta \\\\log \\\\pi_\\\\theta(a_t|s_t) \\\\cdot R_t<\/span><\/span>\u03b8<\/span><\/span>\u2190<\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b1<\/span><\/span><\/span>t<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>T<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2207<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>log<\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>R<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d Rt=\u2211t\u2032=tT\u03b3t\u2032\u2212trt\u2032R_t = \\\\sum_{t'=t}^{T} \\\\gamma^{t'-t} r_{t'}<\/span><\/span>R<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2211<\/span><\/span>t<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span>t<\/span><\/span><\/span><\/span><\/span>T<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b3<\/span><\/span>t<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>r<\/span><\/span>t<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u4ece\u65f6\u523b tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u5f00\u59cb\u7684\u7d2f\u79ef\u6298\u6263\u5956\u52b1\u3002REINFORCE\u7b97\u6cd5\u7684\u4f18\u70b9\u662f\u65e0\u9700\u5b66\u4e60\u73af\u5883\u6a21\u578b，\u4f46\u5b58\u5728\u9ad8\u65b9\u5dee\u95ee\u9898，\u56e0\u4e3a\u76f4\u63a5\u4f7f\u7528\u8499\u7279\u5361\u6d1b\u56de\u62a5\u4f5c\u4e3a\u6743\u91cd\u3002<\/p>\n

2.2.2 \u57fa\u7ebf\u51fd\u6570\u4e0e\u65b9\u5dee\u7f29\u51cf<\/h4>\n

\u4e3a\u964d\u4f4e\u7b56\u7565\u68af\u5ea6\u7684\u65b9\u5dee，\u7814\u7a76\u8005\u5f15\u5165\u4e86\u4e0e\u52a8\u4f5c\u65e0\u5173\u7684\u57fa\u7ebf\u51fd\u6570（Baseline Function）b(st)b(s_t)<\/span><\/span>b<\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002\u7531\u4e8e E[\u2207\u03b8log\u2061\u03c0\u03b8(at\u2223st)]=0\\\\mathbb{E}[\\\\nabla_\\\\theta \\\\log \\\\pi_\\\\theta(a_t|s_t)] = 0<\/span><\/span>E<\/span>[<\/span>\u2207<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>log<\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)]<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>，\u6dfb\u52a0\u57fa\u7ebf\u4e0d\u6539\u53d8\u68af\u5ea6\u7684\u671f\u671b\u503c：<\/p>\n

\u2207\u03b8J(\u03b8)=E\u03c4\u223c\u03c0\u03b8[\u2211t=0T\u2207\u03b8log\u2061\u03c0\u03b8(at\u2223st)\u22c5(Q\u03c0\u03b8(st,at)\u2212b(st))]\\\\nabla_\\\\theta J(\\\\theta) = \\\\mathbb{E}_{\\\\tau \\\\sim \\\\pi_\\\\theta} \\\\left[ \\\\sum_{t=0}^{T} \\\\nabla_\\\\theta \\\\log \\\\pi_\\\\theta(a_t|s_t) \\\\cdot (Q^{\\\\pi_\\\\theta}(s_t, a_t) – b(s_t)) \\\\right]<\/span><\/span>\u2207<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>J<\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>E<\/span><\/span>\u03c4<\/span>\u223c<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>t<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>T<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2207<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>log<\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u22c5<\/span><\/span>(<\/span>Q<\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span>b<\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>))<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6700\u4f18\u57fa\u7ebf\u51fd\u6570\u4e3a b\u2217(st)=Eat\u223c\u03c0\u03b8[Q\u03c0\u03b8(st,at)]=V\u03c0\u03b8(st)b^*(s_t) = \\\\mathbb{E}_{a_t \\\\sim \\\\pi_\\\\theta}[Q^{\\\\pi_\\\\theta}(s_t, a_t)] = V^{\\\\pi_\\\\theta}(s_t)<\/span><\/span>b<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>E<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u223c<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>Q<\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)]<\/span><\/span>=<\/span><\/span><\/span><\/span>V<\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>，\u5373\u72b6\u6001\u503c\u51fd\u6570\u3002\u6b64\u65f6 Q\u03c0\u03b8(st,at)\u2212V\u03c0\u03b8(st)Q^{\\\\pi_\\\\theta}(s_t, a_t) – V^{\\\\pi_\\\\theta}(s_t)<\/span><\/span>Q<\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>V<\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u88ab\u79f0\u4e3a\u4f18\u52bf\u51fd\u6570（Advantage Function），\u8bb0\u4e3a A\u03c0\u03b8(st,at)A^{\\\\pi_\\\\theta}(s_t, a_t)<\/span><\/span>A<\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>[16]\u3002<\/p>\n

\u4f18\u52bf\u51fd\u6570\u8861\u91cf\u4e86\u91c7\u53d6\u52a8\u4f5c ata_t<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u76f8\u5bf9\u4e8e\u5e73\u5747\u6c34\u5e73\u7684\u597d\u574f\u7a0b\u5ea6\u3002\u5f53 A(s,a)>0A(s,a) > 0<\/span><\/span>A<\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span><\/span>><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u65f6，\u8bf4\u660e\u8be5\u52a8\u4f5c\u4f18\u4e8e\u5e73\u5747\u8868\u73b0，\u5e94\u589e\u52a0\u5176\u6982\u7387；\u53cd\u4e4b\u5219\u5e94\u964d\u4f4e\u3002\u4f7f\u7528\u4f18\u52bf\u51fd\u6570\u7684\u7b56\u7565\u68af\u5ea6\u5177\u6709\u66f4\u5c0f\u7684\u65b9\u5dee，\u56e0\u4e3a b(st)b(s_t)<\/span><\/span>b<\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u62b5\u6d88\u4e86\u72b6\u6001\u672c\u8eab\u7684\u4ef7\u503c\u6ce2\u52a8\u3002<\/p>\n

2.2.3 Actor-Critic\u7b97\u6cd5\u7684\u534f\u540c\u673a\u5236<\/h4>\n

Actor-Critic\u67b6\u6784\u5c06\u7b56\u7565\u68af\u5ea6\u65b9\u6cd5\u5206\u4e3a\u4e24\u4e2a\u534f\u540c\u5de5\u4f5c\u7684\u7ec4\u4ef6：Actor（\u7b56\u7565\u7f51\u7edc）\u8d1f\u8d23\u751f\u6210\u52a8\u4f5c，Critic（\u4ef7\u503c\u7f51\u7edc）\u8d1f\u8d23\u8bc4\u4f30\u72b6\u6001\u6216\u52a8\u4f5c\u503c\u3002\u8fd9\u79cd\u5206\u79bb\u8bbe\u8ba1\u4f7f\u5f97\u7b97\u6cd5\u80fd\u591f\u540c\u65f6\u5229\u7528\u7b56\u7565\u68af\u5ea6\u7684\u7a33\u5b9a\u6027\u548c\u503c\u51fd\u6570\u4f30\u8ba1\u7684\u51c6\u786e\u6027[16]\u3002<\/p>\n

Critic\u901a\u8fc7\u65f6\u5e8f\u5dee\u5206（Temporal Difference, TD）\u5b66\u4e60\u66f4\u65b0\u4ef7\u503c\u4f30\u8ba1\u3002\u5bf9\u4e8e\u72b6\u6001\u503c\u51fd\u6570，TD\u8bef\u5dee\u4e3a：<\/p>\n

\u03b4t=rt+\u03b3V\u03d5(st+1)\u2212V\u03d5(st)\\\\delta_t = r_t + \\\\gamma V_\\\\phi(s_{t+1}) – V_\\\\phi(s_t)<\/span><\/span>\u03b4<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b3<\/span>V<\/span><\/span>\u03d5<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>V<\/span><\/span>\u03d5<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Critic\u53c2\u6570 \u03d5\\\\phi<\/span><\/span>\u03d5<\/span><\/span><\/span><\/span><\/span> \u901a\u8fc7\u6700\u5c0f\u5316TD\u8bef\u5dee\u7684\u5e73\u65b9\u66f4\u65b0：<\/p>\n

\u03d5\u2190\u03d5+\u03b2\u22c5\u03b4t\u22c5\u2207\u03d5V\u03d5(st)\\\\phi \\\\leftarrow \\\\phi + \\\\beta \\\\cdot \\\\delta_t \\\\cdot \\\\nabla_\\\\phi V_\\\\phi(s_t)<\/span><\/span>\u03d5<\/span><\/span>\u2190<\/span><\/span><\/span><\/span>\u03d5<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b2<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>\u03b4<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>\u2207<\/span><\/span>\u03d5<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>V<\/span><\/span>\u03d5<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Actor\u5219\u5229\u7528Critic\u63d0\u4f9b\u7684\u4f18\u52bf\u4f30\u8ba1\u66f4\u65b0\u7b56\u7565：<\/p>\n

\u03b8\u2190\u03b8+\u03b1\u22c5\u2207\u03b8log\u2061\u03c0\u03b8(at\u2223st)\u22c5\u03b4t\\\\theta \\\\leftarrow \\\\theta + \\\\alpha \\\\cdot \\\\nabla_\\\\theta \\\\log \\\\pi_\\\\theta(a_t|s_t) \\\\cdot \\\\delta_t<\/span><\/span>\u03b8<\/span><\/span>\u2190<\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b1<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>\u2207<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>log<\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>\u03b4<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5728Agent\u5de5\u4f5c\u6d41\u4f18\u5316\u4e2d，Actor-Critic\u67b6\u6784\u7684\u4f18\u52bf\u5c24\u4e3a\u660e\u663e\u3002Critic\u53ef\u4ee5\u5b66\u4e60\u8bc4\u4f30\u4e0d\u540c\u5de5\u4f5c\u6d41\u6b65\u9aa4\u7684\u8d28\u91cf，\u4e3aActor\u63d0\u4f9b\u7ec6\u7c92\u5ea6\u7684\u4f18\u5316\u4fe1\u53f7\u3002\u7814\u7a76\u8868\u660e，\u5f15\u5165Critic\u540e，Agent\u5728\u590d\u6742\u4efb\u52a1\u4e0a\u7684\u6536\u655b\u901f\u5ea6\u53ef\u63d0\u53472-3\u500d[16]\u3002<\/p>\n

2.3 \u8fd1\u7aef\u7b56\u7565\u4f18\u5316（PPO）\u4e0e\u4fe1\u4efb\u57df\u65b9\u6cd5<\/h3>\n

2.3.1 \u4fe1\u4efb\u57df\u7b56\u7565\u4f18\u5316\u7684\u7406\u8bba\u52a8\u673a<\/h4>\n

\u4f20\u7edf\u7b56\u7565\u68af\u5ea6\u65b9\u6cd5\u5b58\u5728\u6b65\u957f\u9009\u62e9\u56f0\u96be\u7684\u95ee\u9898：\u6b65\u957f\u8fc7\u5927\u5bfc\u81f4\u7b56\u7565\u5d29\u6e83，\u6b65\u957f\u8fc7\u5c0f\u5219\u6536\u655b\u7f13\u6162\u3002\u4fe1\u4efb\u57df\u7b56\u7565\u4f18\u5316（Trust Region Policy Optimization, TRPO）\u901a\u8fc7\u7ea6\u675f\u7b56\u7565\u66f4\u65b0\u7684\u5e45\u5ea6\u6765\u89e3\u51b3\u8fd9\u4e00\u95ee\u9898[16]\u3002<\/p>\n

TRPO\u7684\u6838\u5fc3\u601d\u60f3\u662f：\u5728\u5f53\u524d\u7b56\u7565 \u03c0\u03b8old\\\\pi_{\\\\theta_{old}}<\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u9644\u8fd1\u5b9a\u4e49\u4e00\u4e2a\u4fe1\u4efb\u57df，\u5728\u8be5\u533a\u57df\u5185\u8fd1\u4f3c\u76ee\u6807\u51fd\u6570，\u5e76\u5bfb\u627e\u6700\u4f18\u66f4\u65b0\u3002\u5177\u4f53\u5730，TRPO\u6c42\u89e3\u4ee5\u4e0b\u7ea6\u675f\u4f18\u5316\u95ee\u9898：<\/p>\n

max\u2061\u03b8Es\u223c\u03c0\u03b8old,a\u223c\u03c0\u03b8old[\u03c0\u03b8(a\u2223s)\u03c0\u03b8old(a\u2223s)A\u03c0\u03b8old(s,a)]\\\\max_\\\\theta \\\\mathbb{E}_{s \\\\sim \\\\pi_{\\\\theta_{old}}, a \\\\sim \\\\pi_{\\\\theta_{old}}} \\\\left[ \\\\frac{\\\\pi_\\\\theta(a|s)}{\\\\pi_{\\\\theta_{old}}(a|s)} A^{\\\\pi_{\\\\theta_{old}}}(s,a) \\\\right]<\/span><\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>max<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>E<\/span><\/span>s<\/span>\u223c<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>a<\/span>\u223c<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span>\u2223<\/span>s<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span>\u2223<\/span>s<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

s.t.\u00a0Es\u223c\u03c0\u03b8old[DKL(\u03c0\u03b8old(\u22c5\u2223s)\u2225\u03c0\u03b8(\u22c5\u2223s))]\u2264\u03b4\\\\text{s.t. } \\\\mathbb{E}_{s \\\\sim \\\\pi_{\\\\theta_{old}}} [D_{KL}(\\\\pi_{\\\\theta_{old}}(\\\\cdot|s) \\\\| \\\\pi_\\\\theta(\\\\cdot|s))] \\\\leq \\\\delta<\/span><\/span>s.t.\u00a0<\/span><\/span>E<\/span><\/span>s<\/span>\u223c<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>D<\/span><\/span>K<\/span>L<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u22c5<\/span>\u2223<\/span>s<\/span>)<\/span>\u2225<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u22c5<\/span>\u2223<\/span>s<\/span>))]<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>\u03b4<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d DKLD_{KL}<\/span><\/span>D<\/span><\/span>K<\/span>L<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3aKL\u6563\u5ea6，\u7528\u4e8e\u5ea6\u91cf\u4e24\u4e2a\u7b56\u7565\u7684\u5dee\u5f02，\u03b4\\\\delta<\/span><\/span>\u03b4<\/span><\/span><\/span><\/span><\/span> \u4e3a\u4fe1\u4efb\u57df\u534a\u5f84\u3002\u8be5\u7ea6\u675f\u786e\u4fdd\u65b0\u7b56\u7565\u4e0d\u4f1a\u504f\u79bb\u65e7\u7b56\u7565\u592a\u8fdc，\u4ece\u800c\u4fdd\u8bc1\u7b56\u7565\u6539\u8fdb\u7684\u5355\u8c03\u6027\u3002<\/p>\n

TRPO\u7684\u7406\u8bba\u57fa\u7840\u662f\u7b56\u7565\u6539\u8fdb\u7684\u5355\u8c03\u6027\u4fdd\u8bc1\u3002\u8bbe \u03c0\u2032\\\\pi'<\/span><\/span>\u03c0<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u66f4\u65b0\u540e\u7684\u7b56\u7565，\u53ef\u4ee5\u8bc1\u660e[16]：<\/p>\n

J(\u03c0\u2032)\u2212J(\u03c0)\u226511\u2212\u03b3Es\u223cd\u03c0,a\u223c\u03c0\u2032[A\u03c0(s,a)]\u22122\u03b3\u03f5(1\u2212\u03b3)2\u22c5max\u2061sDTV(\u03c0(\u22c5\u2223s)\u2225\u03c0\u2032(\u22c5\u2223s))J(\\\\pi') – J(\\\\pi) \\\\geq \\\\frac{1}{1-\\\\gamma} \\\\mathbb{E}_{s \\\\sim d^\\\\pi, a \\\\sim \\\\pi'} [A^\\\\pi(s,a)] – \\\\frac{2\\\\gamma \\\\epsilon}{(1-\\\\gamma)^2} \\\\cdot \\\\max_s D_{TV}(\\\\pi(\\\\cdot|s) \\\\| \\\\pi'(\\\\cdot|s))<\/span><\/span>J<\/span>(<\/span>\u03c0<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>J<\/span>(<\/span>\u03c0<\/span>)<\/span><\/span>\u2265<\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span>\u03b3<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>E<\/span><\/span>s<\/span>\u223c<\/span>d<\/span><\/span>\u03c0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span>a<\/span>\u223c<\/span>\u03c0<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>A<\/span><\/span>\u03c0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span>)]<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1<\/span><\/span>\u2212<\/span><\/span>\u03b3<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>\u03b3<\/span>\u03f5<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span><\/span>s<\/span><\/span><\/span><\/span>max<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>D<\/span><\/span>T<\/span>V<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c0<\/span>(<\/span>\u22c5<\/span>\u2223<\/span>s<\/span>)<\/span>\u2225<\/span>\u03c0<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u22c5<\/span>\u2223<\/span>s<\/span>))<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d DTVD_{TV}<\/span><\/span>D<\/span><\/span>T<\/span>V<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u603b\u53d8\u5dee\u8ddd\u79bb，\u03f5=max\u2061s,a\u2223A\u03c0(s,a)\u2223\\\\epsilon = \\\\max_{s,a} |A^\\\\pi(s,a)|<\/span><\/span>\u03f5<\/span><\/span>=<\/span><\/span><\/span><\/span>max<\/span><\/span>s<\/span>,<\/span>a<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>A<\/span><\/span>\u03c0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span>\u2223<\/span><\/span><\/span><\/span><\/span>\u3002\u8be5\u4e0b\u754c\u8868\u660e，\u53ea\u8981\u4f18\u52bf\u51fd\u6570\u7684\u671f\u671b\u589e\u76ca\u8d85\u8fc7\u7531\u7b56\u7565\u53d8\u5316\u5e26\u6765\u7684\u60e9\u7f5a，\u7b56\u7565\u5c31\u80fd\u4fdd\u8bc1\u6539\u8fdb\u3002<\/p>\n

2.3.2 PPO\u7684\u88c1\u526a\u76ee\u6807\u51fd\u6570<\/h4>\n

TRPO\u9700\u8981\u8ba1\u7b97Fisher\u4fe1\u606f\u77e9\u9635\u5e76\u6c42\u89e3\u7ea6\u675f\u4f18\u5316，\u8ba1\u7b97\u6210\u672c\u9ad8\u6602\u3002\u8fd1\u7aef\u7b56\u7565\u4f18\u5316（Proximal Policy Optimization, PPO）\u901a\u8fc7\u88c1\u526a\u76ee\u6807\u51fd\u6570\u8fd1\u4f3c\u5b9e\u73b0\u4fe1\u4efb\u57df\u7ea6\u675f，\u5927\u5e45\u63d0\u5347\u4e86\u8ba1\u7b97\u6548\u7387[16]\u3002<\/p>\n

PPO\u5b9a\u4e49\u6982\u7387\u6bd4 rt(\u03b8)=\u03c0\u03b8(at\u2223st)\u03c0\u03b8old(at\u2223st)r_t(\\\\theta) = \\\\frac{\\\\pi_\\\\theta(a_t|s_t)}{\\\\pi_{\\\\theta_{old}}(a_t|s_t)}<\/span><\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u88c1\u526a\u76ee\u6807\u51fd\u6570\u4e3a：<\/p>\n

LCLIP(\u03b8)=Et[min\u2061(rt(\u03b8)At,clip(rt(\u03b8),1\u2212\u03f5,1+\u03f5)At)]L^{CLIP}(\\\\theta) = \\\\mathbb{E}_t \\\\left[ \\\\min(r_t(\\\\theta) A_t, \\\\text{clip}(r_t(\\\\theta), 1-\\\\epsilon, 1+\\\\epsilon) A_t) \\\\right]<\/span><\/span>L<\/span><\/span>C<\/span>L<\/span>I<\/span>P<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>E<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>min<\/span>(<\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span>A<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>clip<\/span><\/span>(<\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span>,<\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span>\u03f5<\/span>,<\/span><\/span>1<\/span><\/span>+<\/span><\/span>\u03f5<\/span>)<\/span>A<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d \u03f5\\\\epsilon<\/span><\/span>\u03f5<\/span><\/span><\/span><\/span><\/span> \u4e3a\u8d85\u53c2\u6570（\u901a\u5e38\u53d60.1\u62160.2），clip\u51fd\u6570\u5c06\u6982\u7387\u6bd4\u9650\u5236\u5728 [1\u2212\u03f5,1+\u03f5][1-\\\\epsilon, 1+\\\\epsilon]<\/span><\/span>[<\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03f5<\/span>,<\/span><\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03f5<\/span>]<\/span><\/span><\/span><\/span><\/span> \u533a\u95f4\u5185\u3002\u8be5\u76ee\u6807\u51fd\u6570\u7684\u7cbe\u5999\u4e4b\u5904\u5728\u4e8e：\u5f53\u4f18\u52bf\u4e3a\u6b63\u65f6，\u9650\u5236\u6982\u7387\u6bd4\u7684\u4e0a\u754c\u9632\u6b62\u8fc7\u5ea6\u4f18\u5316；\u5f53\u4f18\u52bf\u4e3a\u8d1f\u65f6，\u9650\u5236\u6982\u7387\u6bd4\u7684\u4e0b\u754c\u9632\u6b62\u8fc7\u5ea6\u60e9\u7f5a[16]\u3002<\/p>\n

PPO\u7684\u5b8c\u6574\u76ee\u6807\u51fd\u6570\u8fd8\u5305\u62ec\u503c\u51fd\u6570\u635f\u5931\u548c\u71b5\u6b63\u5219\u9879：<\/p>\n

LPPO(\u03b8)=Et[LCLIP(\u03b8)\u2212c1(V\u03b8(st)\u2212Vttarget)2+c2H(\u03c0\u03b8(\u22c5\u2223st))]L^{PPO}(\\\\theta) = \\\\mathbb{E}_t \\\\left[ L^{CLIP}(\\\\theta) – c_1 (V_\\\\theta(s_t) – V_t^{target})^2 + c_2 H(\\\\pi_\\\\theta(\\\\cdot|s_t)) \\\\right]<\/span><\/span>L<\/span><\/span>PPO<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>E<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span>L<\/span><\/span>C<\/span>L<\/span>I<\/span>P<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>\u2212<\/span><\/span>c<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>V<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span>V<\/span><\/span>t<\/span><\/span><\/span><\/span>t<\/span>a<\/span>r<\/span>g<\/span>e<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>c<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>H<\/span>(<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u22c5<\/span>\u2223<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>))<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d c1,c2c_1, c_2<\/span><\/span>c<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>c<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u7cfb\u6570，HH<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7b56\u7565\u71b5，\u7528\u4e8e\u9f13\u52b1\u63a2\u7d22\u3002<\/p>\n

2.3.3 Group Relative Policy Optimization（GRPO）\u7684\u7ec4\u5185\u76f8\u5bf9\u4f18\u52bf<\/h4>\n

\u5728\u5927\u578b\u8bed\u8a00\u6a21\u578b（LLM）Agent\u7684\u8bad\u7ec3\u4e2d，\u4f20\u7edf\u7684PPO\u7b97\u6cd5\u9762\u4e34\u4e24\u4e2a\u4e3b\u8981\u6311\u6218：\u4e00\u662f\u9700\u8981\u7ef4\u62a4\u4e0e\u7b56\u7565\u6a21\u578b\u540c\u7b49\u89c4\u6a21\u7684Critic\u6a21\u578b，\u8ba1\u7b97\u5f00\u9500\u5de8\u5927；\u4e8c\u662f\u7a00\u758f\u5956\u52b1\u4fe1\u53f7\u5bfc\u81f4\u4fe1\u7528\u5206\u914d\u56f0\u96be\u3002Group Relative Policy Optimization（GRPO）\u7b97\u6cd5\u901a\u8fc7\u7ec4\u5185\u76f8\u5bf9\u4f18\u52bf\u4f30\u8ba1\u6709\u6548\u89e3\u51b3\u4e86\u8fd9\u4e9b\u95ee\u9898[16]\u3002<\/p>\n

GRPO\u7684\u6838\u5fc3\u521b\u65b0\u5728\u4e8e\u6452\u5f03\u4e86\u663e\u5f0f\u7684Critic\u7f51\u7edc，\u8f6c\u800c\u901a\u8fc7\u91c7\u6837\u540c\u4e00\u95ee\u9898\u7684\u591a\u4e2a\u56de\u7b54\u5e76\u8ba1\u7b97\u7ec4\u5185\u76f8\u5bf9\u5f97\u5206\u6765\u4f30\u8ba1\u4f18\u52bf\u3002\u5177\u4f53\u5730，\u5bf9\u4e8e\u95ee\u9898 qq<\/span><\/span>q<\/span><\/span><\/span><\/span><\/span>，\u4ece\u65e7\u7b56\u7565 \u03c0\u03b8old\\\\pi_{\\\\theta_{old}}<\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u91c7\u6837 GG<\/span><\/span>G<\/span><\/span><\/span><\/span><\/span> \u4e2a\u56de\u7b54 {o1,o2,…,oG}\\\\{o_1, o_2, …, o_G\\\\}<\/span><\/span>{<\/span>o<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>o<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>o<\/span><\/span>G<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>}<\/span><\/span><\/span><\/span><\/span>，\u83b7\u5f97\u5bf9\u5e94\u5956\u52b1 {r1,r2,…,rG}\\\\{r_1, r_2, …, r_G\\\\}<\/span><\/span>{<\/span>r<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>r<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>r<\/span><\/span>G<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>}<\/span><\/span><\/span><\/span><\/span>\u3002\u7b2c ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u4e2a\u56de\u7b54\u7684\u4f18\u52bf\u4f30\u8ba1\u4e3a[16]：<\/p>\n

A^i=ri\u2212mean({r1,r2,…,rG})std({r1,r2,…,rG})\\\\hat{A}_i = \\\\frac{r_i – \\\\text{mean}(\\\\{r_1, r_2, …, r_G\\\\})}{\\\\text{std}(\\\\{r_1, r_2, …, r_G\\\\})}<\/span><\/span><\/span>A<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>std<\/span><\/span>({<\/span>r<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>r<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>r<\/span><\/span>G<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>})<\/span><\/span><\/span><\/span><\/span><\/span><\/span>r<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>mean<\/span><\/span>({<\/span>r<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>r<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>r<\/span><\/span>G<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>})<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8be5\u4f30\u8ba1\u7684\u76f4\u89c2\u610f\u4e49\u662f：\u5c06\u7edd\u5bf9\u5956\u52b1\u8f6c\u6362\u4e3a\u7ec4\u5185\u76f8\u5bf9\u6392\u540d，\u9ad8\u4e8e\u5e73\u5747\u6c34\u5e73\u7684\u56de\u7b54\u83b7\u5f97\u6b63\u4f18\u52bf，\u4f4e\u4e8e\u5e73\u5747\u6c34\u5e73\u7684\u83b7\u5f97\u8d1f\u4f18\u52bf\u3002\u8fd9\u79cd\u5f52\u4e00\u5316\u5904\u7406\u6d88\u9664\u4e86\u4e0d\u540c\u95ee\u9898\u95f4\u5956\u52b1\u5c3a\u5ea6\u7684\u5dee\u5f02，\u4f7f\u5f97\u4f18\u52bf\u4f30\u8ba1\u66f4\u52a0\u7a33\u5b9a\u3002<\/p>\n

GRPO\u7684\u76ee\u6807\u51fd\u6570\u4e0ePPO\u7c7b\u4f3c，\u4f46\u4f7f\u7528\u7ec4\u5185\u4f30\u8ba1\u7684\u4f18\u52bf：<\/p>\n

JGRPO(\u03b8)=Eq\u223cP(Q),{oi}i=1G\u223c\u03c0\u03b8old[1G\u2211i=1G1\u2223oi\u2223\u2211t=1\u2223oi\u2223min\u2061(\u03c0\u03b8(oi,t\u2223q,oi,<t)\u03c0\u03b8old(oi,t\u2223q,oi,<t)A^i,clip(\u03c0\u03b8(oi,t\u2223q,oi,<t)\u03c0\u03b8old(oi,t\u2223q,oi,<t),1\u2212\u03f5,1+\u03f5)A^i)\u2212\u03b2DKL(\u03c0\u03b8\u2225\u03c0ref)]J_{GRPO}(\\\\theta) = \\\\mathbb{E}_{q \\\\sim P(Q), \\\\{o_i\\\\}_{i=1}^G \\\\sim \\\\pi_{\\\\theta_{old}}} \\\\left[ \\\\frac{1}{G} \\\\sum_{i=1}^{G} \\\\frac{1}{|o_i|} \\\\sum_{t=1}^{|o_i|} \\\\min\\\\left( \\\\frac{\\\\pi_\\\\theta(o_{i,t}|q,o_{i,<t})}{\\\\pi_{\\\\theta_{old}}(o_{i,t}|q,o_{i,<t})} \\\\hat{A}_i, \\\\text{clip}\\\\left(\\\\frac{\\\\pi_\\\\theta(o_{i,t}|q,o_{i,<t})}{\\\\pi_{\\\\theta_{old}}(o_{i,t}|q,o_{i,<t})}, 1-\\\\epsilon, 1+\\\\epsilon\\\\right) \\\\hat{A}_i \\\\right) – \\\\beta D_{KL}(\\\\pi_\\\\theta \\\\| \\\\pi_{ref}) \\\\right]<\/span><\/span>J<\/span><\/span>GRPO<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>E<\/span><\/span>q<\/span>\u223c<\/span>P<\/span>(<\/span>Q<\/span>)<\/span>,<\/span>{<\/span>o<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>}<\/span><\/span>i<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>G<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u223c<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>G<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>G<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>o<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>\u2223<\/span>o<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>min<\/span><\/span>(<\/span><\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>o<\/span><\/span>i<\/span>,<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>q<\/span>,<\/span><\/span>o<\/span><\/span>i<\/span>,<\/span><<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>o<\/span><\/span>i<\/span>,<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>q<\/span>,<\/span><\/span>o<\/span><\/span>i<\/span>,<\/span><<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>clip<\/span><\/span><\/span>(<\/span><\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>o<\/span><\/span>i<\/span>,<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>q<\/span>,<\/span><\/span>o<\/span><\/span>i<\/span>,<\/span><<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>o<\/span><\/span>i<\/span>,<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>q<\/span>,<\/span><\/span>o<\/span><\/span>i<\/span>,<\/span><<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span>\u03f5<\/span>,<\/span><\/span>1<\/span><\/span>+<\/span><\/span>\u03f5<\/span>)<\/span><\/span><\/span><\/span><\/span>A<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u2212<\/span><\/span>\u03b2<\/span>D<\/span><\/span>K<\/span>L<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2225<\/span>\u03c0<\/span><\/span>re<\/span>f<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d \u2223oi\u2223|o_i|<\/span><\/span>\u2223<\/span>o<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7b2c ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u4e2a\u56de\u7b54\u7684token\u6570，\u03c0ref\\\\pi_{ref}<\/span><\/span>\u03c0<\/span><\/span>re<\/span>f<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u53c2\u8003\u7b56\u7565（\u901a\u5e38\u662f\u521d\u59cb\u6a21\u578b），\u03b2\\\\beta<\/span><\/span>\u03b2<\/span><\/span><\/span><\/span><\/span> \u63a7\u5236KL\u60e9\u7f5a\u5f3a\u5ea6\u3002GRPO\u5df2\u5728DeepSeek-R1\u7b49\u6a21\u578b\u7684\u8bad\u7ec3\u4e2d\u5c55\u73b0\u51fa\u5353\u8d8a\u6027\u80fd，\u6210\u4e3a\u5f53\u524dLLM Agent RL\u8bad\u7ec3\u7684\u4e3b\u6d41\u7b97\u6cd5[16]\u3002<\/p>\n

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\u6838\u5fc3\u521b\u65b0<\/p>\n

<\/span><\/p>\n

\u7b56\u7565\u4f18\u5316\u6f14\u8fdb<\/p>\n

<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u7b56\u7565\u68af\u5ea6<\/p>\n

<\/span><\/p>\n

Actor-Critic<\/p>\n

<\/span><\/p>\n

TRPO\u4fe1\u4efb\u57df<\/p>\n

<\/span><\/p>\n

PPO\u88c1\u526a<\/p>\n

<\/span><\/p>\n

GRPO\u7ec4\u5185\u4f18\u52bf<\/p>\n

<\/span><\/p>\n

KL\u7ea6\u675f<\/p>\n

<\/span><\/p>\n

\u6982\u7387\u6bd4\u88c1\u526a<\/p>\n

<\/span><\/p>\n

\u65e0Critic\u7f51\u7edc<\/p>\n

<\/span><\/p>\n

\u7ec4\u5185\u5f52\u4e00\u5316<\/p>\n

<\/span><\/p>\n

3 Agent\u5de5\u4f5c\u6d41\u7684\u6570\u5b66\u5efa\u6a21：SOP\u5bfb\u627e\u7684\u5f62\u5f0f\u5316<\/h2>\n

3.1 \u5de5\u4f5c\u6d41\u4f5c\u4e3a\u5c42\u6b21\u5316\u51b3\u7b56\u5e8f\u5217<\/h3>\n

3.1.1 \u5de5\u4f5c\u6d41\u7684\u6811\u72b6\u7ed3\u6784\u8868\u793a<\/h4>\n

Agent\u5de5\u4f5c\u6d41\u53ef\u4ee5\u81ea\u7136\u5730\u5efa\u6a21\u4e3a\u5c42\u6b21\u5316\u7684\u51b3\u7b56\u6811\u7ed3\u6784\u3002\u5728\u8fd9\u79cd\u8868\u793a\u4e2d，\u6bcf\u4e2a\u8282\u70b9\u4ee3\u8868\u4e00\u4e2a\u51b3\u7b56\u70b9，\u8fb9\u4ee3\u8868\u53ef\u9009\u7684\u64cd\u4f5c，\u800c\u8def\u5f84\u5219\u5bf9\u5e94\u5b8c\u6574\u7684\u5de5\u4f5c\u6d41\u6267\u884c\u5e8f\u5217\u3002\u5f62\u5f0f\u5316\u5730，\u5de5\u4f5c\u6d41\u6811 T\\\\mathcal{T}<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span> \u5b9a\u4e49\u4e3a (N,E,s0)(\\\\mathcal{N}, \\\\mathcal{E}, s_0)<\/span><\/span>(<\/span>N<\/span>,<\/span><\/span>E<\/span>,<\/span><\/span>s<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>，\u5176\u4e2d N\\\\mathcal{N}<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u4e3a\u8282\u70b9\u96c6\u5408，E\u2286N\u00d7N\\\\mathcal{E} \\\\subseteq \\\\mathcal{N} \\\\times \\\\mathcal{N}<\/span><\/span>E<\/span><\/span>\u2286<\/span><\/span><\/span><\/span>N<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u4e3a\u8fb9\u96c6\u5408，s0\u2208Ns_0 \\\\in \\\\mathcal{N}<\/span><\/span>s<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2208<\/span><\/span><\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u4e3a\u6839\u8282\u70b9[16]\u3002<\/p>\n

\u5bf9\u4e8e\u590d\u6742\u4efb\u52a1，\u5de5\u4f5c\u6d41\u6811\u53ef\u80fd\u975e\u5e38\u5e9e\u5927\u3002\u4ee5\u5305\u542b nn<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6b65\u9aa4\u7684\u5de5\u4f5c\u6d41\u4e3a\u4f8b，\u82e5\u6bcf\u6b65\u6709 kk<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span> \u4e2a\u53ef\u9009\u64cd\u4f5c，\u5219\u5b8c\u6574\u7684\u5de5\u4f5c\u6d41\u6811\u5305\u542b O(kn)O(k^n)<\/span><\/span>O<\/span>(<\/span>k<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u6761\u8def\u5f84\u3002\u8fd9\u79cd\u6307\u6570\u7ea7\u589e\u957f\u4f7f\u5f97\u7a77\u4e3e\u641c\u7d22\u4e0d\u53ef\u884c，\u5fc5\u987b\u501f\u52a9\u5f3a\u5316\u5b66\u4e60\u7684\u5f15\u5bfc\u641c\u7d22\u673a\u5236\u3002<\/p>\n

\u5c42\u6b21\u5316\u5f3a\u5316\u5b66\u4e60（Hierarchical Reinforcement Learning, HRL）\u4e3a\u5de5\u4f5c\u6d41\u4f18\u5316\u63d0\u4f9b\u4e86\u6709\u6548\u7684\u62bd\u8c61\u673a\u5236\u3002\u5728HRL\u6846\u67b6\u4e2d，\u7b56\u7565\u88ab\u7ec4\u7ec7\u4e3a\u4e24\u5c42\u7ed3\u6784：\u9ad8\u5c42\u7b56\u7565（Meta-Policy）\u8d1f\u8d23\u9009\u62e9\u5b50\u76ee\u6807（Subgoal），\u4f4e\u5c42\u7b56\u7565（Sub-Policy）\u8d1f\u8d23\u5b9e\u73b0\u5b50\u76ee\u6807\u3002\u8fd9\u79cd\u5206\u89e3\u663e\u8457\u964d\u4f4e\u4e86\u641c\u7d22\u7a7a\u95f4\u590d\u6742\u5ea6[16]\u3002<\/p>\n

Options\u6846\u67b6\u662fHRL\u7684\u7ecf\u5178\u5b9e\u73b0，\u5b83\u5c06"\u9009\u9879"（Option）\u5b9a\u4e49\u4e3a\u4e09\u5143\u7ec4 \u03c9=(I\u03c9,\u03c0\u03c9,\u03b2\u03c9)\\\\omega = (\\\\mathcal{I}_\\\\omega, \\\\pi_\\\\omega, \\\\beta_\\\\omega)<\/span><\/span>\u03c9<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>I<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u03c0<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u03b2<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>，\u5176\u4e2d I\u03c9\u2286S\\\\mathcal{I}_\\\\omega \\\\subseteq \\\\mathcal{S}<\/span><\/span>I<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2286<\/span><\/span><\/span><\/span>S<\/span><\/span><\/span><\/span><\/span> \u4e3a\u542f\u52a8\u96c6（Initiation Set），\u8868\u793a\u9009\u9879\u53ef\u6267\u884c\u7684\u72b6\u6001\u96c6\u5408；\u03c0\u03c9\\\\pi_\\\\omega<\/span><\/span>\u03c0<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u9009\u9879\u5185\u90e8\u7b56\u7565；\u03b2\u03c9:S\u2192[0,1]\\\\beta_\\\\omega: \\\\mathcal{S} \\\\rightarrow [0,1]<\/span><\/span>\u03b2<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>:<\/span><\/span><\/span><\/span>S<\/span><\/span>\u2192<\/span><\/span><\/span><\/span>[<\/span>0<\/span>,<\/span><\/span>1<\/span>]<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7ec8\u6b62\u6761\u4ef6，\u8868\u793a\u5728\u5404\u72b6\u6001\u4e0b\u9009\u9879\u7ec8\u6b62\u7684\u6982\u7387[16]\u3002<\/p>\n

\u5728Agent\u5de5\u4f5c\u6d41\u573a\u666f\u4e2d，\u9009\u9879\u53ef\u4ee5\u5bf9\u5e94\u4e8e\u6807\u51c6\u7684\u64cd\u4f5c\u6a21\u5757，\u5982"\u4fe1\u606f\u68c0\u7d22"\u3001\u201c\u6570\u636e\u5206\u6790\u201d\u3001"\u7ed3\u679c\u9a8c\u8bc1"\u7b49\u3002\u901a\u8fc7\u9884\u5b9a\u4e49\u8fd9\u4e9b\u9009\u9879，Agent\u53ef\u4ee5\u5728\u66f4\u9ad8\u62bd\u8c61\u5c42\u6b21\u4e0a\u89c4\u5212\u5de5\u4f5c\u6d41，\u907f\u514d\u9677\u5165\u4f4e\u5c42\u7ec6\u8282\u3002<\/p>\n

3.1.2 \u6807\u51c6\u64cd\u4f5c\u7a0b\u5e8f（SOP）\u7684\u6570\u5b66\u5b9a\u4e49<\/h4>\n

\u6807\u51c6\u64cd\u4f5c\u7a0b\u5e8f（SOP）\u662f\u5de5\u4f5c\u6d41\u7684\u89c4\u8303\u5316\u8868\u8fbe，\u5b9a\u4e49\u4e86\u5728\u7279\u5b9a\u573a\u666f\u4e0b\u5e94\u9075\u5faa\u7684\u64cd\u4f5c\u5e8f\u5217\u3002\u4ece\u6570\u5b66\u89d2\u5ea6，SOP\u53ef\u4ee5\u5b9a\u4e49\u4e3a\u6761\u4ef6-\u52a8\u4f5c\u89c4\u5219\u7684\u96c6\u5408：<\/p>\n

SOP={(ci,ai,pi)}i=1M\\\\text{SOP} = \\\\{(c_i, a_i, p_i)\\\\}_{i=1}^{M}<\/span><\/span>SOP<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>{(<\/span>c<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>p<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>}<\/span><\/span>i<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>M<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d cic_i<\/span><\/span>c<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u89e6\u53d1\u6761\u4ef6（Context Condition），aia_i<\/span><\/span>a<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u6267\u884c\u52a8\u4f5c，pip_i<\/span><\/span>p<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u4f18\u5148\u7ea7\u5206\u6570\u3002\u5f53\u591a\u4e2a\u6761\u4ef6\u540c\u65f6\u6ee1\u8db3\u65f6，Agent\u9009\u62e9\u4f18\u5148\u7ea7\u6700\u9ad8\u7684\u89c4\u5219\u6267\u884c[16]\u3002<\/p>\n

SOP\u7684\u4f18\u5316\u76ee\u6807\u53ef\u4ee5\u5f62\u5f0f\u5316\u4e3a：<\/p>\n

max\u2061SOPE\u03c4\u223cD[R(\u03c4,SOP)]\\\\max_{\\\\text{SOP}} \\\\mathbb{E}_{\\\\tau \\\\sim \\\\mathcal{D}} \\\\left[ R(\\\\tau, \\\\text{SOP}) \\\\right]<\/span><\/span><\/span>SOP<\/span><\/span><\/span><\/span><\/span><\/span>max<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>E<\/span><\/span>\u03c4<\/span>\u223c<\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>R<\/span>(<\/span>\u03c4<\/span>,<\/span><\/span>SOP<\/span><\/span>)<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d D\\\\mathcal{D}<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span> \u4e3a\u4efb\u52a1\u5206\u5e03，R(\u03c4,SOP)R(\\\\tau, \\\\text{SOP})<\/span><\/span>R<\/span>(<\/span>\u03c4<\/span>,<\/span><\/span>SOP<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u4f7f\u7528SOP\u6267\u884c\u4efb\u52a1 \u03c4\\\\tau<\/span><\/span>\u03c4<\/span><\/span><\/span><\/span><\/span> \u83b7\u5f97\u7684\u5956\u52b1\u3002\u8be5\u4f18\u5316\u95ee\u9898\u5177\u6709\u7ec4\u5408\u7279\u6027，\u56e0\u4e3aSOP\u7684\u89c4\u5219\u96c6\u5408\u3001\u6761\u4ef6\u5b9a\u4e49\u548c\u4f18\u5148\u7ea7\u5206\u914d\u90fd\u662f\u79bb\u6563\u9009\u62e9\u3002<\/p>\n

\u4e00\u79cd\u6709\u6548\u7684\u4f18\u5316\u7b56\u7565\u662f\u5c06SOP\u5b66\u4e60\u5206\u89e3\u4e3a\u4e24\u4e2a\u5b50\u95ee\u9898：\u89c4\u5219\u53d1\u73b0（Rule Discovery）\u548c\u89c4\u5219\u6392\u5e8f（Rule Ranking）\u3002\u89c4\u5219\u53d1\u73b0\u8d1f\u8d23\u8bc6\u522b\u6709\u7528\u7684\u6761\u4ef6-\u52a8\u4f5c\u6a21\u5f0f，\u89c4\u5219\u6392\u5e8f\u5219\u786e\u5b9a\u89c4\u5219\u7684\u6267\u884c\u4f18\u5148\u7ea7\u3002\u5f3a\u5316\u5b66\u4e60\u53ef\u4ee5\u540c\u65f6\u4f18\u5316\u8fd9\u4e24\u4e2a\u65b9\u9762：\u901a\u8fc7\u63a2\u7d22\u53d1\u73b0\u65b0\u89c4\u5219，\u901a\u8fc7\u5229\u7528\u4f18\u5316\u89c4\u5219\u7ec4\u5408[16]\u3002<\/p>\n

3.1.3 \u5de5\u4f5c\u6d41\u72b6\u6001\u7a7a\u95f4\u7684\u7ef4\u5ea6\u707e\u96be\u4e0e\u5e94\u5bf9<\/h4>\n

Agent\u5de5\u4f5c\u6d41\u7684\u72b6\u6001\u7a7a\u95f4\u901a\u5e38\u5177\u6709\u9ad8\u7ef4\u5ea6\u548c\u590d\u6742\u7ed3\u6784，\u8fd9\u5e26\u6765\u4e86\u7ef4\u5ea6\u707e\u96be（Curse of Dimensionality）\u95ee\u9898\u3002\u72b6\u6001\u53ef\u80fd\u5305\u542b\u6587\u672c\u5e8f\u5217\u3001\u6570\u503c\u5411\u91cf\u3001\u7ed3\u6784\u5316\u6570\u636e\u7b49\u591a\u79cd\u6a21\u6001，\u4f20\u7edf\u8868\u683c\u578b\u65b9\u6cd5\u65e0\u6cd5\u6709\u6548\u5904\u7406[16]\u3002<\/p>\n

\u6df1\u5ea6\u5f3a\u5316\u5b66\u4e60（Deep Reinforcement Learning）\u901a\u8fc7\u795e\u7ecf\u7f51\u7edc\u51fd\u6570\u903c\u8fd1\u89e3\u51b3\u4e86\u8fd9\u4e00\u6311\u6218\u3002\u7b56\u7565\u7f51\u7edc\u548c\u4ef7\u503c\u7f51\u7edc\u5c06\u539f\u59cb\u72b6\u6001\u6620\u5c04\u4e3a\u52a8\u4f5c\u6982\u7387\u6216\u4ef7\u503c\u4f30\u8ba1，\u5b9e\u73b0\u4e86\u5bf9\u9ad8\u7ef4\u72b6\u6001\u7a7a\u95f4\u7684\u6709\u6548\u6cdb\u5316\u3002\u5bf9\u4e8e\u6587\u672c\u578b\u72b6\u6001，\u901a\u5e38\u4f7f\u7528\u9884\u8bad\u7ec3\u7684\u8bed\u8a00\u6a21\u578b（\u5982BERT\u3001GPT）\u63d0\u53d6\u8bed\u4e49\u7279\u5f81；\u5bf9\u4e8e\u7ed3\u6784\u5316\u6570\u636e，\u5219\u4f7f\u7528\u56fe\u795e\u7ecf\u7f51\u7edc（Graph Neural Network）\u7f16\u7801\u5173\u7cfb\u4fe1\u606f[16]\u3002<\/p>\n

\u72b6\u6001\u538b\u7f29（State Compression）\u662f\u53e6\u4e00\u91cd\u8981\u6280\u672f\u3002\u901a\u8fc7\u81ea\u7f16\u7801\u5668（Autoencoder）\u6216\u53d8\u5206\u81ea\u7f16\u7801\u5668（Variational Autoencoder, VAE），\u53ef\u4ee5\u5c06\u9ad8\u7ef4\u72b6\u6001\u538b\u7f29\u4e3a\u4f4e\u7ef4\u6f5c\u5728\u8868\u793a，\u540c\u65f6\u4fdd\u7559\u51b3\u7b56\u76f8\u5173\u7684\u5173\u952e\u4fe1\u606f\u3002\u538b\u7f29\u540e\u7684\u72b6\u6001\u4e0d\u4ec5\u964d\u4f4e\u4e86\u8ba1\u7b97\u590d\u6742\u5ea6，\u8fd8\u6709\u52a9\u4e8e\u53d1\u73b0\u72b6\u6001\u7a7a\u95f4\u7684\u5185\u5728\u7ed3\u6784[16]\u3002<\/p>\n

3.2 \u5de5\u4f5c\u6d41\u4f18\u5316\u7684\u5f3a\u5316\u5b66\u4e60\u5f62\u5f0f\u5316<\/h3>\n

3.2.1 \u5c06SOP\u5bfb\u627e\u5efa\u6a21\u4e3a\u7b56\u7565\u641c\u7d22\u95ee\u9898<\/h4>\n

\u5c06SOP\u5bfb\u627e\u95ee\u9898\u5f62\u5f0f\u5316\u4e3a\u5f3a\u5316\u5b66\u4e60\u95ee\u9898\u9700\u8981\u660e\u786e\u5b9a\u4e49\u72b6\u6001\u3001\u52a8\u4f5c\u548c\u5956\u52b1\u3002\u5728\u8fd9\u79cd\u5f62\u5f0f\u5316\u4e2d，Agent\u7684\u76ee\u6807\u662f\u5b66\u4e60\u5230\u4e00\u79cd\u7b56\u7565，\u8be5\u7b56\u7565\u80fd\u591f\u6839\u636e\u5f53\u524d\u4efb\u52a1\u4e0a\u4e0b\u6587\u9009\u62e9\u6700\u4f18\u7684\u64cd\u4f5c\u5e8f\u5217[15]\u3002<\/p>\n

\u72b6\u6001\u8bbe\u8ba1：\u72b6\u6001\u9700\u8981\u7f16\u7801\u4efb\u52a1\u76f8\u5173\u7684\u5168\u90e8\u4fe1\u606f\u3002\u5bf9\u4e8e\u5de5\u4f5c\u6d41\u4f18\u5316\u95ee\u9898，\u72b6\u6001\u901a\u5e38\u5305\u542b：<\/p>\n

    \n
  • \u4efb\u52a1\u63cf\u8ff0\u7684\u7279\u5f81\u5411\u91cf etaske_{task}<\/span><\/span>e<\/span><\/span>t<\/span>a<\/span>s<\/span>k<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n
  • \u5f53\u524d\u5df2\u6267\u884c\u7684\u64cd\u4f5c\u5e8f\u5217 h=(a1,a2,…,at)h = (a_1, a_2, …, a_t)<\/span><\/span>h<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/li>\n
  • \u5404\u4e2d\u95f4\u6b65\u9aa4\u7684\u6267\u884c\u7ed3\u679c {r1,r2,…,rt}\\\\{r_1, r_2, …, r_t\\\\}<\/span><\/span>{<\/span>r<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>r<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>}<\/span><\/span><\/span><\/span><\/span><\/li>\n
  • \u5f53\u524d\u53ef\u7528\u7684\u64cd\u4f5c\u96c6\u5408 Aavailable\\\\mathcal{A}_{available}<\/span><\/span>A<\/span><\/span>a<\/span>v<\/span>ai<\/span>l<\/span>ab<\/span>l<\/span>e<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n

    \u7efc\u5408\u72b6\u6001\u8868\u793a\u4e3a st=Encoder(etask,h,{ri},Aavailable)s_t = \\\\text{Encoder}(e_{task}, h, \\\\{r_i\\\\}, \\\\mathcal{A}_{available})<\/span><\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>Encoder<\/span><\/span>(<\/span>e<\/span><\/span>t<\/span>a<\/span>s<\/span>k<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>h<\/span>,<\/span><\/span>{<\/span>r<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>}<\/span>,<\/span><\/span>A<\/span><\/span>a<\/span>v<\/span>ai<\/span>l<\/span>ab<\/span>l<\/span>e<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>，\u5176\u4e2dEncoder\u4e3a\u7f16\u7801\u7f51\u7edc\u3002<\/p>\n

    \u52a8\u4f5c\u8bbe\u8ba1：\u52a8\u4f5c\u7a7a\u95f4\u5bf9\u5e94\u4e8e\u5de5\u4f5c\u6d41\u4e2d\u7684\u53ef\u6267\u884c\u64cd\u4f5c\u3002\u6839\u636e\u7c92\u5ea6\u4e0d\u540c，\u52a8\u4f5c\u53ef\u4ee5\u662f：<\/p>\n

      \n
    • \u539f\u5b50\u64cd\u4f5c：\u5982\u8c03\u7528\u7279\u5b9aAPI\u3001\u6267\u884c\u7279\u5b9a\u4ee3\u7801\u7247\u6bb5<\/li>\n
    • \u590d\u5408\u64cd\u4f5c：\u5982"\u68c0\u7d22\u76f8\u5173\u4fe1\u606f\u5e76\u603b\u7ed3"\u3001\u201c\u751f\u6210\u5019\u9009\u65b9\u6848\u5e76\u8bc4\u4f30\u201d<\/li>\n
    • \u5143\u64cd\u4f5c：\u5982"\u56de\u9000\u5230\u4e0a\u4e00\u6b65"\u3001\u201c\u8bf7\u6c42\u4eba\u5de5\u534f\u52a9\u201d<\/li>\n<\/ul>\n

      \u5956\u52b1\u8bbe\u8ba1：\u5956\u52b1\u51fd\u6570\u9700\u8981\u53cd\u6620\u5de5\u4f5c\u6d41\u7684\u6267\u884c\u8d28\u91cf\u3002\u5e38\u89c1\u7684\u5956\u52b1\u6784\u6210\u5305\u62ec：<\/p>\n

        \n
      • \u7ed3\u679c\u5956\u52b1：\u4efb\u52a1\u5b8c\u6210\u65f6\u6839\u636e\u6b63\u786e\u6027\u7ed9\u4e88\u5956\u52b1 routcome\u2208{\u22121,0,+1}r_{outcome} \\\\in \\\\{-1, 0, +1\\\\}<\/span><\/span>r<\/span><\/span>o<\/span>u<\/span>t<\/span>co<\/span>m<\/span>e<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2208<\/span><\/span><\/span><\/span>{<\/span>\u2212<\/span>1<\/span>,<\/span><\/span>0<\/span>,<\/span><\/span>+<\/span>1<\/span>}<\/span><\/span><\/span><\/span><\/span><\/li>\n
      • \u6548\u7387\u5956\u52b1：\u6839\u636e\u6267\u884c\u6b65\u9aa4\u6570\u6216\u8d44\u6e90\u6d88\u8017\u7ed9\u4e88\u60e9\u7f5a refficiency=\u2212\u03b1\u22c5Tr_{efficiency} = -\\\\alpha \\\\cdot T<\/span><\/span>r<\/span><\/span>e<\/span>ff<\/span>i<\/span>c<\/span>i<\/span>e<\/span>n<\/span>cy<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>\u03b1<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/li>\n
      • \u8fc7\u7a0b\u5956\u52b1：\u7531\u8fc7\u7a0b\u5956\u52b1\u6a21\u578b\u63d0\u4f9b\u7684\u4e2d\u95f4\u6b65\u9aa4\u8d28\u91cf\u8bc4\u4f30 rprocessr_{process}<\/span><\/span>r<\/span><\/span>p<\/span>rocess<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n

        \u603b\u5956\u52b1\u4e3a\u5404\u7ec4\u6210\u90e8\u5206\u7684\u52a0\u6743\u548c：R=routcome+refficiency+\u2211trprocess(t)R = r_{outcome} + r_{efficiency} + \\\\sum_t r_{process}(t)<\/span><\/span>R<\/span><\/span>=<\/span><\/span><\/span><\/span>r<\/span><\/span>o<\/span>u<\/span>t<\/span>co<\/span>m<\/span>e<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>r<\/span><\/span>e<\/span>ff<\/span>i<\/span>c<\/span>i<\/span>e<\/span>n<\/span>cy<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u2211<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>r<\/span><\/span>p<\/span>rocess<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span>[16]\u3002<\/p>\n

        3.2.2 \u52a8\u4f5c\u7a7a\u95f4\u7684\u7ed3\u6784\u5316\u8bbe\u8ba1<\/h4>\n

        Agent\u5de5\u4f5c\u6d41\u7684\u52a8\u4f5c\u7a7a\u95f4\u5177\u6709\u5185\u5728\u7ed3\u6784，\u5408\u7406\u5229\u7528\u8fd9\u79cd\u7ed3\u6784\u53ef\u4ee5\u63d0\u5347\u5b66\u4e60\u6548\u7387\u3002\u52a8\u4f5c\u7a7a\u95f4\u53ef\u4ee5\u5206\u89e3\u4e3a\u591a\u4e2a\u6b63\u4ea4\u7684\u5b50\u7a7a\u95f4，\u6bcf\u4e2a\u5b50\u7a7a\u95f4\u5bf9\u5e94\u4e00\u7c7b\u7279\u5b9a\u64cd\u4f5c[42]\u3002<\/p>\n

        \u5de5\u5177\u8c03\u7528\u5b50\u7a7a\u95f4：\u5305\u542b\u6240\u6709\u53ef\u8c03\u7528\u7684\u5916\u90e8\u5de5\u5177（\u5982\u641c\u7d22\u5f15\u64ce\u3001\u8ba1\u7b97\u5668\u3001\u4ee3\u7801\u6267\u884c\u5668）\u3002\u6bcf\u4e2a\u5de5\u5177\u5bf9\u5e94\u4e00\u4e2a\u52a8\u4f5c，\u52a8\u4f5c\u7684\u53c2\u6570（\u5982\u641c\u7d22\u67e5\u8be2\u3001\u4ee3\u7801\u5185\u5bb9）\u7531\u7b56\u7565\u7f51\u7edc\u751f\u6210\u3002<\/p>\n

        \u63a8\u7406\u6a21\u5f0f\u5b50\u7a7a\u95f4：\u5b9a\u4e49\u4e86Agent\u7684\u601d\u8003\u65b9\u5f0f，\u5982：<\/p>\n

          \n
        • Chain-of-Thought（CoT）：\u9010\u6b65\u63a8\u7406，\u663e\u5f0f\u5c55\u793a\u601d\u8003\u8fc7\u7a0b<\/li>\n
        • Tree-of-Thought（ToT）：\u751f\u6210\u591a\u4e2a\u5019\u9009\u601d\u8def，\u8bc4\u4f30\u540e\u9009\u62e9\u6700\u4f18<\/li>\n
        • ReAct：\u63a8\u7406\u4e0e\u884c\u52a8\u4ea4\u66ff\u8fdb\u884c，\u6839\u636e\u89c2\u5bdf\u8c03\u6574\u7b56\u7565<\/li>\n<\/ul>\n

          \u63a7\u5236\u6d41\u5b50\u7a7a\u95f4：\u63a7\u5236\u5de5\u4f5c\u6d41\u7684\u6267\u884c\u903b\u8f91，\u5305\u62ec：<\/p>\n

            \n
          • \u987a\u5e8f\u6267\u884c：\u6309\u9884\u5b9a\u987a\u5e8f\u6267\u884c\u64cd\u4f5c\u5e8f\u5217<\/li>\n
          • \u6761\u4ef6\u5206\u652f：\u6839\u636e\u4e2d\u95f4\u7ed3\u679c\u9009\u62e9\u4e0d\u540c\u6267\u884c\u8def\u5f84<\/li>\n
          • \u5faa\u73af\u8fed\u4ee3：\u91cd\u590d\u6267\u884c\u67d0\u64cd\u4f5c\u76f4\u5230\u6ee1\u8db3\u7ec8\u6b62\u6761\u4ef6<\/li>\n
          • \u5e76\u884c\u6267\u884c：\u540c\u65f6\u6267\u884c\u591a\u4e2a\u72ec\u7acb\u64cd\u4f5c<\/li>\n<\/ul>\n

            \u52a8\u4f5c\u7a7a\u95f4\u7684\u7ed3\u6784\u5316\u8bbe\u8ba1\u4f7f\u5f97\u7b56\u7565\u53ef\u4ee5\u5206\u5c42\u5b66\u4e60：\u9996\u5148\u5b66\u4e60\u9ad8\u5c42\u63a7\u5236\u7b56\u7565（\u9009\u62e9\u63a8\u7406\u6a21\u5f0f\u548c\u63a7\u5236\u6d41），\u7136\u540e\u5728\u9009\u5b9a\u6846\u67b6\u5185\u5b66\u4e60\u4f4e\u5c42\u64cd\u4f5c\u9009\u62e9\u3002\u8fd9\u79cd\u5c42\u6b21\u5316\u5b66\u4e60\u663e\u8457\u964d\u4f4e\u4e86\u6837\u672c\u590d\u6742\u5ea6[16]\u3002<\/p>\n

            3.2.3 \u591a\u76ee\u6807\u4f18\u5316\u4e0e\u5e15\u7d2f\u6258\u524d\u6cbf<\/h4>\n

            \u5b9e\u9645\u5de5\u4f5c\u6d41\u4f18\u5316\u5f80\u5f80\u6d89\u53ca\u591a\u4e2a\u76f8\u4e92\u51b2\u7a81\u7684\u76ee\u6807，\u5982\u51c6\u786e\u7387\u3001\u54cd\u5e94\u65f6\u95f4\u3001\u8d44\u6e90\u6d88\u8017\u7b49\u3002\u591a\u76ee\u6807\u4f18\u5316（Multi-Objective Optimization）\u6846\u67b6\u4e3a\u5904\u7406\u8fd9\u79cd\u590d\u6742\u6027\u63d0\u4f9b\u4e86\u7cfb\u7edf\u65b9\u6cd5[42]\u3002<\/p>\n

            \u8bbe\u6709 mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u4e2a\u4f18\u5316\u76ee\u6807 f1,f2,…,fmf_1, f_2, …, f_m<\/span><\/span>f<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>f<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>f<\/span><\/span>m<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u591a\u76ee\u6807\u4f18\u5316\u95ee\u9898\u5f62\u5f0f\u5316\u4e3a：<\/p>\n

            min\u2061\u03c0(f1(\u03c0),f2(\u03c0),…,fm(\u03c0))\\\\min_{\\\\pi} (f_1(\\\\pi), f_2(\\\\pi), …, f_m(\\\\pi))<\/span><\/span><\/span>\u03c0<\/span><\/span><\/span><\/span><\/span>min<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>f<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c0<\/span>)<\/span>,<\/span><\/span>f<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c0<\/span>)<\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>f<\/span><\/span>m<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c0<\/span>))<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

            \u5e15\u7d2f\u6258\u6700\u4f18（Pareto Optimality）\u662f\u591a\u76ee\u6807\u4f18\u5316\u7684\u6838\u5fc3\u6982\u5ff5\u3002\u7b56\u7565 \u03c0\u2217\\\\pi^*<\/span><\/span>\u03c0<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u5e15\u7d2f\u6258\u6700\u4f18\u7684，\u5982\u679c\u4e0d\u5b58\u5728\u5176\u4ed6\u7b56\u7565 \u03c0\u2032\\\\pi'<\/span><\/span>\u03c0<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5728\u6240\u6709\u76ee\u6807\u4e0a\u90fd\u4e0d\u52a3\u4e8e \u03c0\u2217\\\\pi^*<\/span><\/span>\u03c0<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e14\u81f3\u5c11\u5728\u4e00\u4e2a\u76ee\u6807\u4e0a\u4e25\u683c\u4f18\u4e8e \u03c0\u2217\\\\pi^*<\/span><\/span>\u03c0<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u6240\u6709\u5e15\u7d2f\u6258\u6700\u4f18\u7b56\u7565\u6784\u6210\u5e15\u7d2f\u6258\u524d\u6cbf（Pareto Front）[16]\u3002<\/p>\n

            \u5728Agent\u5de5\u4f5c\u6d41\u573a\u666f\u4e2d，\u4e0d\u540c\u5e94\u7528\u573a\u666f\u5bf9\u76ee\u6807\u7684\u504f\u597d\u4e0d\u540c\u3002\u4f8b\u5982，\u5b9e\u65f6\u4ea4\u4e92\u573a\u666f\u4f18\u5148\u8003\u8651\u54cd\u5e94\u901f\u5ea6，\u800c\u79bb\u7ebf\u5206\u6790\u573a\u666f\u66f4\u5173\u6ce8\u7ed3\u679c\u51c6\u786e\u6027\u3002\u901a\u8fc7\u6c42\u89e3\u5e15\u7d2f\u6258\u524d\u6cbf，\u53ef\u4ee5\u83b7\u5f97\u9002\u5e94\u4e0d\u540c\u504f\u597d\u7684\u7b56\u7565\u96c6\u5408\u3002<\/p>\n

            \u6807\u91cf\u5316（Scalarization）\u662f\u5904\u7406\u591a\u76ee\u6807\u4f18\u5316\u7684\u5e38\u7528\u65b9\u6cd5，\u5c06\u591a\u4e2a\u76ee\u6807\u7ec4\u5408\u4e3a\u5355\u4e00\u6807\u91cf\u76ee\u6807：<\/p>\n

            J(\u03c0;\u03bb)=\u2211i=1m\u03bbifi(\u03c0)J(\\\\pi; \\\\lambda) = \\\\sum_{i=1}^{m} \\\\lambda_i f_i(\\\\pi)<\/span><\/span>J<\/span>(<\/span>\u03c0<\/span>;<\/span><\/span>\u03bb<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03bb<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>f<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c0<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

            \u5176\u4e2d \u03bb=(\u03bb1,…,\u03bbm)\\\\lambda = (\\\\lambda_1, …, \\\\lambda_m)<\/span><\/span>\u03bb<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>\u03bb<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>\u03bb<\/span><\/span>m<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u6743\u91cd\u5411\u91cf，\u2211i\u03bbi=1\\\\sum_i \\\\lambda_i = 1<\/span><\/span>\u2211<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03bb<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u3002\u901a\u8fc7\u6539\u53d8\u6743\u91cd\u5411\u91cf，\u53ef\u4ee5\u63a2\u7d22\u5e15\u7d2f\u6258\u524d\u6cbf\u4e0a\u7684\u4e0d\u540c\u70b9\u3002\u5728\u5f3a\u5316\u5b66\u4e60\u4e2d，\u53ef\u4ee5\u901a\u8fc7\u8bad\u7ec3\u591a\u4e2a\u5177\u6709\u4e0d\u540c\u5956\u52b1\u6743\u91cd\u7684\u7b56\u7565\u6765\u8fd1\u4f3c\u5e15\u7d2f\u6258\u524d\u6cbf[42]\u3002<\/p>\n

            3.3 \u957f\u7a0b\u4fe1\u7528\u5206\u914d\u95ee\u9898\u4e0e\u89e3\u51b3\u65b9\u6848<\/h3>\n

            3.3.1 \u4fe1\u7528\u5206\u914d\u95ee\u9898\u7684\u672c\u8d28\u5206\u6790<\/h4>\n

            \u957f\u7a0b\u4fe1\u7528\u5206\u914d（Long-Term Credit Assignment）\u662f\u5f3a\u5316\u5b66\u4e60\u4e2d\u7684\u6838\u5fc3\u6311\u6218，\u5c24\u5176\u5728Agent\u5de5\u4f5c\u6d41\u573a\u666f\u4e2d\u8868\u73b0\u7a81\u51fa\u3002\u5f53Agent\u6267\u884c\u5305\u542b\u6570\u5341\u751a\u81f3\u4e0a\u767e\u4e2a\u6b65\u9aa4\u7684\u5de5\u4f5c\u6d41\u65f6，\u6700\u7ec8\u5956\u52b1\u53ef\u80fd\u4ec5\u4e0e\u5c11\u6570\u5173\u952e\u6b65\u9aa4\u76f8\u5173，\u5982\u4f55\u51c6\u786e\u8bc6\u522b\u8fd9\u4e9b\u5173\u952e\u6b65\u9aa4\u5e76\u5206\u914d\u76f8\u5e94\u7684\u4fe1\u7528\u81f3\u5173\u91cd\u8981[16]\u3002<\/p>\n

            \u5f62\u5f0f\u5316\u5730，\u8bbe\u5de5\u4f5c\u6d41\u5305\u542b TT<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6b65\u9aa4，\u6700\u7ec8\u5956\u52b1\u4e3a RTR_T<\/span><\/span>R<\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u4fe1\u7528\u5206\u914d\u95ee\u9898\u8981\u6c42\u8ba1\u7b97\u6bcf\u4e2a\u6b65\u9aa4 tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u5bf9\u6700\u7ec8\u5956\u52b1\u7684\u8d21\u732e \u2202RT\u2202at\\\\frac{\\\\partial R_T}{\\\\partial a_t}<\/span><\/span><\/span><\/span>\u2202<\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>R<\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u5728\u590d\u6742\u5de5\u4f5c\u6d41\u4e2d，\u8fd9\u79cd\u8d21\u732e\u53ef\u80fd\u662f\u95f4\u63a5\u7684\u3001\u5ef6\u8fdf\u7684，\u4e14\u5b58\u5728\u975e\u7ebf\u6027\u4ea4\u4e92\u3002<\/p>\n

            \u4fe1\u7528\u5206\u914d\u56f0\u96be\u7684\u539f\u56e0\u5305\u62ec：<\/p>\n

              \n
            • \u5ef6\u8fdf\u6548\u5e94：\u65e9\u671f\u6b65\u9aa4\u7684\u5f71\u54cd\u53ef\u80fd\u901a\u8fc7\u72b6\u6001\u8f6c\u79fb\u7d2f\u79ef\u5230\u540e\u671f\u624d\u663e\u73b0<\/li>\n
            • \u5197\u4f59\u64cd\u4f5c：\u67d0\u4e9b\u6b65\u9aa4\u53ef\u80fd\u5bf9\u6700\u7ec8\u7ed3\u679c\u65e0\u5b9e\u8d28\u5f71\u54cd<\/li>\n
            • \u975e\u7ebf\u6027\u4ea4\u4e92：\u591a\u4e2a\u6b65\u9aa4\u7684\u7ec4\u5408\u6548\u5e94\u4e0d\u7b49\u4e8e\u5404\u81ea\u6548\u5e94\u7684\u7b80\u5355\u52a0\u548c<\/li>\n
            • \u968f\u673a\u6027：\u73af\u5883\u968f\u673a\u6027\u4f7f\u5f97\u5355\u6b21\u6267\u884c\u7684\u4fe1\u7528\u4f30\u8ba1\u4e0d\u53ef\u9760<\/li>\n<\/ul>\n

              3.3.2 \u65f6\u5e8f\u5dee\u5206\u4e0e\u8d44\u683c\u8ff9\u65b9\u6cd5<\/h4>\n

              \u65f6\u5e8f\u5dee\u5206（Temporal Difference, TD）\u5b66\u4e60\u901a\u8fc7\u81ea\u4e3e（Bootstrapping）\u673a\u5236\u5b9e\u73b0\u4fe1\u7528\u7684\u9010\u6b65\u4f20\u64ad\u3002TD(0)\u7b97\u6cd5\u4f7f\u7528\u524d\u4e00\u6b65\u7684\u4ef7\u503c\u4f30\u8ba1\u66f4\u65b0\u5f53\u524d\u4f30\u8ba1：<\/p>\n

              V(st)\u2190V(st)+\u03b1[rt+\u03b3V(st+1)\u2212V(st)]V(s_t) \\\\leftarrow V(s_t) + \\\\alpha [r_t + \\\\gamma V(s_{t+1}) – V(s_t)]<\/span><\/span>V<\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2190<\/span><\/span><\/span><\/span>V<\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b1<\/span>[<\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b3V<\/span>(<\/span>s<\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>V<\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)]<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              TD\u8bef\u5dee \u03b4t=rt+\u03b3V(st+1)\u2212V(st)\\\\delta_t = r_t + \\\\gamma V(s_{t+1}) – V(s_t)<\/span><\/span>\u03b4<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b3V<\/span>(<\/span>s<\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>V<\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u53cd\u6620\u4e86\u5f53\u524d\u4ef7\u503c\u4f30\u8ba1\u4e0e\u5b9e\u9645\u56de\u62a5\u7684\u504f\u5dee，\u6cbf\u7740\u8f68\u8ff9\u53cd\u5411\u4f20\u64adTD\u8bef\u5dee\u53ef\u4ee5\u5b9e\u73b0\u4fe1\u7528\u7684\u5206\u914d[42]\u3002<\/p>\n

              TD(\u03bb\\\\lambda<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span>)\u7b97\u6cd5\u901a\u8fc7\u8d44\u683c\u8ff9（Eligibility Trace）\u673a\u5236\u5b9e\u73b0\u4e86\u591a\u6b65TD\u7684\u52a0\u6743\u5e73\u5747\u3002\u8d44\u683c\u8ff9\u8bb0\u5f55\u4e86\u5404\u72b6\u6001\u88ab\u8bbf\u95ee\u7684\u5386\u53f2，\u5e76\u5728\u83b7\u5f97\u5956\u52b1\u65f6\u6309\u8ff9\u5206\u914d\u4fe1\u7528：<\/p>\n

              et(s)=\u03b3\u03bbet\u22121(s)+1[st=s]e_t(s) = \\\\gamma \\\\lambda e_{t-1}(s) + \\\\mathbf{1}[s_t = s]<\/span><\/span>e<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03b3\u03bb<\/span>e<\/span><\/span>t<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>[<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>s<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              V(s)\u2190V(s)+\u03b1\u03b4tet(s)V(s) \\\\leftarrow V(s) + \\\\alpha \\\\delta_t e_t(s)<\/span><\/span>V<\/span>(<\/span>s<\/span>)<\/span><\/span>\u2190<\/span><\/span><\/span><\/span>V<\/span>(<\/span>s<\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b1<\/span>\u03b4<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              \u5176\u4e2d \u03bb\u2208[0,1]\\\\lambda \\\\in [0,1]<\/span><\/span>\u03bb<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>[<\/span>0<\/span>,<\/span><\/span>1<\/span>]<\/span><\/span><\/span><\/span><\/span> \u63a7\u5236\u8ff9\u7684\u8870\u51cf\u901f\u5ea6\u3002\u5f53 \u03bb=0\\\\lambda = 0<\/span><\/span>\u03bb<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u65f6\u9000\u5316\u4e3aTD(0)，\u03bb=1\\\\lambda = 1<\/span><\/span>\u03bb<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u65f6\u7b49\u4ef7\u4e8e\u8499\u7279\u5361\u6d1b\u65b9\u6cd5\u3002\u9002\u4e2d\u7684\u03bb\\\\lambda<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span>\u503c（\u59820.9）\u901a\u5e38\u80fd\u5728\u504f\u5dee\u548c\u65b9\u5dee\u95f4\u53d6\u5f97\u826f\u597d\u5e73\u8861[16]\u3002<\/p>\n

              3.3.3 \u6ce8\u610f\u529b\u673a\u5236\u5728\u4fe1\u7528\u5206\u914d\u4e2d\u7684\u5e94\u7528<\/h4>\n

              Transformer\u67b6\u6784\u4e2d\u7684\u81ea\u6ce8\u610f\u529b\u673a\u5236（Self-Attention）\u4e3a\u4fe1\u7528\u5206\u914d\u63d0\u4f9b\u4e86\u65b0\u7684\u89c6\u89d2\u3002\u6ce8\u610f\u529b\u6743\u91cd\u5929\u7136\u5730\u91cf\u5316\u4e86\u4e0d\u540c\u4f4d\u7f6e\u4e4b\u95f4\u7684\u5173\u8054\u5f3a\u5ea6，\u53ef\u4ee5\u76f4\u63a5\u7528\u4e8e\u4fe1\u7528\u5206\u914d[42]\u3002<\/p>\n

              \u5728\u5de5\u4f5c\u6d41\u573a\u666f\u4e2d，\u53ef\u4ee5\u5c06\u5386\u53f2\u6b65\u9aa4\u5e8f\u5217\u4f5c\u4e3a\u8f93\u5165，\u901a\u8fc7Transformer\u7f16\u7801\u5668\u8ba1\u7b97\u5404\u6b65\u9aa4\u7684\u4e0a\u4e0b\u6587\u8868\u793a\u3002\u6ce8\u610f\u529b\u77e9\u9635 A\u2208RT\u00d7TA \\\\in \\\\mathbb{R}^{T \\\\times T}<\/span><\/span>A<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>R<\/span><\/span>T<\/span>\u00d7<\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5143\u7d20 AijA_{ij}<\/span><\/span>A<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u7b2c jj<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span> \u6b65\u5bf9\u7b2c ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u6b65\u7684\u91cd\u8981\u6027\u3002\u5f53\u5728\u7b2c TT<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span> \u6b65\u83b7\u5f97\u6700\u7ec8\u5956\u52b1\u65f6，\u53ef\u4ee5\u901a\u8fc7\u53cd\u5411\u4f20\u64ad\u6ce8\u610f\u529b\u6743\u91cd\u8ba1\u7b97\u5404\u6b65\u9aa4\u7684\u8d21\u732e\u5ea6\u3002<\/p>\n

              \u5177\u4f53\u5730，\u7b2c tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u6b65\u7684\u4fe1\u7528\u53ef\u4ee5\u8ba1\u7b97\u4e3a：<\/p>\n

              Credit(t)=\u2211i=tTAi,t\u22c5\u03b4i\\\\text{Credit}(t) = \\\\sum_{i=t}^{T} A_{i,t} \\\\cdot \\\\delta_i<\/span><\/span>Credit<\/span><\/span>(<\/span>t<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>t<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>T<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span>i<\/span>,<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>\u03b4<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              \u5176\u4e2d \u03b4i\\\\delta_i<\/span><\/span>\u03b4<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u7b2c ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u6b65\u7684TD\u8bef\u5dee\u3002\u8fd9\u79cd\u57fa\u4e8e\u6ce8\u610f\u529b\u7684\u4fe1\u7528\u5206\u914d\u65b9\u6cd5\u80fd\u591f\u6355\u6349\u957f\u8ddd\u79bb\u4f9d\u8d56\u5173\u7cfb，\u5728\u590d\u6742\u5de5\u4f5c\u6d41\u4e2d\u8868\u73b0\u4f18\u4e8e\u4f20\u7edf\u65b9\u6cd5[16]\u3002<\/p>\n

              4 \u8fc7\u7a0b\u5956\u52b1\u6a21\u578b：\u7ec6\u7c92\u5ea6\u4fe1\u7528\u5206\u914d\u7684\u6838\u5fc3\u673a\u5236<\/h2>\n

              4.1 \u4ece\u7ed3\u679c\u5956\u52b1\u5230\u8fc7\u7a0b\u5956\u52b1\u7684\u8303\u5f0f\u8f6c\u53d8<\/h3>\n

              4.1.1 \u7ed3\u679c\u5956\u52b1\u6a21\u578b\u7684\u5c40\u9650\u6027<\/h4>\n

              \u4f20\u7edf\u5f3a\u5316\u5b66\u4e60\u5728Agent\u5de5\u4f5c\u6d41\u8bad\u7ec3\u4e2d\u4e3b\u8981\u4f9d\u8d56\u7ed3\u679c\u5956\u52b1\u6a21\u578b（Outcome Reward Model, ORM），\u5373\u4ec5\u5728\u4efb\u52a1\u5b8c\u6210\u65f6\u6839\u636e\u6700\u7ec8\u7ed3\u679c\u7ed9\u4e88\u5956\u52b1\u3002\u8fd9\u79cd\u7a00\u758f\u5956\u52b1\u673a\u5236\u5b58\u5728\u6839\u672c\u6027\u5c40\u9650[42]\u3002<\/p>\n

              \u9996\u5148，ORM\u65e0\u6cd5\u63d0\u4f9b\u4e2d\u95f4\u6b65\u9aa4\u7684\u8d28\u91cf\u53cd\u9988\u3002\u5728\u590d\u6742\u5de5\u4f5c\u6d41\u4e2d，Agent\u53ef\u80fd\u5728\u65e9\u671f\u6b65\u9aa4\u5c31\u72af\u4e0b\u5173\u952e\u9519\u8bef，\u4f46\u8fd9\u4e9b\u9519\u8bef\u76f4\u5230\u6700\u540e\u624d\u901a\u8fc7\u5931\u8d25\u7ed3\u679c\u663e\u73b0\u3002\u7f3a\u4e4f\u53ca\u65f6\u53cd\u9988\u4f7f\u5f97Agent\u96be\u4ee5\u5b9a\u4f4d\u95ee\u9898\u6839\u6e90，\u5b66\u4e60\u6548\u7387\u4f4e\u4e0b\u3002<\/p>\n

              \u5176\u6b21，ORM\u9762\u4e34\u4e25\u91cd\u7684\u4fe1\u7528\u5206\u914d\u56f0\u96be\u3002\u5f53\u5de5\u4f5c\u6d41\u5305\u542b\u6570\u5341\u4e2a\u6b65\u9aa4\u65f6，\u5c06\u6700\u7ec8\u5956\u52b1\u5f52\u56e0\u4e8e\u5177\u4f53\u6b65\u9aa4\u51e0\u4e4e\u4e0d\u53ef\u80fd\u3002\u8fd9\u5bfc\u81f4\u7b56\u7565\u68af\u5ea6\u4f30\u8ba1\u7684\u9ad8\u65b9\u5dee，\u8bad\u7ec3\u8fc7\u7a0b\u4e0d\u7a33\u5b9a\u3002<\/p>\n

              \u7b2c\u4e09，ORM\u65e0\u6cd5\u533a\u5206\u4e0d\u540c\u7a0b\u5ea6\u7684\u5931\u8d25\u3002\u4e24\u4e2a\u90fd\u5bfc\u81f4\u5931\u8d25\u7684\u5de5\u4f5c\u6d41，\u4e00\u4e2a\u53ef\u80fd\u5728\u7b2c\u4e00\u6b65\u5c31\u51fa\u9519，\u53e6\u4e00\u4e2a\u4ec5\u5728\u6700\u540e\u4e00\u6b65\u5931\u8bef，ORM\u5bf9\u4e24\u8005\u7ed9\u4e88\u76f8\u540c\u7684\u60e9\u7f5a，\u8fd9\u663e\u7136\u4e0d\u5408\u7406\u3002<\/p>\n

              4.1.2 \u8fc7\u7a0b\u5956\u52b1\u6a21\u578b\u7684\u5b9a\u4e49\u4e0e\u6570\u5b66\u5f62\u5f0f<\/h4>\n

              \u8fc7\u7a0b\u5956\u52b1\u6a21\u578b（Process Reward Model, PRM）\u901a\u8fc7\u5728\u6bcf\u4e00\u6b65\u63d0\u4f9b\u7ec6\u7c92\u5ea6\u7684\u8bc4\u4f30\u4fe1\u53f7，\u6709\u6548\u89e3\u51b3\u4e86ORM\u7684\u5c40\u9650\u6027\u3002PRM\u4e3a\u5de5\u4f5c\u6d41\u7684\u6bcf\u4e2a\u4e2d\u95f4\u6b65\u9aa4\u5206\u914d\u4e00\u4e2a\u5956\u52b1\u503c，\u53cd\u6620\u8be5\u6b65\u9aa4\u7684\u8d28\u91cf\u548c\u8fdb\u5c55[16]\u3002<\/p>\n

              \u5f62\u5f0f\u5316\u5730，\u5bf9\u4e8e\u5de5\u4f5c\u6d41\u8f68\u8ff9 \u03c4=(s0,a0,r0,s1,a1,r1,…,sT,aT,rT)\\\\tau = (s_0, a_0, r_0, s_1, a_1, r_1, …, s_T, a_T, r_T)<\/span><\/span>\u03c4<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>r<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>r<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>s<\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>r<\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>，PRM\u5b9a\u4e49\u4e3a\u6620\u5c04：<\/p>\n

              PRM:(st,at)\u21a6rtproc\u2208R\\\\text{PRM}: (s_t, a_t) \\\\mapsto r_t^{proc} \\\\in \\\\mathbb{R}<\/span><\/span>PRM<\/span><\/span><\/span>:<\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u21a6<\/span><\/span><\/span><\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>p<\/span>roc<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2208<\/span><\/span><\/span><\/span>R<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              \u5176\u4e2d rtprocr_t^{proc}<\/span><\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>p<\/span>roc<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u7b2c tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u6b65\u7684\u8fc7\u7a0b\u5956\u52b1，\u53ef\u4ee5\u57fa\u4e8e\u4ee5\u4e0b\u51c6\u5219\u8ba1\u7b97：<\/p>\n

                \n
              • \u6b63\u786e\u6027：\u8be5\u6b65\u9aa4\u7684\u903b\u8f91\u662f\u5426\u6b63\u786e，\u662f\u5426\u7b26\u5408\u4e8b\u5b9e<\/li>\n
              • \u8fdb\u5c55\u6027：\u8be5\u6b65\u9aa4\u662f\u5426\u671d\u7740\u6700\u7ec8\u76ee\u6807\u63a8\u8fdb<\/li>\n
              • \u6548\u7387\u6027：\u8be5\u6b65\u9aa4\u662f\u5426\u7b80\u6d01\u9ad8\u6548，\u65e0\u5197\u4f59\u64cd\u4f5c<\/li>\n
              • \u4e00\u81f4\u6027：\u8be5\u6b65\u9aa4\u4e0e\u524d\u540e\u6b65\u9aa4\u662f\u5426\u903b\u8f91\u4e00\u81f4<\/li>\n<\/ul>\n

                PRM\u7684\u8bad\u7ec3\u901a\u5e38\u91c7\u7528\u76d1\u7763\u5b66\u4e60\u65b9\u6cd5\u3002\u9996\u5148\u9700\u8981\u6784\u5efa\u6b65\u9aa4\u7ea7\u6807\u6ce8\u6570\u636e\u96c6，\u5bf9\u6bcf\u4e2a\u4e2d\u95f4\u6b65\u9aa4\u6807\u6ce8\u5176\u8d28\u91cf\u5206\u6570\u3002\u7531\u4e8e\u4eba\u5de5\u6807\u6ce8\u6210\u672c\u9ad8\u6602，\u7814\u7a76\u8005\u63d0\u51fa\u4e86\u591a\u79cd\u81ea\u52a8\u6807\u6ce8\u65b9\u6cd5[16]\u3002<\/p>\n

                4.1.3 PRM\u4e0eORM\u7684\u534f\u540c\u673a\u5236<\/h4>\n

                \u5728\u5b9e\u9645\u5e94\u7528\u4e2d，PRM\u4e0eORM\u5e76\u975e\u76f8\u4e92\u66ff\u4ee3，\u800c\u662f\u534f\u540c\u5de5\u4f5c\u3002ORM\u63d0\u4f9b\u6700\u7ec8\u7ed3\u679c\u7684\u5ba2\u89c2\u8bc4\u4f30，PRM\u63d0\u4f9b\u4e2d\u95f4\u8fc7\u7a0b\u7684\u7ec6\u7c92\u5ea6\u6307\u5bfc，\u4e24\u8005\u7ed3\u5408\u5f62\u6210\u5b8c\u6574\u7684\u5956\u52b1\u4fe1\u53f7[42]\u3002<\/p>\n

                \u7ec4\u5408\u5956\u52b1\u51fd\u6570\u53ef\u4ee5\u8868\u793a\u4e3a：<\/p>\n

                Rtotal=\u03b1\u22c5Routcome+(1\u2212\u03b1)\u22c5\u2211t=1T\u03b3t\u22121rtprocR_{total} = \\\\alpha \\\\cdot R_{outcome} + (1-\\\\alpha) \\\\cdot \\\\sum_{t=1}^{T} \\\\gamma^{t-1} r_t^{proc}<\/span><\/span>R<\/span><\/span>t<\/span>o<\/span>t<\/span>a<\/span>l<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u03b1<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>R<\/span><\/span>o<\/span>u<\/span>t<\/span>co<\/span>m<\/span>e<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>(<\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03b1<\/span>)<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span><\/span>t<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>T<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b3<\/span><\/span>t<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>p<\/span>roc<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u5176\u4e2d \u03b1\u2208[0,1]\\\\alpha \\\\in [0,1]<\/span><\/span>\u03b1<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>[<\/span>0<\/span>,<\/span><\/span>1<\/span>]<\/span><\/span><\/span><\/span><\/span> \u63a7\u5236\u4e24\u79cd\u5956\u52b1\u7684\u6743\u91cd，\u03b3\\\\gamma<\/span><\/span>\u03b3<\/span><\/span><\/span><\/span><\/span> \u4e3a\u6298\u6263\u56e0\u5b50\u3002\u5728\u8bad\u7ec3\u521d\u671f，\u53ef\u4ee5\u589e\u5927 \u03b1\\\\alpha<\/span><\/span>\u03b1<\/span><\/span><\/span><\/span><\/span> \u4f7fAgent\u9996\u5148\u5b66\u4f1a\u5b8c\u6210\u4efb\u52a1；\u968f\u7740\u8bad\u7ec3\u8fdb\u884c，\u9010\u6e10\u964d\u4f4e \u03b1\\\\alpha<\/span><\/span>\u03b1<\/span><\/span><\/span><\/span><\/span> \u4ee5\u5f3a\u5316\u5bf9\u8fc7\u7a0b\u8d28\u91cf\u7684\u5173\u6ce8\u3002<\/p>\n

                PRM\u8fd8\u53ef\u4ee5\u5728\u63a8\u7406\u9636\u6bb5\u6307\u5bfc\u641c\u7d22\u3002\u901a\u8fc7PRM\u8bc4\u5206，\u53ef\u4ee5\u5b9e\u73b0\u6b65\u9aa4\u7ea7\u7684\u675f\u641c\u7d22（Beam Search）：\u5728\u6bcf\u4e00\u6b65\u751f\u6210\u591a\u4e2a\u5019\u9009\u52a8\u4f5c，\u7531PRM\u8bc4\u5206\u540e\u4fdd\u7559Top-K\u4e2a\u6700\u6709\u5e0c\u671b\u7684\u5019\u9009\u3002\u8fd9\u79cdPRM\u5f15\u5bfc\u7684\u641c\u7d22\u663e\u8457\u63d0\u5347\u4e86Agent\u5728\u590d\u6742\u4efb\u52a1\u4e0a\u7684\u8868\u73b0[16]\u3002<\/p>\n

                #mermaid-svg-hOQH51wFsilKanIW{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-hOQH51wFsilKanIW .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-hOQH51wFsilKanIW .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-hOQH51wFsilKanIW .error-icon{fill:#552222;}#mermaid-svg-hOQH51wFsilKanIW .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-hOQH51wFsilKanIW .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-hOQH51wFsilKanIW .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-hOQH51wFsilKanIW .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-hOQH51wFsilKanIW .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-hOQH51wFsilKanIW .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-hOQH51wFsilKanIW .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-hOQH51wFsilKanIW .marker{fill:#333333;stroke:#333333;}#mermaid-svg-hOQH51wFsilKanIW .marker.cross{stroke:#333333;}#mermaid-svg-hOQH51wFsilKanIW svg{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-hOQH51wFsilKanIW p{margin:0;}#mermaid-svg-hOQH51wFsilKanIW .label{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;color:#333;}#mermaid-svg-hOQH51wFsilKanIW .cluster-label text{fill:#333;}#mermaid-svg-hOQH51wFsilKanIW .cluster-label span{color:#333;}#mermaid-svg-hOQH51wFsilKanIW .cluster-label span p{background-color:transparent;}#mermaid-svg-hOQH51wFsilKanIW .label text,#mermaid-svg-hOQH51wFsilKanIW span{fill:#333;color:#333;}#mermaid-svg-hOQH51wFsilKanIW .node rect,#mermaid-svg-hOQH51wFsilKanIW .node circle,#mermaid-svg-hOQH51wFsilKanIW .node ellipse,#mermaid-svg-hOQH51wFsilKanIW .node polygon,#mermaid-svg-hOQH51wFsilKanIW .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-hOQH51wFsilKanIW .rough-node .label text,#mermaid-svg-hOQH51wFsilKanIW .node .label text,#mermaid-svg-hOQH51wFsilKanIW .image-shape .label,#mermaid-svg-hOQH51wFsilKanIW .icon-shape .label{text-anchor:middle;}#mermaid-svg-hOQH51wFsilKanIW .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-hOQH51wFsilKanIW .rough-node .label,#mermaid-svg-hOQH51wFsilKanIW .node .label,#mermaid-svg-hOQH51wFsilKanIW .image-shape .label,#mermaid-svg-hOQH51wFsilKanIW .icon-shape .label{text-align:center;}#mermaid-svg-hOQH51wFsilKanIW .node.clickable{cursor:pointer;}#mermaid-svg-hOQH51wFsilKanIW .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-hOQH51wFsilKanIW .arrowheadPath{fill:#333333;}#mermaid-svg-hOQH51wFsilKanIW .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-hOQH51wFsilKanIW .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-hOQH51wFsilKanIW .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-hOQH51wFsilKanIW .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-hOQH51wFsilKanIW .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-hOQH51wFsilKanIW .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-hOQH51wFsilKanIW .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-hOQH51wFsilKanIW .cluster text{fill:#333;}#mermaid-svg-hOQH51wFsilKanIW .cluster span{color:#333;}#mermaid-svg-hOQH51wFsilKanIW div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-hOQH51wFsilKanIW .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-hOQH51wFsilKanIW rect.text{fill:none;stroke-width:0;}#mermaid-svg-hOQH51wFsilKanIW .icon-shape,#mermaid-svg-hOQH51wFsilKanIW .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-hOQH51wFsilKanIW .icon-shape p,#mermaid-svg-hOQH51wFsilKanIW .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-hOQH51wFsilKanIW .icon-shape rect,#mermaid-svg-hOQH51wFsilKanIW .image-shape rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-hOQH51wFsilKanIW .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-hOQH51wFsilKanIW .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-hOQH51wFsilKanIW :root{–mermaid-font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;}<\/p>\n

                PRM\u8fc7\u7a0b\u5956\u52b1<\/p>\n

                <\/span><\/p>\n

                r1<\/p>\n

                <\/span><\/p>\n

                r2<\/p>\n

                <\/span><\/p>\n

                r3<\/p>\n

                <\/span><\/p>\n

                r4<\/p>\n

                <\/span><\/p>\n

                \u6b65\u9aa41<\/p>\n

                <\/span><\/p>\n

                \u6b65\u9aa42<\/p>\n

                <\/span><\/p>\n

                \u6b65\u9aa43<\/p>\n

                <\/span><\/p>\n

                \u6700\u7ec8\u7ed3\u679c<\/p>\n

                <\/span><\/p>\n

                \u5956\u52b1\u4fe1\u53f7<\/p>\n

                <\/span><\/p>\n

                ORM\u7ed3\u679c\u5956\u52b1<\/p>\n

                <\/span><\/span><\/span><\/span><\/p>\n

                \u53ea\u6709\u6700\u7ec8\u5956\u52b1<\/p>\n

                <\/span><\/p>\n

                \u6b65\u9aa41<\/p>\n

                <\/span><\/p>\n

                \u6b65\u9aa42<\/p>\n

                <\/span><\/p>\n

                \u6b65\u9aa43<\/p>\n

                <\/span><\/p>\n

                \u6700\u7ec8\u7ed3\u679c<\/p>\n

                <\/span><\/p>\n

                \u5956\u52b1\u4fe1\u53f7<\/p>\n

                <\/span><\/p>\n

                PRM<\/p>\n

                <\/span><\/p>\n

                r1<\/p>\n

                <\/span><\/p>\n

                r2<\/p>\n

                <\/span><\/p>\n

                r3<\/p>\n

                <\/span><\/p>\n

                r4<\/p>\n

                <\/span><\/p>\n

                4.2 \u8fc7\u7a0b\u5956\u52b1\u6a21\u578b\u7684\u8bad\u7ec3\u65b9\u6cd5<\/h3>\n

                4.2.1 \u8499\u7279\u5361\u6d1b\u4f30\u8ba1\u4e0e\u81ea\u52a8\u6807\u6ce8<\/h4>\n

                \u8499\u7279\u5361\u6d1b（Monte Carlo, MC）\u4f30\u8ba1\u662fPRM\u81ea\u52a8\u6807\u6ce8\u7684\u4e3b\u6d41\u65b9\u6cd5\u3002\u5176\u6838\u5fc3\u601d\u60f3\u662f：\u4ece\u67d0\u4e00\u6b65\u51fa\u53d1，\u91c7\u6837\u591a\u6761\u540e\u7eed\u8f68\u8ff9，\u6839\u636e\u8fd9\u4e9b\u8f68\u8ff9\u7684\u6700\u7ec8\u6210\u529f\u7387\u4f30\u8ba1\u8be5\u6b65\u7684\u8d28\u91cf[56]\u3002<\/p>\n

                \u5177\u4f53\u5730，\u5bf9\u4e8e\u6b65\u9aa4 (st,at)(s_t, a_t)<\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>，\u4ece\u8be5\u6b65\u5f00\u59cb\u91c7\u6837 NN<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u6761\u5b8c\u6210\u8f68\u8ff9 {\u03c4(i)}i=1N\\\\{\\\\tau^{(i)}\\\\}_{i=1}^N<\/span><\/span>{<\/span>\u03c4<\/span><\/span>(<\/span>i<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>}<\/span><\/span>i<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>N<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u6bcf\u6761\u8f68\u8ff9\u4f7f\u7528\u5f53\u524d\u7b56\u7565\u6216\u968f\u673a\u7b56\u7565\u751f\u6210\u3002\u8be5\u6b65\u7684\u8fc7\u7a0b\u5956\u52b1\u4f30\u8ba1\u4e3a：<\/p>\n

                r^tproc=1N\u2211i=1NR(\u03c4(i))\\\\hat{r}_t^{proc} = \\\\frac{1}{N} \\\\sum_{i=1}^{N} R(\\\\tau^{(i)})<\/span><\/span><\/span>r<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span>p<\/span>roc<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>N<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>R<\/span>(<\/span>\u03c4<\/span><\/span>(<\/span>i<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u5176\u4e2d R(\u03c4(i))R(\\\\tau^{(i)})<\/span><\/span>R<\/span>(<\/span>\u03c4<\/span><\/span>(<\/span>i<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7b2c ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u6761\u8f68\u8ff9\u7684\u6700\u7ec8\u5956\u52b1（\u901a\u5e38\u4e3a0\u62161）\u3002\u5f53 NN<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u8db3\u591f\u5927\u65f6，\u8be5\u4f30\u8ba1\u6536\u655b\u5230\u771f\u5b9e\u7684\u671f\u671b\u56de\u62a5\u3002<\/p>\n

                MC\u4f30\u8ba1\u7684\u65b9\u5dee\u4e0e NN<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u6210\u53cd\u6bd4\u3002\u4e3a\u964d\u4f4e\u65b9\u5dee，\u53ef\u4ee5\u91c7\u7528\u91cd\u8981\u6027\u91c7\u6837（Importance Sampling）\u6280\u672f，\u4f7f\u7528\u66f4\u9ad8\u6548\u7684\u7b56\u7565\u751f\u6210\u8f68\u8ff9，\u7136\u540e\u901a\u8fc7\u91cd\u8981\u6027\u6743\u91cd\u6821\u6b63\u504f\u5dee\u3002\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u4f7f\u7528\u5171\u540c\u968f\u673a\u6570（Common Random Numbers），\u5728\u4e0d\u540c\u6b65\u9aa4\u7684\u4f30\u8ba1\u4e2d\u4f7f\u7528\u76f8\u540c\u7684\u968f\u673a\u79cd\u5b50，\u51cf\u5c11\u4f30\u8ba1\u95f4\u7684\u65b9\u5dee[42]\u3002<\/p>\n

                4.2.2 \u65f6\u5e8f\u5dee\u5206\u4f30\u8ba1\u4e0e\u4ef7\u503c\u4f20\u64ad<\/h4>\n

                \u65f6\u5e8f\u5dee\u5206（TD）\u4f30\u8ba1\u63d0\u4f9b\u4e86\u53e6\u4e00\u79cdPRM\u8bad\u7ec3\u65b9\u6cd5，\u5b83\u901a\u8fc7\u81ea\u4e3e\u673a\u5236\u5b9e\u73b0\u4ef7\u503c\u7684\u9010\u6b65\u4f20\u64ad\u3002\u4e0eMC\u4f30\u8ba1\u9700\u8981\u5b8c\u6574\u8f68\u8ff9\u4e0d\u540c，TD\u4f30\u8ba1\u53ef\u4ee5\u5728\u6bcf\u4e00\u6b65\u66f4\u65b0，\u5177\u6709\u66f4\u4f4e\u7684\u8ba1\u7b97\u6210\u672c[14]\u3002<\/p>\n

                TD-based PRM\u8bad\u7ec3\u4f7f\u7528\u4ee5\u4e0b\u66f4\u65b0\u89c4\u5219：<\/p>\n

                PRM(st,at)\u2190PRM(st,at)+\u03b2[rt+\u03b3max\u2061a\u2032PRM(st+1,a\u2032)\u2212PRM(st,at)]\\\\text{PRM}(s_t, a_t) \\\\leftarrow \\\\text{PRM}(s_t, a_t) + \\\\beta [r_t + \\\\gamma \\\\max_{a'} \\\\text{PRM}(s_{t+1}, a') – \\\\text{PRM}(s_t, a_t)]<\/span><\/span>PRM<\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2190<\/span><\/span><\/span><\/span>PRM<\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b2<\/span>[<\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b3<\/span><\/span><\/span>a<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>max<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>PRM<\/span><\/span>(<\/span>s<\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>PRM<\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)]<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u8be5\u66f4\u65b0\u4f7f\u5f97PRM\u503c\u6cbf\u7740\u8f68\u8ff9\u5411\u540e\u4f20\u64ad，\u6700\u7ec8\u6b65\u9aa4\u7684\u7ed3\u679c\u5956\u52b1\u901a\u8fc7\u591a\u6b65TD\u8bef\u5dee\u4f20\u9012\u5230\u524d\u9762\u5404\u6b65\u3002<\/p>\n

                \u5e7f\u4e49\u4f18\u52bf\u4f30\u8ba1（Generalized Advantage Estimation, GAE）\u7ed3\u5408\u4e86MC\u548cTD\u7684\u4f18\u70b9，\u901a\u8fc7\u53c2\u6570 \u03bb\\\\lambda<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span> \u63a7\u5236\u4e24\u8005\u7684\u6743\u8861[16]：<\/p>\n

                A^tGAE=\u2211l=0\u221e(\u03b3\u03bb)l\u03b4t+l\\\\hat{A}_t^{GAE} = \\\\sum_{l=0}^{\\\\infty} (\\\\gamma \\\\lambda)^l \\\\delta_{t+l}<\/span><\/span><\/span>A<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span>G<\/span>A<\/span>E<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>l<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>\u221e<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b3\u03bb<\/span>)<\/span><\/span>l<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b4<\/span><\/span>t<\/span>+<\/span>l<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u5176\u4e2d \u03b4t=rt+\u03b3V(st+1)\u2212V(st)\\\\delta_t = r_t + \\\\gamma V(s_{t+1}) – V(s_t)<\/span><\/span>\u03b4<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b3V<\/span>(<\/span>s<\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>V<\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3aTD\u8bef\u5dee\u3002\u5f53 \u03bb=0\\\\lambda = 0<\/span><\/span>\u03bb<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u65f6\u9000\u5316\u4e3a\u5355\u6b65TD，\u03bb=1\\\\lambda = 1<\/span><\/span>\u03bb<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u65f6\u7b49\u4ef7\u4e8eMC\u4f30\u8ba1\u3002\u9002\u4e2d\u7684\u03bb\\\\lambda<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span>\u503c（\u59820.95）\u5728\u5b9e\u8df5\u4e2d\u8868\u73b0\u6700\u4f73\u3002<\/p>\n

                4.2.3 \u5bf9\u6bd4\u5b66\u4e60\u4e0e\u6392\u540d\u635f\u5931<\/h4>\n

                PRM\u7684\u8bad\u7ec3\u53ef\u4ee5\u5efa\u6a21\u4e3a\u6392\u5e8f\u95ee\u9898：\u7ed9\u5b9a\u4e24\u4e2a\u6b65\u9aa4，\u5224\u65ad\u54ea\u4e2a\u66f4\u4f18\u3002\u8fd9\u79cd\u6392\u5e8f\u89c6\u89d2\u81ea\u7136\u5730\u5bfc\u51fa\u4e86\u5bf9\u6bd4\u5b66\u4e60（Contrastive Learning）\u65b9\u6cd5[16]\u3002<\/p>\n

                \u5bf9\u4e8e\u540c\u4e00\u95ee\u9898\u7684\u4e24\u4e2a\u4e0d\u540c\u6267\u884c\u8def\u5f84，\u5982\u679c\u8def\u5f84A\u6700\u7ec8\u6210\u529f\u800c\u8def\u5f84B\u5931\u8d25，\u5219\u8def\u5f84A\u4e2d\u7684\u6240\u6709\u6b65\u9aa4\u5e94\u83b7\u5f97\u6bd4\u8def\u5f84B\u5bf9\u5e94\u6b65\u9aa4\u66f4\u9ad8\u7684PRM\u5206\u6570\u3002\u5f62\u5f0f\u5316\u5730，\u8bbe (stA,atA)(s_t^A, a_t^A)<\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u548c (stB,atB)(s_t^B, a_t^B)<\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u4e24\u6761\u8def\u5f84\u7684\u7b2c tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u6b65，\u6392\u540d\u635f\u5931\u5b9a\u4e49\u4e3a：<\/p>\n

                Lrank=max\u2061(0,m\u2212PRM(stA,atA)+PRM(stB,atB))\\\\mathcal{L}_{rank} = \\\\max(0, m – \\\\text{PRM}(s_t^A, a_t^A) + \\\\text{PRM}(s_t^B, a_t^B))<\/span><\/span>L<\/span><\/span>r<\/span>ank<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>max<\/span>(<\/span>0<\/span>,<\/span><\/span>m<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>PRM<\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>PRM<\/span><\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>))<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u5176\u4e2d mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u4e3a\u8fb9\u9645\u53c2\u6570\u3002\u8be5\u635f\u5931\u9f13\u52b1\u6210\u529f\u8def\u5f84\u7684\u6b65\u9aa4\u5f97\u5206\u6bd4\u5931\u8d25\u8def\u5f84\u9ad8\u81f3\u5c11 mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

                \u5bf9\u6bd4\u5b66\u4e60\u8fd8\u53ef\u4ee5\u6269\u5c55\u5230\u591a\u8def\u5f84\u6bd4\u8f83\u3002\u7ed9\u5b9a\u540c\u4e00\u95ee\u9898\u7684 KK<\/span><\/span>K<\/span><\/span><\/span><\/span><\/span> \u6761\u8def\u5f84\u53ca\u5176\u6700\u7ec8\u6210\u529f\u7387，\u53ef\u4ee5\u4f7f\u7528ListNet\u6216ListMLE\u7b49\u6392\u5e8f\u635f\u5931\u51fd\u6570\u8bad\u7ec3PRM，\u4f7f\u5176\u8f93\u51fa\u7684\u6b65\u9aa4\u5206\u6570\u4e0e\u6700\u7ec8\u6210\u529f\u7387\u4e00\u81f4[56]\u3002<\/p>\n

                4.3 PRM\u5728\u5de5\u4f5c\u6d41\u4f18\u5316\u4e2d\u7684\u5e94\u7528<\/h3>\n

                4.3.1 \u6b65\u9aa4\u7ea7\u675f\u641c\u7d22\u4e0e\u63a8\u7406\u5f15\u5bfc<\/h4>\n

                PRM\u6700\u76f4\u63a5\u7684\u5e94\u7528\u662f\u5728\u63a8\u7406\u9636\u6bb5\u5f15\u5bfc\u641c\u7d22\u8fc7\u7a0b\u3002\u4f20\u7edf\u7684\u8d2a\u5a6a\u89e3\u7801（Greedy Decoding）\u6bcf\u4e00\u6b65\u9009\u62e9\u6982\u7387\u6700\u9ad8\u7684\u52a8\u4f5c，\u5bb9\u6613\u9677\u5165\u5c40\u90e8\u6700\u4f18\u3002PRM\u5f15\u5bfc\u7684\u675f\u641c\u7d22（Beam Search）\u5219\u8003\u8651\u591a\u6b65\u7d2f\u79ef\u4ef7\u503c，\u80fd\u591f\u53d1\u73b0\u66f4\u4f18\u7684\u5168\u5c40\u89e3[42]\u3002<\/p>\n

                \u675f\u641c\u7d22\u7b97\u6cd5\u7ef4\u62a4 KK<\/span><\/span>K<\/span><\/span><\/span><\/span><\/span> \u4e2a\u5019\u9009\u8def\u5f84（\u675f\u5bbd）\u3002\u5728\u6bcf\u4e00\u6b65，\u5bf9\u6bcf\u4e2a\u5019\u9009\u8def\u5f84\u6269\u5c55\u6240\u6709\u53ef\u80fd\u7684\u52a8\u4f5c，\u7531PRM\u8bc4\u4f30\u6269\u5c55\u540e\u7684\u8d28\u91cf，\u4fdd\u7559\u5f97\u5206\u6700\u9ad8\u7684 KK<\/span><\/span>K<\/span><\/span><\/span><\/span><\/span> \u4e2a\u5019\u9009\u3002\u5f62\u5f0f\u5316\u5730，\u8bbe\u7b2c tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u6b65\u7684\u5019\u9009\u96c6\u5408\u4e3a Bt={(st(i),scorei)}i=1K\\\\mathcal{B}_t = \\\\{(s_t^{(i)}, \\\\text{score}_i)\\\\}_{i=1}^K<\/span><\/span>B<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>{(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>(<\/span>i<\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>score<\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>}<\/span><\/span>i<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>K<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5219\u7b2c t+1t+1<\/span><\/span>t<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u6b65\u7684\u5019\u9009\u4e3a：<\/p>\n

                Bt+1=TopK(s,a){score(s)+PRM(s,a)\u2223s\u2208Bt,a\u2208A(s)}\\\\mathcal{B}_{t+1} = \\\\text{TopK}_{(s,a)} \\\\left\\\\{ \\\\text{score}(s) + \\\\text{PRM}(s, a) \\\\mid s \\\\in \\\\mathcal{B}_t, a \\\\in \\\\mathcal{A}(s) \\\\right\\\\}<\/span><\/span>B<\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>TopK<\/span><\/span><\/span>(<\/span>s<\/span>,<\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>{<\/span>score<\/span><\/span>(<\/span>s<\/span>)<\/span><\/span>+<\/span><\/span>PRM<\/span><\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span><\/span>\u2223<\/span><\/span>s<\/span><\/span>\u2208<\/span><\/span>B<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>\u2208<\/span><\/span>A<\/span>(<\/span>s<\/span>)<\/span>}<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                PRM\u5f15\u5bfc\u7684\u675f\u641c\u7d22\u663e\u8457\u63d0\u5347\u4e86Agent\u5728\u6570\u5b66\u63a8\u7406\u3001\u4ee3\u7801\u751f\u6210\u7b49\u590d\u6742\u4efb\u52a1\u4e0a\u7684\u8868\u73b0\u3002\u7814\u7a76\u8868\u660e，\u4f7f\u7528PRM\u5f15\u5bfc\u7684\u641c\u7d22，7B\u53c2\u6570\u7684\u6a21\u578b\u53ef\u4ee5\u8fbe\u5230\u4e0e175B\u6a21\u578b\u76f8\u5f53\u7684\u6027\u80fd[7]\u3002<\/p>\n

                4.3.2 PRM\u4e0e\u7b56\u7565\u4f18\u5316\u7684\u7aef\u5230\u7aef\u8bad\u7ec3<\/h4>\n

                PRM\u4e0d\u4ec5\u53ef\u4ee5\u7528\u4e8e\u63a8\u7406\u5f15\u5bfc，\u8fd8\u53ef\u4ee5\u4e0e\u7b56\u7565\u7f51\u7edc\u7aef\u5230\u7aef\u8054\u5408\u8bad\u7ec3，\u5b9e\u73b0\u8fc7\u7a0b\u76d1\u7763\u5f3a\u5316\u5b66\u4e60（Process-Supervised RL）\u3002\u5728\u8fd9\u79cd\u6846\u67b6\u4e0b，PRM\u63d0\u4f9b\u7684\u6b65\u9aa4\u7ea7\u5956\u52b1\u76f4\u63a5\u7528\u4e8e\u7b56\u7565\u66f4\u65b0[61]\u3002<\/p>\n

                \u8bad\u7ec3\u8fc7\u7a0b\u4ea4\u66ff\u8fdb\u884c\u4ee5\u4e0b\u6b65\u9aa4：<\/p>\n

              • \u4f7f\u7528\u5f53\u524d\u7b56\u7565\u91c7\u6837\u5de5\u4f5c\u6d41\u8f68\u8ff9<\/li>\n
              • \u4f7f\u7528PRM\u8bc4\u4f30\u5404\u6b65\u9aa4\u8d28\u91cf，\u751f\u6210\u8fc7\u7a0b\u5956\u52b1<\/li>\n
              • \u4f7f\u7528PPO\u6216GRPO\u7b97\u6cd5\u66f4\u65b0\u7b56\u7565，\u6700\u5927\u5316\u7d2f\u79ef\u8fc7\u7a0b\u5956\u52b1<\/li>\n
              • \u4f7f\u7528\u65b0\u91c7\u6837\u7684\u8f68\u8ff9\u66f4\u65b0PRM，\u63d0\u9ad8\u8bc4\u4f30\u51c6\u786e\u6027<\/li>\n

                \u8fd9\u79cd\u8054\u5408\u8bad\u7ec3\u4f7f\u5f97\u7b56\u7565\u548cPRM\u76f8\u4e92\u4fc3\u8fdb：\u66f4\u597d\u7684\u7b56\u7565\u751f\u6210\u66f4\u9ad8\u8d28\u91cf\u7684\u8f68\u8ff9，\u7528\u4e8e\u8bad\u7ec3\u66f4\u51c6\u786e\u7684PRM；\u66f4\u51c6\u786e\u7684PRM\u63d0\u4f9b\u66f4\u53ef\u9760\u7684\u5956\u52b1\u4fe1\u53f7，\u5f15\u5bfc\u7b56\u7565\u8fdb\u4e00\u6b65\u4f18\u5316\u3002<\/p>\n

                4.3.3 \u9519\u8bef\u5b9a\u4f4d\u4e0e\u56de\u6eaf\u673a\u5236<\/h4>\n

                PRM\u7684\u4e00\u4e2a\u91cd\u8981\u5e94\u7528\u662f\u9519\u8bef\u5b9a\u4f4d（Error Localization）\u3002\u5f53\u5de5\u4f5c\u6d41\u6267\u884c\u5931\u8d25\u65f6，PRM\u53ef\u4ee5\u5e2e\u52a9\u8bc6\u522b\u7b2c\u4e00\u4e2a\u9519\u8bef\u53d1\u751f\u7684\u6b65\u9aa4，\u4e3a\u56de\u6eaf\u548c\u4fee\u6b63\u63d0\u4f9b\u4f9d\u636e[62]\u3002<\/p>\n

                OmegaPRM\u7b97\u6cd5\u901a\u8fc7\u4e8c\u5206\u641c\u7d22\u9ad8\u6548\u5b9a\u4f4d\u9519\u8bef\u6b65\u9aa4\u3002\u7ed9\u5b9a\u4e00\u6761\u5931\u8d25\u8f68\u8ff9，\u7b97\u6cd5\u9996\u5148\u68c0\u67e5\u4e2d\u70b9\u6b65\u9aa4\u7684PRM\u5206\u6570\u3002\u5982\u679c\u4e2d\u70b9\u524d\u7684\u6b65\u9aa4\u5f97\u5206\u6b63\u5e38\u800c\u4e2d\u70b9\u540e\u5f97\u5206\u9aa4\u964d，\u5219\u9519\u8bef\u4f4d\u4e8e\u4e2d\u70b9\u9644\u8fd1\u3002\u901a\u8fc7\u9012\u5f52\u4e8c\u5206，\u53ef\u4ee5\u5728 O(log\u2061T)O(\\\\log T)<\/span><\/span>O<\/span>(<\/span>log<\/span><\/span><\/span>T<\/span>)<\/span><\/span><\/span><\/span><\/span> \u6b21\u8bc4\u4f30\u5185\u5b9a\u4f4d\u7b2c\u4e00\u4e2a\u9519\u8bef\u6b65\u9aa4[16]\u3002<\/p>\n

                \u5b9a\u4f4d\u9519\u8bef\u540e，Agent\u53ef\u4ee5\u6267\u884c\u56de\u6eaf（Backtracking）\u64cd\u4f5c，\u56de\u9000\u5230\u9519\u8bef\u524d\u7684\u72b6\u6001\u5e76\u5c1d\u8bd5\u66ff\u4ee3\u52a8\u4f5c\u3002\u8fd9\u79cd\u8bd5\u9519\u5b66\u4e60\u673a\u5236\u4f7f\u5f97Agent\u80fd\u591f\u4ece\u5931\u8d25\u4e2d\u5feb\u901f\u6062\u590d，\u6301\u7eed\u63d0\u5347\u5de5\u4f5c\u6d41\u8d28\u91cf\u3002<\/p>\n

                #mermaid-svg-tj5FxsjQOBEbuNS1{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-tj5FxsjQOBEbuNS1 .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-tj5FxsjQOBEbuNS1 .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-tj5FxsjQOBEbuNS1 .error-icon{fill:#552222;}#mermaid-svg-tj5FxsjQOBEbuNS1 .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-tj5FxsjQOBEbuNS1 .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-tj5FxsjQOBEbuNS1 .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-tj5FxsjQOBEbuNS1 .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-tj5FxsjQOBEbuNS1 .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-tj5FxsjQOBEbuNS1 .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-tj5FxsjQOBEbuNS1 .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-tj5FxsjQOBEbuNS1 .marker{fill:#333333;stroke:#333333;}#mermaid-svg-tj5FxsjQOBEbuNS1 .marker.cross{stroke:#333333;}#mermaid-svg-tj5FxsjQOBEbuNS1 svg{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-tj5FxsjQOBEbuNS1 p{margin:0;}#mermaid-svg-tj5FxsjQOBEbuNS1 .label{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;color:#333;}#mermaid-svg-tj5FxsjQOBEbuNS1 .cluster-label text{fill:#333;}#mermaid-svg-tj5FxsjQOBEbuNS1 .cluster-label span{color:#333;}#mermaid-svg-tj5FxsjQOBEbuNS1 .cluster-label span p{background-color:transparent;}#mermaid-svg-tj5FxsjQOBEbuNS1 .label text,#mermaid-svg-tj5FxsjQOBEbuNS1 span{fill:#333;color:#333;}#mermaid-svg-tj5FxsjQOBEbuNS1 .node rect,#mermaid-svg-tj5FxsjQOBEbuNS1 .node circle,#mermaid-svg-tj5FxsjQOBEbuNS1 .node ellipse,#mermaid-svg-tj5FxsjQOBEbuNS1 .node polygon,#mermaid-svg-tj5FxsjQOBEbuNS1 .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-tj5FxsjQOBEbuNS1 .rough-node .label text,#mermaid-svg-tj5FxsjQOBEbuNS1 .node .label text,#mermaid-svg-tj5FxsjQOBEbuNS1 .image-shape .label,#mermaid-svg-tj5FxsjQOBEbuNS1 .icon-shape .label{text-anchor:middle;}#mermaid-svg-tj5FxsjQOBEbuNS1 .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-tj5FxsjQOBEbuNS1 .rough-node .label,#mermaid-svg-tj5FxsjQOBEbuNS1 .node .label,#mermaid-svg-tj5FxsjQOBEbuNS1 .image-shape .label,#mermaid-svg-tj5FxsjQOBEbuNS1 .icon-shape .label{text-align:center;}#mermaid-svg-tj5FxsjQOBEbuNS1 .node.clickable{cursor:pointer;}#mermaid-svg-tj5FxsjQOBEbuNS1 .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-tj5FxsjQOBEbuNS1 .arrowheadPath{fill:#333333;}#mermaid-svg-tj5FxsjQOBEbuNS1 .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-tj5FxsjQOBEbuNS1 .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-tj5FxsjQOBEbuNS1 .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-tj5FxsjQOBEbuNS1 .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-tj5FxsjQOBEbuNS1 .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-tj5FxsjQOBEbuNS1 .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-tj5FxsjQOBEbuNS1 .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-tj5FxsjQOBEbuNS1 .cluster text{fill:#333;}#mermaid-svg-tj5FxsjQOBEbuNS1 .cluster span{color:#333;}#mermaid-svg-tj5FxsjQOBEbuNS1 div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-tj5FxsjQOBEbuNS1 .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-tj5FxsjQOBEbuNS1 rect.text{fill:none;stroke-width:0;}#mermaid-svg-tj5FxsjQOBEbuNS1 .icon-shape,#mermaid-svg-tj5FxsjQOBEbuNS1 .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-tj5FxsjQOBEbuNS1 .icon-shape p,#mermaid-svg-tj5FxsjQOBEbuNS1 .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-tj5FxsjQOBEbuNS1 .icon-shape rect,#mermaid-svg-tj5FxsjQOBEbuNS1 .image-shape rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-tj5FxsjQOBEbuNS1 .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-tj5FxsjQOBEbuNS1 .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-tj5FxsjQOBEbuNS1 :root{–mermaid-font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;}<\/p>\n

                \u9519\u8bef\u5b9a\u4f4d<\/p>\n

                <\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u5931\u8d25\u8f68\u8ff9<\/p>\n

                <\/span><\/p>\n

                \u4e8c\u5206\u641c\u7d22<\/p>\n

                <\/span><\/p>\n

                PRM\u8bc4\u5206<\/p>\n

                <\/span><\/p>\n

                \u5b9a\u4f4d\u9996\u4e2a\u9519\u8bef<\/p>\n

                <\/span><\/p>\n

                \u56de\u6eaf\u4fee\u6b63<\/p>\n

                <\/span><\/p>\n

                PRM\u8bad\u7ec3\u6d41\u7a0b<\/p>\n

                <\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u91c7\u6837\u8f68\u8ff9<\/p>\n

                <\/span><\/p>\n

                PRM\u8bc4\u4f30\u6b65\u9aa4<\/p>\n

                <\/span><\/p>\n

                \u751f\u6210\u8fc7\u7a0b\u5956\u52b1<\/p>\n

                <\/span><\/p>\n

                \u7b56\u7565\u66f4\u65b0PPO\/GRPO<\/p>\n

                <\/span><\/p>\n

                \u65b0\u8f68\u8ff9\u91c7\u6837<\/p>\n

                <\/span><\/p>\n

                \u66f4\u65b0PRM<\/p>\n

                <\/span><\/p>\n

                5 \u591a\u667a\u80fd\u4f53\u534f\u4f5c\u4e0e\u81ea\u6211\u5bf9\u5f08：\u5206\u5e03\u5f0f\u8fdb\u5316\u673a\u5236<\/h2>\n

                5.1 \u591a\u667a\u80fd\u4f53\u7cfb\u7edf\u7684\u535a\u5f08\u8bba\u57fa\u7840<\/h3>\n

                5.1.1 \u7eb3\u4ec0\u5747\u8861\u4e0e\u7b56\u7565\u7a33\u5b9a\u6027<\/h4>\n

                \u591a\u667a\u80fd\u4f53\u7cfb\u7edf（Multi-Agent System, MAS）\u7684\u7814\u7a76\u4e3a\u7406\u89e3Agent\u95f4\u7684\u4ea4\u4e92\u63d0\u4f9b\u4e86\u535a\u5f08\u8bba\u6846\u67b6\u3002\u5728MAS\u4e2d，\u6bcf\u4e2aAgent\u90fd\u662f\u7406\u6027\u7684\u51b3\u7b56\u8005，\u5176\u6536\u76ca\u4e0d\u4ec5\u53d6\u51b3\u4e8e\u81ea\u8eab\u7b56\u7565，\u8fd8\u53d7\u5176\u4ed6Agent\u7b56\u7565\u7684\u5f71\u54cd[56]\u3002<\/p>\n

                \u5f62\u5f0f\u5316\u5730，NN<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u4e2aAgent\u7684\u535a\u5f08\u53ef\u4ee5\u8868\u793a\u4e3a G=(N,{Ai}i\u2208N,{ui}i\u2208N)G = (\\\\mathcal{N}, \\\\{\\\\mathcal{A}_i\\\\}_{i \\\\in \\\\mathcal{N}}, \\\\{u_i\\\\}_{i \\\\in \\\\mathcal{N}})<\/span><\/span>G<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>N<\/span>,<\/span><\/span>{<\/span>A<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>}<\/span><\/span>i<\/span>\u2208<\/span>N<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>{<\/span>u<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>}<\/span><\/span>i<\/span>\u2208<\/span>N<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>，\u5176\u4e2d N={1,2,…,N}\\\\mathcal{N} = \\\\{1, 2, …, N\\\\}<\/span><\/span>N<\/span><\/span>=<\/span><\/span><\/span><\/span>{<\/span>1<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>N<\/span>}<\/span><\/span><\/span><\/span><\/span> \u4e3aAgent\u96c6\u5408，Ai\\\\mathcal{A}_i<\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3aAgent ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u7684\u52a8\u4f5c\u7a7a\u95f4，ui:A1\u00d7…\u00d7AN\u2192Ru_i: \\\\mathcal{A}_1 \\\\times … \\\\times \\\\mathcal{A}_N \\\\rightarrow \\\\mathbb{R}<\/span><\/span>u<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>:<\/span><\/span><\/span><\/span>A<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>…<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>A<\/span><\/span>N<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2192<\/span><\/span><\/span><\/span>R<\/span><\/span><\/span><\/span><\/span> \u4e3aAgent ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u7684\u6548\u7528\u51fd\u6570\u3002<\/p>\n

                \u7eb3\u4ec0\u5747\u8861（Nash Equilibrium）\u662f\u535a\u5f08\u8bba\u7684\u6838\u5fc3\u89e3\u6982\u5ff5\u3002\u7b56\u7565\u7ec4\u5408 \u03c3\u2217=(\u03c31\u2217,…,\u03c3N\u2217)\\\\sigma^* = (\\\\sigma_1^*, …, \\\\sigma_N^*)<\/span><\/span>\u03c3<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>\u03c3<\/span><\/span>1<\/span><\/span><\/span><\/span>\u2217<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>\u03c3<\/span><\/span>N<\/span><\/span><\/span><\/span>\u2217<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u662f\u7eb3\u4ec0\u5747\u8861，\u5982\u679c\u5bf9\u4e8e\u6bcf\u4e2aAgent ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>，\u6ee1\u8db3[42]：<\/p>\n

                ui(\u03c3i\u2217,\u03c3\u2212i\u2217)\u2265ui(\u03c3i\u2032,\u03c3\u2212i\u2217),\u2200\u03c3i\u2032\u2208\u0394(Ai)u_i(\\\\sigma_i^*, \\\\sigma_{-i}^*) \\\\geq u_i(\\\\sigma_i', \\\\sigma_{-i}^*), \\\\quad \\\\forall \\\\sigma_i' \\\\in \\\\Delta(\\\\mathcal{A}_i)<\/span><\/span>u<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c3<\/span><\/span>i<\/span><\/span><\/span><\/span>\u2217<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u03c3<\/span><\/span>\u2212<\/span>i<\/span><\/span><\/span><\/span><\/span>\u2217<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>u<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c3<\/span><\/span>i<\/span><\/span><\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u03c3<\/span><\/span>\u2212<\/span>i<\/span><\/span><\/span><\/span><\/span>\u2217<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>,<\/span><\/span><\/span>\u2200<\/span>\u03c3<\/span><\/span>i<\/span><\/span><\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2208<\/span><\/span><\/span><\/span>\u0394<\/span>(<\/span>A<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u5176\u4e2d \u03c3\u2212i\u2217\\\\sigma_{-i}^*<\/span><\/span>\u03c3<\/span><\/span>\u2212<\/span>i<\/span><\/span><\/span><\/span><\/span>\u2217<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u9664Agent ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u5916\u5176\u4ed6Agent\u7684\u5747\u8861\u7b56\u7565\u3002\u7eb3\u4ec0\u5747\u8861\u7684\u76f4\u89c2\u542b\u4e49\u662f：\u5728\u5747\u8861\u72b6\u6001\u4e0b，\u4efb\u4f55Agent\u5355\u65b9\u9762\u6539\u53d8\u7b56\u7565\u90fd\u65e0\u6cd5\u83b7\u5f97\u66f4\u9ad8\u6536\u76ca\u3002<\/p>\n

                \u5728Agent\u5de5\u4f5c\u6d41\u573a\u666f\u4e2d，\u7eb3\u4ec0\u5747\u8861\u5bf9\u5e94\u4e8e\u7a33\u5b9a\u7684\u591aAgent\u534f\u4f5c\u6a21\u5f0f\u3002\u5f53\u6240\u6709Agent\u90fd\u91c7\u7528\u5747\u8861\u7b56\u7565\u65f6，\u7cfb\u7edf\u8fbe\u5230\u81ea\u6d3d\u72b6\u6001，\u6ca1\u6709Agent\u6709\u52a8\u529b\u504f\u79bb\u5f53\u524d\u884c\u4e3a\u6a21\u5f0f[66]\u3002<\/p>\n

                5.1.2 \u96f6\u548c\u535a\u5f08\u4e0e\u5bf9\u6297\u8bad\u7ec3<\/h4>\n

                \u96f6\u548c\u535a\u5f08（Zero-Sum Game）\u662f\u4e00\u7c7b\u7279\u6b8a\u7684\u535a\u5f08，\u5176\u4e2d\u4e00\u4e2aAgent\u7684\u6536\u76ca\u7b49\u4e8e\u5176\u4ed6Agent\u7684\u635f\u5931\u4e4b\u548c\u3002\u5f62\u5f0f\u5316\u5730，\u5bf9\u4e8e\u4e24\u4e2aAgent\u7684\u96f6\u548c\u535a\u5f08，\u6ee1\u8db3 u1(a1,a2)+u2(a1,a2)=0u_1(a_1, a_2) + u_2(a_1, a_2) = 0<\/span><\/span>u<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>u<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>[61]\u3002<\/p>\n

                \u96f6\u548c\u535a\u5f08\u7684\u6c42\u89e3\u76ee\u6807\u662f\u627e\u5230\u6781\u5927\u6781\u5c0f\u7b56\u7565（Maximin Strategy）：<\/p>\n

                \u03c31\u2217=arg\u2061max\u2061\u03c31min\u2061\u03c32u1(\u03c31,\u03c32)\\\\sigma_1^* = \\\\arg\\\\max_{\\\\sigma_1} \\\\min_{\\\\sigma_2} u_1(\\\\sigma_1, \\\\sigma_2)<\/span><\/span>\u03c3<\/span><\/span>1<\/span><\/span><\/span><\/span>\u2217<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>arg<\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>max<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>min<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>u<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c3<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u6839\u636e\u6781\u5c0f\u6781\u5927\u5b9a\u7406（Minimax Theorem），\u5728\u96f6\u548c\u535a\u5f08\u4e2d\u6781\u5927\u6781\u5c0f\u503c\u7b49\u4e8e\u6781\u5c0f\u6781\u5927\u503c，\u5373：<\/p>\n

                max\u2061\u03c31min\u2061\u03c32u1(\u03c31,\u03c32)=min\u2061\u03c32max\u2061\u03c31u1(\u03c31,\u03c32)\\\\max_{\\\\sigma_1} \\\\min_{\\\\sigma_2} u_1(\\\\sigma_1, \\\\sigma_2) = \\\\min_{\\\\sigma_2} \\\\max_{\\\\sigma_1} u_1(\\\\sigma_1, \\\\sigma_2)<\/span><\/span><\/span>\u03c3<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>max<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>min<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>u<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c3<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>min<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>max<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>u<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c3<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u5bf9\u6297\u8bad\u7ec3（Adversarial Training）\u5229\u7528\u96f6\u548c\u535a\u5f08\u6846\u67b6\u63d0\u5347Agent\u7684\u9c81\u68d2\u6027\u3002\u901a\u8fc7\u8ba9Agent\u4e0e\u5bf9\u6297\u6027\u5bf9\u624b\u535a\u5f08，Agent\u5b66\u4f1a\u5e94\u5bf9\u6700\u574f\u60c5\u51b5，\u4ece\u800c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u8868\u73b0\u66f4\u7a33\u5b9a\u3002\u5728\u81ea\u6211\u8fdb\u5316\u573a\u666f\u4e2d，\u53ef\u4ee5\u5c06\u8fc7\u53bb\u7684\u81ea\u5df1\u4f5c\u4e3a\u5bf9\u624b，\u901a\u8fc7\u81ea\u6211\u5bf9\u5f08（Self-Play）\u5b9e\u73b0\u6301\u7eed\u6539\u8fdb[62]\u3002<\/p>\n

                5.1.3 \u5408\u4f5c\u535a\u5f08\u4e0e\u8054\u76df\u5f62\u6210<\/h4>\n

                \u4e0e\u96f6\u548c\u535a\u5f08\u4e0d\u540c，\u5408\u4f5c\u535a\u5f08（Cooperative Game）\u5141\u8bb8\u591a\u4e2aAgent\u901a\u8fc7\u534f\u4f5c\u5b9e\u73b0\u5171\u8d62\u3002\u5728Agent\u5de5\u4f5c\u6d41\u4e2d，\u4e0d\u540cAgent\u901a\u5e38\u626e\u6f14\u4e0d\u540c\u89d2\u8272（\u5982\u89c4\u5212\u8005\u3001\u6267\u884c\u8005\u3001\u9a8c\u8bc1\u8005），\u901a\u8fc7\u534f\u4f5c\u5b8c\u6210\u590d\u6742\u4efb\u52a1[16]\u3002<\/p>\n

                \u5408\u4f5c\u535a\u5f08\u7684\u6838\u5fc3\u95ee\u9898\u662f\u8054\u76df\u5f62\u6210（Coalition Formation）\u548c\u6536\u76ca\u5206\u914d（Payoff Allocation）\u3002\u8bbe S\u2286NS \\\\subseteq \\\\mathcal{N}<\/span><\/span>S<\/span><\/span>\u2286<\/span><\/span><\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u4e3a\u4e00\u4e2a\u8054\u76df，v(S)v(S)<\/span><\/span>v<\/span>(<\/span>S<\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u8054\u76df SS<\/span><\/span>S<\/span><\/span><\/span><\/span><\/span> \u80fd\u591f\u83b7\u5f97\u7684\u96c6\u4f53\u6536\u76ca\u3002\u7279\u5f81\u51fd\u6570（Characteristic Function）v:2N\u2192Rv: 2^{\\\\mathcal{N}} \\\\rightarrow \\\\mathbb{R}<\/span><\/span>v<\/span><\/span>:<\/span><\/span><\/span><\/span>2<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2192<\/span><\/span><\/span><\/span>R<\/span><\/span><\/span><\/span><\/span> \u5b9a\u4e49\u4e86\u6240\u6709\u53ef\u80fd\u8054\u76df\u7684\u6536\u76ca\u3002<\/p>\n

                \u590f\u666e\u5229\u503c（Shapley Value）\u662f\u5408\u4f5c\u535a\u5f08\u4e2d\u516c\u5e73\u5206\u914d\u6536\u76ca\u7684\u7ecf\u5178\u65b9\u6cd5\u3002Agent ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u7684\u590f\u666e\u5229\u503c\u4e3a[56]：<\/p>\n

                \u03d5i(v)=\u2211S\u2286N\u2216{i}\u2223S\u2223!(N\u2212\u2223S\u2223\u22121)!N![v(S\u222a{i})\u2212v(S)]\\\\phi_i(v) = \\\\sum_{S \\\\subseteq \\\\mathcal{N} \\\\setminus \\\\{i\\\\}} \\\\frac{|S|!(N-|S|-1)!}{N!} [v(S \\\\cup \\\\{i\\\\}) – v(S)]<\/span><\/span>\u03d5<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>v<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>S<\/span>\u2286<\/span>N<\/span>\u2216<\/span>{<\/span>i<\/span>}<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span>!<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>S<\/span>\u2223<\/span>!<\/span>(<\/span>N<\/span><\/span>\u2212<\/span><\/span>\u2223<\/span>S<\/span>\u2223<\/span><\/span>\u2212<\/span><\/span>1<\/span>)!<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>v<\/span>(<\/span>S<\/span><\/span>\u222a<\/span><\/span><\/span><\/span>{<\/span>i<\/span>})<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>v<\/span>(<\/span>S<\/span>)]<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u590f\u666e\u5229\u503c\u6ee1\u8db3\u6548\u7387\u6027\u3001\u5bf9\u79f0\u6027\u3001\u54d1\u5143\u6027\u548c\u53ef\u52a0\u6027\u56db\u4e2a\u516c\u7406，\u88ab\u8ba4\u4e3a\u662f\u516c\u5e73\u5206\u914d\u7684\u9ec4\u91d1\u6807\u51c6\u3002\u5728\u591aAgent\u5de5\u4f5c\u6d41\u4e2d，\u590f\u666e\u5229\u503c\u53ef\u4ee5\u7528\u4e8e\u8bc4\u4f30\u5404Agent\u5bf9\u4efb\u52a1\u5b8c\u6210\u7684\u8fb9\u9645\u8d21\u732e，\u6307\u5bfc\u89d2\u8272\u5206\u914d\u548c\u6fc0\u52b1\u673a\u5236\u8bbe\u8ba1[42]\u3002<\/p>\n

                5.2 \u591a\u667a\u80fd\u4f53\u5f3a\u5316\u5b66\u4e60\u6846\u67b6<\/h3>\n

                5.2.1 \u72ec\u7acb\u5b66\u4e60\u4e0e\u8054\u5408\u5b66\u4e60\u7684\u6743\u8861<\/h4>\n

                \u591a\u667a\u80fd\u4f53\u5f3a\u5316\u5b66\u4e60（Multi-Agent Reinforcement Learning, MARL）\u9762\u4e34\u72ec\u7acb\u5b66\u4e60（Independent Learning）\u4e0e\u8054\u5408\u5b66\u4e60（Joint Learning）\u7684\u6743\u8861\u3002\u72ec\u7acb\u5b66\u4e60\u4e2d\u6bcf\u4e2aAgent\u5c06\u5176\u4ed6Agent\u89c6\u4e3a\u73af\u5883\u7684\u4e00\u90e8\u5206，\u72ec\u7acb\u8fd0\u884c\u5355Agent RL\u7b97\u6cd5；\u8054\u5408\u5b66\u4e60\u5219\u5c06\u591aAgent\u7cfb\u7edf\u5efa\u6a21\u4e3a\u8054\u5408MDP，\u5b66\u4e60\u5168\u5c40\u6700\u4f18\u7b56\u7565[66]\u3002<\/p>\n

                \u72ec\u7acb\u5b66\u4e60\u7684\u4f18\u70b9\u662f\u8ba1\u7b97\u590d\u6742\u5ea6\u4f4e，\u6bcf\u4e2aAgent\u53ea\u9700\u7ef4\u62a4\u81ea\u8eab\u7b56\u7565；\u7f3a\u70b9\u662f\u975e\u5e73\u7a33\u6027（Non-Stationarity）\u95ee\u9898\u2014\u2014\u4ece\u5355\u4e2aAgent\u89c6\u89d2，\u73af\u5883\u52a8\u6001\u56e0\u5176\u4ed6Agent\u7b56\u7565\u53d8\u5316\u800c\u6539\u53d8，\u8fdd\u53cd\u4e86MDP\u7684\u5e73\u7a33\u6027\u5047\u8bbe\u3002<\/p>\n

                \u8054\u5408\u5b66\u4e60\u7406\u8bba\u4e0a\u53ef\u4ee5\u627e\u5230\u5168\u5c40\u6700\u4f18，\u4f46\u9762\u4e34\u7ef4\u5ea6\u707e\u96be：\u8054\u5408\u52a8\u4f5c\u7a7a\u95f4\u968fAgent\u6570\u91cf\u6307\u6570\u589e\u957f，\u2223Ajoint\u2223=\u220fi=1N\u2223Ai\u2223|\\\\mathcal{A}_{joint}| = \\\\prod_{i=1}^N |\\\\mathcal{A}_i|<\/span><\/span>\u2223<\/span>A<\/span><\/span>j<\/span>o<\/span>in<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span>=<\/span><\/span><\/span><\/span>\u220f<\/span><\/span>i<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>N<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>A<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span><\/span><\/span><\/span>\u3002\u5bf9\u4e8e\u5927\u89c4\u6a21\u7cfb\u7edf，\u8054\u5408\u5b66\u4e60\u4e0d\u53ef\u884c\u3002<\/p>\n

                \u5b9e\u8df5\u4e2d\u5e38\u7528\u7684\u6298\u8877\u65b9\u6848\u662f\u96c6\u4e2d\u5f0f\u8bad\u7ec3\u5206\u5e03\u5f0f\u6267\u884c（Centralized Training with Decentralized Execution, CTDE）\u3002\u5728\u8bad\u7ec3\u9636\u6bb5，\u4f7f\u7528\u5168\u5c40\u4fe1\u606f\u5b66\u4e60\u7b56\u7565；\u5728\u6267\u884c\u9636\u6bb5，\u6bcf\u4e2aAgent\u4ec5\u57fa\u4e8e\u5c40\u90e8\u89c2\u6d4b\u51b3\u7b56\u3002\u8fd9\u79cd\u67b6\u6784\u65e2\u5229\u7528\u4e86\u5168\u5c40\u4fe1\u606f\u63d0\u5347\u8bad\u7ec3\u6548\u7387，\u53c8\u4fdd\u6301\u4e86\u6267\u884c\u7684\u5206\u5e03\u5f0f\u7279\u6027[61]\u3002<\/p>\n

                5.2.2 \u503c\u5206\u89e3\u4e0eQMIX\u7b97\u6cd5<\/h4>\n

                \u503c\u5206\u89e3（Value Decomposition）\u662fCTDE\u67b6\u6784\u4e0b\u7684\u91cd\u8981\u6280\u672f，\u5b83\u5c06\u8054\u5408Q\u51fd\u6570\u5206\u89e3\u4e3a\u5404Agent Q\u51fd\u6570\u7684\u7ec4\u5408，\u4f7f\u5f97\u6bcf\u4e2aAgent\u53ef\u4ee5\u72ec\u7acb\u51b3\u7b56\u540c\u65f6\u4fdd\u8bc1\u5168\u5c40\u4e00\u81f4\u6027[62]\u3002<\/p>\n

                QMIX\u7b97\u6cd5\u662f\u503c\u5206\u89e3\u7684\u4ee3\u8868\u6027\u65b9\u6cd5\u3002\u5b83\u5047\u8bbe\u8054\u5408Q\u51fd\u6570\u53ef\u4ee5\u8868\u793a\u4e3a\u5404Agent Q\u51fd\u6570\u7684\u975e\u7ebf\u6027\u7ec4\u5408：<\/p>\n

                Qjoint(s,a)=f(Q1(s,a1),Q2(s,a2),…,QN(s,aN);s)Q_{joint}(s, \\\\mathbf{a}) = f(Q_1(s, a_1), Q_2(s, a_2), …, Q_N(s, a_N); s)<\/span><\/span>Q<\/span><\/span>j<\/span>o<\/span>in<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>f<\/span>(<\/span>Q<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>,<\/span><\/span>Q<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>Q<\/span><\/span>N<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span><\/span>N<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>;<\/span><\/span>s<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u5176\u4e2d ff<\/span><\/span>f<\/span><\/span><\/span><\/span><\/span> \u4e3a\u6df7\u5408\u7f51\u7edc，a=(a1,…,aN)\\\\mathbf{a} = (a_1, …, a_N)<\/span><\/span>a<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>a<\/span><\/span>N<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u8054\u5408\u52a8\u4f5c\u3002\u4e3a\u4fdd\u8bc1\u5206\u5e03\u5f0f\u6267\u884c\u7684\u6700\u4f18\u6027，ff<\/span><\/span>f<\/span><\/span><\/span><\/span><\/span> \u9700\u8981\u6ee1\u8db3\u5355\u8c03\u6027\u7ea6\u675f：<\/p>\n

                \u2202Qjoint\u2202Qi\u22650,\u2200i\\\\frac{\\\\partial Q_{joint}}{\\\\partial Q_i} \\\\geq 0, \\\\quad \\\\forall i<\/span><\/span><\/span><\/span>\u2202<\/span>Q<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>Q<\/span><\/span>j<\/span>o<\/span>in<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2265<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span><\/span>\u2200<\/span>i<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u8be5\u7ea6\u675f\u786e\u4fdd\u5355\u4e2aAgent\u6700\u5927\u5316\u81ea\u8eabQ\u51fd\u6570\u4e5f\u6700\u5927\u5316\u8054\u5408Q\u51fd\u6570\u3002QMIX\u4f7f\u7528\u8d85\u7f51\u7edc（Hypernetwork）\u751f\u6210\u6df7\u5408\u7f51\u7edc\u7684\u6743\u91cd，\u4ee5\u72b6\u6001\u4e3a\u6761\u4ef6\u5b9e\u73b0\u7075\u6d3b\u7684\u975e\u7ebf\u6027\u7ec4\u5408[16]\u3002<\/p>\n

                5.2.3 \u901a\u4fe1\u534f\u8bae\u4e0e\u4fe1\u606f\u5171\u4eab<\/h4>\n

                \u6709\u6548\u7684\u901a\u4fe1\u662f\u591aAgent\u534f\u4f5c\u7684\u5173\u952e\u3002\u5728\u90e8\u5206\u53ef\u89c2\u6d4b\u73af\u5883\u4e2d，Agent\u9700\u8981\u901a\u8fc7\u901a\u4fe1\u5171\u4eab\u4fe1\u606f，\u5f25\u8865\u5c40\u90e8\u89c2\u6d4b\u7684\u4e0d\u8db3\u3002\u901a\u4fe1\u534f\u8bae\u7684\u8bbe\u8ba1\u9700\u8981\u5728\u4fe1\u606f\u4e30\u5bcc\u6027\u548c\u901a\u4fe1\u5f00\u9500\u4e4b\u95f4\u53d6\u5f97\u5e73\u8861[56]\u3002<\/p>\n

                \u901a\u4fe1\u5185\u5bb9\u53ef\u4ee5\u5206\u4e3a\u4ee5\u4e0b\u51e0\u7c7b：<\/p>\n

                  \n
                • \u89c2\u6d4b\u5171\u4eab：Agent\u5206\u4eab\u5c40\u90e8\u89c2\u6d4b，\u6269\u5927\u5176\u4ed6Agent\u7684\u4fe1\u606f\u8303\u56f4<\/li>\n
                • \u610f\u56fe\u5e7f\u64ad：Agent\u5ba3\u5e03\u5373\u5c06\u6267\u884c\u7684\u52a8\u4f5c，\u4fbf\u4e8e\u534f\u8c03\u907f\u514d\u51b2\u7a81<\/li>\n
                • \u8bf7\u6c42-\u54cd\u5e94：Agent\u4e3b\u52a8\u8bf7\u6c42\u7279\u5b9a\u4fe1\u606f，\u5176\u4ed6Agent\u54cd\u5e94<\/li>\n
                • \u5171\u8bc6\u8fbe\u6210：Agent\u901a\u8fc7\u591a\u8f6e\u901a\u4fe1\u5c31\u5171\u540c\u8ba1\u5212\u8fbe\u6210\u4e00\u81f4<\/li>\n<\/ul>\n

                  TarMAC（Targeted Multi-Agent Communication）\u7b97\u6cd5\u5f15\u5165\u4e86\u6ce8\u610f\u529b\u673a\u5236\u6307\u5bfc\u901a\u4fe1\u3002\u6bcf\u4e2aAgent\u8ba1\u7b97\u5bf9\u5176\u4ed6Agent\u7684\u6ce8\u610f\u529b\u6743\u91cd，\u4ec5\u4e0e\u6ce8\u610f\u529b\u9ad8\u7684Agent\u901a\u4fe1，\u6709\u6548\u964d\u4f4e\u4e86\u901a\u4fe1\u5f00\u9500[42]\u3002<\/p>\n

                  \u5728Agent\u5de5\u4f5c\u6d41\u573a\u666f\u4e2d，\u901a\u4fe1\u534f\u8bae\u7684\u8bbe\u8ba1\u5c24\u4e3a\u91cd\u8981\u3002\u4e0d\u540cAgent\u53ef\u80fd\u8d1f\u8d23\u5de5\u4f5c\u6d41\u7684\u4e0d\u540c\u9636\u6bb5（\u5982\u4fe1\u606f\u6536\u96c6\u3001\u5206\u6790\u63a8\u7406\u3001\u7ed3\u679c\u9a8c\u8bc1），\u901a\u8fc7\u6807\u51c6\u5316\u901a\u4fe1\u534f\u8bae，\u53ef\u4ee5\u5b9e\u73b0\u65e0\u7f1d\u7684\u4efb\u52a1\u4ea4\u63a5\u548c\u72b6\u6001\u540c\u6b65[66]\u3002<\/p>\n

                  5.3 \u81ea\u6211\u5bf9\u5f08\u4e0e\u81ea\u52a8\u8bfe\u7a0b\u5b66\u4e60<\/h3>\n

                  5.3.1 \u81ea\u6211\u5bf9\u5f08\u7684\u7406\u8bba\u57fa\u7840<\/h4>\n

                  \u81ea\u6211\u5bf9\u5f08（Self-Play）\u662f\u4e00\u79cd\u5f3a\u5927\u7684\u591aAgent\u8bad\u7ec3\u8303\u5f0f，Agent\u901a\u8fc7\u4e0e\u81ea\u8eab\u5386\u53f2\u7248\u672c\u535a\u5f08\u6765\u5b66\u4e60\u3002\u8fd9\u79cd\u65b9\u6cd5\u6700\u65e9\u5728\u535a\u5f08\u8bba\u4e2d\u63d0\u51fa，\u8fd1\u5e74\u6765\u5728AlphaGo\u3001OpenAI Five\u7b49\u7cfb\u7edf\u4e2d\u5c55\u73b0\u51fa\u60ca\u4eba\u6548\u679c[61]\u3002<\/p>\n

                  \u81ea\u6211\u5bf9\u5f08\u7684\u6838\u5fc3\u4f18\u52bf\u5728\u4e8e\u81ea\u52a8\u751f\u6210\u9002\u5e94Agent\u5f53\u524d\u6c34\u5e73\u7684\u5bf9\u624b\u3002\u5f53Agent\u8f83\u5f31\u65f6，\u5386\u53f2\u7248\u672c\u4e5f\u8f83\u5f31，Agent\u5bb9\u6613\u83b7\u80dc\u83b7\u5f97\u6b63\u53cd\u9988；\u968f\u7740Agent\u53d8\u5f3a，\u5386\u53f2\u7248\u672c\u4e5f\u53d8\u5f3a，\u63d0\u4f9b\u9002\u5ea6\u6311\u6218\u4fc3\u8fdb\u8fdb\u4e00\u6b65\u5b66\u4e60\u3002\u8fd9\u79cd\u81ea\u52a8\u8c03\u6574\u7684\u96be\u5ea6\u66f2\u7ebf\u7c7b\u4f3c\u4e8e\u8bfe\u7a0b\u5b66\u4e60（Curriculum Learning）[62]\u3002<\/p>\n

                  \u865a\u6784\u81ea\u6211\u5bf9\u5f08（Fictitious Self-Play, FSP）\u662f\u4e00\u79cd\u7406\u8bba\u4e0a\u6709\u4fdd\u8bc1\u7684\u81ea\u6211\u5bf9\u5f08\u53d8\u4f53\u3002\u5728FSP\u4e2d，Agent\u4e0d\u662f\u4e0e\u5355\u4e00\u5386\u53f2\u7248\u672c\u535a\u5f08，\u800c\u662f\u4e0e\u5386\u53f2\u7b56\u7565\u7684\u6df7\u5408\u5206\u5e03\u535a\u5f08\u3002\u8bbe \u03c0t\\\\pi_t<\/span><\/span>\u03c0<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u7b2c tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u8fed\u4ee3\u7684\u7b56\u7565，FSP\u7ef4\u62a4\u5e73\u5747\u7b56\u7565 \u03c0\u02c9t=1t\u2211i=1t\u03c0i\\\\bar{\\\\pi}_t = \\\\frac{1}{t} \\\\sum_{i=1}^t \\\\pi_i<\/span><\/span><\/span>\u03c0<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c0<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，Agent\u4e0e \u03c0\u02c9t\\\\bar{\\\\pi}_t<\/span><\/span><\/span>\u03c0<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u535a\u5f08\u5e76\u66f4\u65b0\u7b56\u7565\u3002\u53ef\u4ee5\u8bc1\u660e，FSP\u6536\u655b\u5230\u7eb3\u4ec0\u5747\u8861[16]\u3002<\/p>\n

                  5.3.2 \u81ea\u52a8\u8bfe\u7a0b\u751f\u6210\u4e0e\u96be\u5ea6\u8c03\u8282<\/h4>\n

                  \u81ea\u52a8\u8bfe\u7a0b\u5b66\u4e60（Automatic Curriculum Learning）\u901a\u8fc7\u52a8\u6001\u8c03\u6574\u8bad\u7ec3\u4efb\u52a1\u7684\u96be\u5ea6，\u52a0\u901f\u5b66\u4e60\u8fdb\u7a0b\u3002\u5728Agent\u5de5\u4f5c\u6d41\u4f18\u5316\u4e2d，\u8bfe\u7a0b\u53ef\u4ee5\u4f53\u73b0\u4e3a\u4efb\u52a1\u590d\u6742\u5ea6\u3001\u73af\u5883\u566a\u58f0\u3001\u5bf9\u624b\u5f3a\u5ea6\u7b49\u591a\u4e2a\u7ef4\u5ea6[56]\u3002<\/p>\n

                  WebRL\u7b97\u6cd5\u63d0\u51fa\u4e86\u57fa\u4e8e\u5931\u8d25\u6a21\u5f0f\u7684\u81ea\u52a8\u8bfe\u7a0b\u751f\u6210\u3002\u5f53Agent\u5728\u7279\u5b9a\u7c7b\u578b\u4efb\u52a1\u4e0a\u5931\u8d25\u65f6，\u7b97\u6cd5\u81ea\u52a8\u751f\u6210\u76f8\u4f3c\u4f46\u7a0d\u7b80\u5355\u7684\u53d8\u4f53\u4efb\u52a1，\u5e2e\u52a9Agent\u9010\u6b65\u638c\u63e1\u6240\u9700\u6280\u80fd\u3002\u5177\u4f53\u5730，\u8bbeAgent\u5728\u4efb\u52a1 tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u4e0a\u5931\u8d25，\u8bfe\u7a0b\u751f\u6210\u5668\u6267\u884c\u4ee5\u4e0b\u6b65\u9aa4[42]：<\/p>\n

                • \u5206\u6790\u5931\u8d25\u539f\u56e0（\u5982\u4fe1\u606f\u7f3a\u5931\u3001\u63a8\u7406\u9519\u8bef\u3001\u5de5\u5177\u4f7f\u7528\u4e0d\u5f53）<\/li>\n
                • \u9488\u5bf9\u5931\u8d25\u539f\u56e0\u751f\u6210\u7b80\u5316\u4efb\u52a1（\u5982\u63d0\u4f9b\u66f4\u591a\u63d0\u793a\u3001\u51cf\u5c11\u63a8\u7406\u6b65\u9aa4\u3001\u9650\u5236\u5de5\u5177\u9009\u62e9）<\/li>\n
                • \u5728\u7b80\u5316\u4efb\u52a1\u4e0a\u8bad\u7ec3Agent\u76f4\u81f3\u638c\u63e1<\/li>\n
                • \u9010\u6b65\u589e\u52a0\u96be\u5ea6，\u6700\u7ec8\u56de\u5230\u539f\u59cb\u4efb\u52a1<\/li>\n

                  \u8fd9\u79cd\u4ece\u6613\u5230\u96be\u7684\u6e10\u8fdb\u5b66\u4e60\u7b26\u5408\u4eba\u7c7b\u8ba4\u77e5\u89c4\u5f8b，\u663e\u8457\u63d0\u5347\u4e86\u6837\u672c\u6548\u7387\u3002<\/p>\n

                  5.3.3 \u591a\u667a\u80fd\u4f53\u534f\u4f5c\u4e2d\u7684\u89d2\u8272\u6d8c\u73b0<\/h4>\n

                  \u5728\u81ea\u6211\u5bf9\u5f08\u8fc7\u7a0b\u4e2d，\u591aAgent\u7cfb\u7edf\u53ef\u80fd\u81ea\u53d1\u6d8c\u73b0\u51fa\u89d2\u8272\u5206\u5de5（Role Emergence）\u3002\u5373\u4f7f\u6240\u6709Agent\u521d\u59cb\u65f6\u5177\u6709\u76f8\u540c\u7684\u80fd\u529b，\u7ecf\u8fc7\u5145\u5206\u8bad\u7ec3\u540e，\u4e0d\u540cAgent\u53ef\u80fd specialize \u5230\u4e0d\u540c\u7684\u5b50\u4efb\u52a1，\u5f62\u6210\u9ad8\u6548\u7684\u534f\u4f5c\u6a21\u5f0f[66]\u3002<\/p>\n

                  \u89d2\u8272\u6d8c\u73b0\u7684\u673a\u5236\u53ef\u4ee5\u901a\u8fc7\u535a\u5f08\u8bba\u89e3\u91ca\u3002\u5728\u91cd\u590d\u535a\u5f08\u4e2d，Agent\u901a\u8fc7\u8bd5\u9519\u53d1\u73b0\u67d0\u4e9b\u7b56\u7565\u7ec4\u5408\u80fd\u591f\u4ea7\u751f\u66f4\u9ad8\u6536\u76ca，\u8fd9\u4e9b\u7b56\u7565\u7ec4\u5408\u9010\u6e10\u56fa\u5316\u4e3a\u7a33\u5b9a\u7684\u89d2\u8272\u5206\u5de5\u3002\u4f8b\u5982，\u5728\u534f\u4f5c\u4efb\u52a1\u4e2d，\u4e00\u4e2aAgent\u53ef\u80fd\u81ea\u53d1\u627f\u62c5\u89c4\u5212\u8005\u89d2\u8272，\u8d1f\u8d23\u5206\u89e3\u4efb\u52a1；\u53e6\u4e00\u4e2aAgent\u627f\u62c5\u6267\u884c\u8005\u89d2\u8272，\u8d1f\u8d23\u5177\u4f53\u64cd\u4f5c[61]\u3002<\/p>\n

                  \u89d2\u8272\u6d8c\u73b0\u7684\u597d\u5904\u5305\u62ec：<\/p>\n

                    \n
                  • \u4e13\u4e1a\u5316\u4f18\u52bf：\u6bcf\u4e2aAgent\u4e13\u6ce8\u4e8e\u7279\u5b9a\u5b50\u4efb\u52a1，\u6280\u80fd\u6df1\u5ea6\u63d0\u5347<\/li>\n
                  • \u534f\u8c03\u7b80\u5316：\u660e\u786e\u7684\u89d2\u8272\u5206\u5de5\u51cf\u5c11\u4e86\u51b3\u7b56\u51b2\u7a81<\/li>\n
                  • \u53ef\u6269\u5c55\u6027：\u65b0\u589eAgent\u53ef\u4ee5\u586b\u8865\u65b0\u89d2\u8272，\u7cfb\u7edf\u80fd\u529b\u6269\u5c55<\/li>\n<\/ul>\n

                    \u5728Agent\u5de5\u4f5c\u6d41\u573a\u666f\u4e2d，\u89d2\u8272\u6d8c\u73b0\u4e3a\u81ea\u52a8\u53d1\u73b0\u6700\u4f18SOP\u63d0\u4f9b\u4e86\u65b0\u601d\u8def\u3002\u901a\u8fc7\u591aAgent\u81ea\u6211\u5bf9\u5f08，\u7cfb\u7edf\u53ef\u4ee5\u81ea\u53d1\u63a2\u7d22\u4e0d\u540c\u7684\u5de5\u4f5c\u6d41\u7ec4\u7ec7\u5f62\u5f0f，\u6700\u7ec8\u6536\u655b\u5230\u9ad8\u6548\u7684\u5206\u5de5\u534f\u4f5c\u6a21\u5f0f[62]\u3002<\/p>\n

                    #mermaid-svg-avVJ2PbQv2Sluhwu{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-avVJ2PbQv2Sluhwu .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-avVJ2PbQv2Sluhwu .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-avVJ2PbQv2Sluhwu .error-icon{fill:#552222;}#mermaid-svg-avVJ2PbQv2Sluhwu .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-avVJ2PbQv2Sluhwu .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-avVJ2PbQv2Sluhwu .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-avVJ2PbQv2Sluhwu .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-avVJ2PbQv2Sluhwu .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-avVJ2PbQv2Sluhwu .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-avVJ2PbQv2Sluhwu .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-avVJ2PbQv2Sluhwu .marker{fill:#333333;stroke:#333333;}#mermaid-svg-avVJ2PbQv2Sluhwu .marker.cross{stroke:#333333;}#mermaid-svg-avVJ2PbQv2Sluhwu svg{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-avVJ2PbQv2Sluhwu p{margin:0;}#mermaid-svg-avVJ2PbQv2Sluhwu .label{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;color:#333;}#mermaid-svg-avVJ2PbQv2Sluhwu .cluster-label text{fill:#333;}#mermaid-svg-avVJ2PbQv2Sluhwu .cluster-label span{color:#333;}#mermaid-svg-avVJ2PbQv2Sluhwu .cluster-label span p{background-color:transparent;}#mermaid-svg-avVJ2PbQv2Sluhwu .label text,#mermaid-svg-avVJ2PbQv2Sluhwu span{fill:#333;color:#333;}#mermaid-svg-avVJ2PbQv2Sluhwu .node rect,#mermaid-svg-avVJ2PbQv2Sluhwu .node circle,#mermaid-svg-avVJ2PbQv2Sluhwu .node ellipse,#mermaid-svg-avVJ2PbQv2Sluhwu .node polygon,#mermaid-svg-avVJ2PbQv2Sluhwu .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-avVJ2PbQv2Sluhwu .rough-node .label text,#mermaid-svg-avVJ2PbQv2Sluhwu .node .label text,#mermaid-svg-avVJ2PbQv2Sluhwu .image-shape .label,#mermaid-svg-avVJ2PbQv2Sluhwu .icon-shape .label{text-anchor:middle;}#mermaid-svg-avVJ2PbQv2Sluhwu .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-avVJ2PbQv2Sluhwu .rough-node .label,#mermaid-svg-avVJ2PbQv2Sluhwu .node .label,#mermaid-svg-avVJ2PbQv2Sluhwu .image-shape .label,#mermaid-svg-avVJ2PbQv2Sluhwu .icon-shape .label{text-align:center;}#mermaid-svg-avVJ2PbQv2Sluhwu .node.clickable{cursor:pointer;}#mermaid-svg-avVJ2PbQv2Sluhwu .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-avVJ2PbQv2Sluhwu .arrowheadPath{fill:#333333;}#mermaid-svg-avVJ2PbQv2Sluhwu .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-avVJ2PbQv2Sluhwu .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-avVJ2PbQv2Sluhwu .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-avVJ2PbQv2Sluhwu .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-avVJ2PbQv2Sluhwu .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-avVJ2PbQv2Sluhwu .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-avVJ2PbQv2Sluhwu .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-avVJ2PbQv2Sluhwu .cluster text{fill:#333;}#mermaid-svg-avVJ2PbQv2Sluhwu .cluster span{color:#333;}#mermaid-svg-avVJ2PbQv2Sluhwu div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-avVJ2PbQv2Sluhwu .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-avVJ2PbQv2Sluhwu rect.text{fill:none;stroke-width:0;}#mermaid-svg-avVJ2PbQv2Sluhwu .icon-shape,#mermaid-svg-avVJ2PbQv2Sluhwu .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-avVJ2PbQv2Sluhwu .icon-shape p,#mermaid-svg-avVJ2PbQv2Sluhwu .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-avVJ2PbQv2Sluhwu .icon-shape rect,#mermaid-svg-avVJ2PbQv2Sluhwu .image-shape rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-avVJ2PbQv2Sluhwu .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-avVJ2PbQv2Sluhwu .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-avVJ2PbQv2Sluhwu :root{–mermaid-font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;}<\/p>\n

                    \u81ea\u6211\u5bf9\u5f08\u8fdb\u5316<\/p>\n

                    <\/span><\/p>\n

                    \u5bf9\u5f08<\/p>\n

                    <\/span><\/p>\n

                    \u5bf9\u5f08<\/p>\n

                    <\/span><\/p>\n

                    …<\/p>\n

                    <\/span><\/p>\n

                    \u6536\u655b<\/p>\n

                    <\/span><\/p>\n

                    \u7b56\u7565v1<\/p>\n

                    <\/span><\/p>\n

                    \u7b56\u7565v2<\/p>\n

                    <\/span><\/p>\n

                    \u7b56\u7565v3<\/p>\n

                    <\/span><\/p>\n

                    \u7b56\u7565vN<\/p>\n

                    <\/span><\/p>\n

                    \u7eb3\u4ec0\u5747\u8861<\/p>\n

                    <\/span><\/p>\n

                    \u591aAgent\u534f\u4f5c\u6846\u67b6<\/p>\n

                    <\/span><\/span><\/span><\/span><\/span><\/p>\n

                    \u4efb\u52a1\u5206\u89e3<\/p>\n

                    <\/span><\/p>\n

                    \u89d2\u8272\u5206\u914d<\/p>\n

                    <\/span><\/p>\n

                    \u5e76\u884c\u6267\u884c<\/p>\n

                    <\/span><\/p>\n

                    \u7ed3\u679c\u6574\u5408<\/p>\n

                    <\/span><\/p>\n

                    \u8d28\u91cf\u9a8c\u8bc1<\/p>\n

                    <\/span><\/p>\n

                    6 \u8bb0\u5fc6\u673a\u5236\u4e0e\u5de5\u4f5c\u6d41\u4f18\u5316：\u7ecf\u9a8c\u79ef\u7d2f\u4e0e\u590d\u7528<\/h2>\n

                    6.1 \u667a\u80fd\u4f53\u8bb0\u5fc6\u7684\u7c7b\u578b\u4e0e\u7ed3\u6784<\/h3>\n

                    6.1.1 \u77ed\u671f\u8bb0\u5fc6\u4e0e\u957f\u671f\u8bb0\u5fc6\u7684\u533a\u5206<\/h4>\n

                    \u8bb0\u5fc6\u673a\u5236\u662f\u667a\u80fd\u4f53\u5b9e\u73b0\u6301\u7eed\u5b66\u4e60\u548c\u7ecf\u9a8c\u79ef\u7d2f\u7684\u57fa\u7840\u3002\u4e0e\u4eba\u7c7b\u8ba4\u77e5\u7cfb\u7edf\u7c7b\u4f3c，Agent\u8bb0\u5fc6\u53ef\u4ee5\u5206\u4e3a\u77ed\u671f\u8bb0\u5fc6（Short-Term Memory, STM）\u548c\u957f\u671f\u8bb0\u5fc6（Long-Term Memory, LTM）\u4e24\u7c7b，\u4e24\u8005\u5728\u529f\u80fd\u7279\u6027\u548c\u5b9e\u73b0\u673a\u5236\u4e0a\u5b58\u5728\u672c\u8d28\u5dee\u5f02[16]\u3002<\/p>\n

                    \u77ed\u671f\u8bb0\u5fc6\u8d1f\u8d23\u7ef4\u62a4\u5f53\u524d\u4efb\u52a1\u6267\u884c\u7684\u4e0a\u4e0b\u6587\u4fe1\u606f，\u7c7b\u4f3c\u4e8e\u4eba\u7c7b\u7684\u5de5\u4f5c\u8bb0\u5fc6（Working Memory）\u3002\u5728LLM Agent\u4e2d，\u77ed\u671f\u8bb0\u5fc6\u901a\u5e38\u901a\u8fc7\u4e0a\u4e0b\u6587\u7a97\u53e3（Context Window）\u5b9e\u73b0，\u5305\u542b\u6700\u8fd1\u7684\u5bf9\u8bdd\u5386\u53f2\u3001\u4e2d\u95f4\u63a8\u7406\u7ed3\u679c\u548c\u5de5\u5177\u8c03\u7528\u8bb0\u5f55\u3002\u77ed\u671f\u8bb0\u5fc6\u7684\u7279\u70b9\u662f\u8bbf\u95ee\u901f\u5ea6\u5feb\u3001\u5bb9\u91cf\u6709\u9650\u3001\u751f\u547d\u5468\u671f\u77ed\u2014\u2014\u968f\u7740\u4efb\u52a1\u7ed3\u675f\u6216\u4e0a\u4e0b\u6587\u91cd\u7f6e\u800c\u6e05\u7a7a[56]\u3002<\/p>\n

                    \u957f\u671f\u8bb0\u5fc6\u8d1f\u8d23\u8de8\u4efb\u52a1\u3001\u8de8\u4f1a\u8bdd\u7684\u4fe1\u606f\u6301\u4e45\u5316\u5b58\u50a8，\u4f7fAgent\u80fd\u591f\u79ef\u7d2f\u77e5\u8bc6\u3001\u5b66\u4e60\u504f\u597d\u3001\u907f\u514d\u91cd\u590d\u9519\u8bef\u3002\u957f\u671f\u8bb0\u5fc6\u7684\u5b9e\u73b0\u901a\u5e38\u4f9d\u8d56\u5916\u90e8\u5b58\u50a8\u7cfb\u7edf，\u5982\u5411\u91cf\u6570\u636e\u5e93（Vector Database）\u6216\u77e5\u8bc6\u56fe\u8c31（Knowledge Graph）\u3002\u4e0e\u77ed\u671f\u8bb0\u5fc6\u76f8\u6bd4，\u957f\u671f\u8bb0\u5fc6\u5bb9\u91cf\u5927\u3001\u751f\u547d\u5468\u671f\u957f，\u4f46\u8bbf\u95ee\u9700\u8981\u989d\u5916\u7684\u68c0\u7d22\u5f00\u9500[42]\u3002<\/p>\n

                    \u88682 \u77ed\u671f\u8bb0\u5fc6\u4e0e\u957f\u671f\u8bb0\u5fc6\u7684\u5bf9\u6bd4<\/p>\n\n\u7279\u6027\u7ef4\u5ea6\u77ed\u671f\u8bb0\u5fc6（STM）\u957f\u671f\u8bb0\u5fc6（LTM）<\/tr>\n\n\n\n\n\n\n\n\n
                    \u5b58\u50a8\u4ecb\u8d28<\/td>\n\u6a21\u578b\u4e0a\u4e0b\u6587\u7a97\u53e3<\/td>\n\u5916\u90e8\u6570\u636e\u5e93\/\u5b58\u50a8<\/td>\n<\/tr>\n
                    \u5bb9\u91cf\u9650\u5236<\/td>\n\u53d7\u9650\u4e8e\u4e0a\u4e0b\u6587\u957f\u5ea6（\u901a\u5e384K-128K tokens）<\/td>\n\u7406\u8bba\u4e0a\u65e0\u4e0a\u9650，\u53d7\u5b58\u50a8\u8d44\u6e90\u7ea6\u675f<\/td>\n<\/tr>\n
                    \u8bbf\u95ee\u5ef6\u8fdf<\/td>\n\u6781\u4f4e（\u6a21\u578b\u524d\u5411\u4f20\u64ad\u7684\u4e00\u90e8\u5206）<\/td>\n\u8f83\u9ad8（\u9700\u8981\u68c0\u7d22\u548c\u7f16\u7801）<\/td>\n<\/tr>\n
                    \u751f\u547d\u5468\u671f<\/td>\n\u5355\u4f1a\u8bdd\u5185\u6709\u6548<\/td>\n\u8de8\u4f1a\u8bdd\u6301\u4e45\u5316<\/td>\n<\/tr>\n
                    \u4fe1\u606f\u7c7b\u578b<\/td>\n\u5f53\u524d\u4efb\u52a1\u4e0a\u4e0b\u6587\u3001\u8fd1\u671f\u4ea4\u4e92<\/td>\n\u5386\u53f2\u7ecf\u9a8c\u3001\u7528\u6237\u504f\u597d\u3001\u9886\u57df\u77e5\u8bc6<\/td>\n<\/tr>\n
                    \u66f4\u65b0\u9891\u7387<\/td>\n\u5b9e\u65f6\u66f4\u65b0<\/td>\n\u5b9a\u671f\u6279\u91cf\u66f4\u65b0\u6216\u4e8b\u4ef6\u89e6\u53d1<\/td>\n<\/tr>\n
                    \u5178\u578b\u5b9e\u73b0<\/td>\nIn-context Learning<\/td>\nVector DB + Embedding Model<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                    6.1.2 \u60c5\u666f\u8bb0\u5fc6\u3001\u8bed\u4e49\u8bb0\u5fc6\u4e0e\u7a0b\u5e8f\u8bb0\u5fc6<\/h4>\n

                    \u957f\u671f\u8bb0\u5fc6\u53ef\u4ee5\u8fdb\u4e00\u6b65\u7ec6\u5206\u4e3a\u4e09\u79cd\u7c7b\u578b，\u5bf9\u5e94\u4eba\u7c7b\u8bb0\u5fc6\u7cfb\u7edf\u7684\u4e0d\u540c\u529f\u80fd[66]：<\/p>\n

                    **\u60c5\u666f\u8bb0\u5fc6（Episodic Memory）**\u5b58\u50a8\u7279\u5b9a\u4e8b\u4ef6\u548c\u7ecf\u5386，\u8bb0\u5f55Agent\u6267\u884c\u8fc7\u7684\u4efb\u52a1\u8f68\u8ff9\u3001\u9047\u5230\u7684\u56f0\u96be\u3001\u6210\u529f\u7684\u89e3\u51b3\u65b9\u6848\u7b49\u3002\u60c5\u666f\u8bb0\u5fc6\u652f\u6301\u57fa\u4e8e\u6848\u4f8b\u7684\u63a8\u7406（Case-Based Reasoning）\u2014\u2014\u5f53\u9762\u5bf9\u65b0\u4efb\u52a1\u65f6，\u68c0\u7d22\u76f8\u4f3c\u5386\u53f2\u6848\u4f8b\u5e76\u590d\u7528\u5176\u89e3\u51b3\u65b9\u6848\u3002\u5f62\u5f0f\u5316\u5730，\u60c5\u666f\u8bb0\u5fc6\u53ef\u4ee5\u8868\u793a\u4e3a\u4e8b\u4ef6\u5e8f\u5217 Mepi={(st,at,rt,ot)}t=1T\\\\mathcal{M}_{epi} = \\\\{(s_t, a_t, r_t, o_t)\\\\}_{t=1}^T<\/span><\/span>M<\/span><\/span>e<\/span>p<\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>{(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>o<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>}<\/span><\/span>t<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5176\u4e2d oto_t<\/span><\/span>o<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u6267\u884c\u89c2\u5bdf[61]\u3002<\/p>\n

                    **\u8bed\u4e49\u8bb0\u5fc6（Semantic Memory）**\u5b58\u50a8\u4e8b\u5b9e\u6027\u77e5\u8bc6\u548c\u6982\u5ff5\u5173\u7cfb，\u5982\u9886\u57df\u77e5\u8bc6\u3001\u7528\u6237\u504f\u597d\u3001\u5de5\u5177\u529f\u80fd\u63cf\u8ff0\u7b49\u3002\u8bed\u4e49\u8bb0\u5fc6\u901a\u5e38\u4ee5\u7ed3\u6784\u5316\u5f62\u5f0f\u7ec4\u7ec7，\u5982\u77e5\u8bc6\u56fe\u8c31\u6216\u952e\u503c\u5bf9\u5b58\u50a8\u3002\u4e0e\u60c5\u666f\u8bb0\u5fc6\u4e0d\u540c，\u8bed\u4e49\u8bb0\u5fc6\u62bd\u8c61\u4e86\u5177\u4f53\u7ecf\u5386，\u63d0\u53d6\u4e86\u901a\u7528\u77e5\u8bc6\u3002\u4f8b\u5982，\u4ece\u591a\u6b21"\u4f7f\u7528Python\u5904\u7406CSV\u6587\u4ef6"\u7684\u7ecf\u5386\u4e2d，Agent\u53ef\u4ee5\u62bd\u8c61\u51fa"pandas\u662f\u5904\u7406\u8868\u683c\u6570\u636e\u7684\u6709\u6548\u5de5\u5177"\u8fd9\u4e00\u8bed\u4e49\u77e5\u8bc6[62]\u3002<\/p>\n

                    **\u7a0b\u5e8f\u8bb0\u5fc6（Procedural Memory）**\u5b58\u50a8\u6280\u80fd\u548c\u64cd\u4f5c\u6d41\u7a0b，\u5373"\u5982\u4f55\u505a"\u7684\u77e5\u8bc6\u3002\u5728Agent\u5de5\u4f5c\u6d41\u573a\u666f\u4e2d，\u7a0b\u5e8f\u8bb0\u5fc6\u5bf9\u5e94\u4e8e\u5b66\u4e60\u5230\u7684SOP\u2014\u2014\u9762\u5bf9\u7279\u5b9a\u7c7b\u578b\u4efb\u52a1\u65f6\u5e94\u9075\u5faa\u7684\u64cd\u4f5c\u5e8f\u5217\u3002\u7a0b\u5e8f\u8bb0\u5fc6\u901a\u5e38\u4ee5\u6761\u4ef6-\u52a8\u4f5c\u89c4\u5219\u6216\u7b56\u7565\u7f51\u7edc\u7684\u5f62\u5f0f\u5b58\u50a8，\u652f\u6301\u5feb\u901f\u3001\u81ea\u52a8\u5316\u7684\u6267\u884c[16]\u3002<\/p>\n

                    6.1.3 \u8bb0\u5fc6\u7684\u7ec4\u7ec7\u4e0e\u7d22\u5f15\u673a\u5236<\/h4>\n

                    \u9ad8\u6548\u7684\u8bb0\u5fc6\u7ec4\u7ec7\u4e0e\u68c0\u7d22\u673a\u5236\u662f\u8bb0\u5fc6\u7cfb\u7edf\u5b9e\u7528\u6027\u7684\u5173\u952e\u3002\u5bf9\u4e8e\u5927\u89c4\u6a21\u8bb0\u5fc6\u5e93，\u7ebf\u6027\u626b\u63cf\u4e0d\u53ef\u884c，\u9700\u8981\u5efa\u7acb\u6709\u6548\u7684\u7d22\u5f15\u7ed3\u6784[56]\u3002<\/p>\n

                    \u5411\u91cf\u7d22\u5f15\u662f\u5f53\u524d\u4e3b\u6d41\u7684\u8bb0\u5fc6\u7ec4\u7ec7\u65b9\u5f0f\u3002\u6bcf\u6761\u8bb0\u5fc6\u901a\u8fc7\u5d4c\u5165\u6a21\u578b（Embedding Model）\u7f16\u7801\u4e3a\u7a20\u5bc6\u5411\u91cf，\u5b58\u50a8\u5728\u5411\u91cf\u6570\u636e\u5e93\u4e2d\u3002\u68c0\u7d22\u65f6，\u5c06\u67e5\u8be2\u7f16\u7801\u4e3a\u5411\u91cf，\u901a\u8fc7\u8fd1\u4f3c\u6700\u8fd1\u90bb（Approximate Nearest Neighbor, ANN）\u7b97\u6cd5\u5feb\u901f\u627e\u5230\u76f8\u4f3c\u8bb0\u5fc6\u3002\u5e38\u7528\u7684ANN\u7b97\u6cd5\u5305\u62ecHNSW（Hierarchical Navigable Small World）\u3001IVF（Inverted File Index）\u7b49，\u80fd\u591f\u5728\u767e\u4e07\u7ea7\u5411\u91cf\u4e2d\u5b9e\u73b0\u6beb\u79d2\u7ea7\u68c0\u7d22[42]\u3002<\/p>\n

                    \u56fe\u7d22\u5f15\u9002\u7528\u4e8e\u5177\u6709\u590d\u6742\u5173\u7cfb\u7684\u8bb0\u5fc6\u3002\u77e5\u8bc6\u56fe\u8c31\u5c06\u5b9e\u4f53\u548c\u5173\u7cfb\u8868\u793a\u4e3a\u8282\u70b9\u548c\u8fb9，\u652f\u6301\u591a\u8df3\u63a8\u7406\u548c\u5173\u7cfb\u67e5\u8be2\u3002\u4f8b\u5982，Agent\u53ef\u4ee5\u67e5\u8be2"\u4e0e\u7528\u6237A\u8ba8\u8bba\u8fc7\u7684\u6240\u6709\u4e0ePython\u76f8\u5173\u7684\u5de5\u5177"，\u8fd9\u79cd\u590d\u6742\u67e5\u8be2\u96be\u4ee5\u901a\u8fc7\u7eaf\u5411\u91cf\u68c0\u7d22\u5b9e\u73b0\u3002\u56fe\u7d22\u5f15\u7684\u6311\u6218\u5728\u4e8e\u6784\u5efa\u548c\u7ef4\u62a4\u6210\u672c\u8f83\u9ad8，\u9700\u8981\u5b9e\u4f53\u94fe\u63a5\u548c\u5173\u7cfb\u62bd\u53d6\u7b49\u9884\u5904\u7406[66]\u3002<\/p>\n

                    \u6df7\u5408\u7d22\u5f15\u7ed3\u5408\u4e86\u591a\u79cd\u7d22\u5f15\u7684\u4f18\u52bf\u3002\u4f8b\u5982，\u5148\u7528\u5411\u91cf\u68c0\u7d22\u53ec\u56de\u5019\u9009\u8bb0\u5fc6，\u518d\u7528\u56fe\u5173\u7cfb\u8fc7\u6ee4\u548c\u6392\u5e8f；\u6216\u5148\u7528\u5173\u952e\u8bcd\u7d22\u5f15\u5feb\u901f\u5b9a\u4f4d\u76f8\u5173\u8bb0\u5fc6\u5b50\u96c6，\u518d\u5728\u5b50\u96c6\u5185\u8fdb\u884c\u5411\u91cf\u76f8\u4f3c\u5ea6\u8ba1\u7b97\u3002\u6df7\u5408\u7d22\u5f15\u5728\u5b9e\u8df5\u4e2d\u5f80\u5f80\u80fd\u8fbe\u5230\u6700\u4f73\u7684\u68c0\u7d22\u6548\u679c[61]\u3002<\/p>\n

                    6.2 \u8bb0\u5fc6\u7684\u7f16\u7801\u3001\u5b58\u50a8\u4e0e\u68c0\u7d22<\/h3>\n

                    6.2.1 \u4fe1\u606f\u62bd\u53d6\u4e0e\u77e5\u8bc6\u84b8\u998f<\/h4>\n

                    \u4ece\u539f\u59cb\u4ea4\u4e92\u8bb0\u5f55\u4e2d\u63d0\u53d6\u6709\u4ef7\u503c\u7684\u8bb0\u5fc6\u4fe1\u606f\u662f\u8bb0\u5fc6\u7cfb\u7edf\u7684\u9996\u8981\u4efb\u52a1\u3002\u76f4\u63a5\u5b58\u50a8\u539f\u59cb\u6587\u672c\u4e0d\u4ec5\u6d6a\u8d39\u5b58\u50a8\u7a7a\u95f4，\u8fd8\u4f1a\u589e\u52a0\u68c0\u7d22\u566a\u58f0，\u9700\u8981\u901a\u8fc7\u4fe1\u606f\u62bd\u53d6（Information Extraction）\u63d0\u70bc\u5173\u952e\u77e5\u8bc6[62]\u3002<\/p>\n

                    \u4fe1\u606f\u62bd\u53d6\u7684\u4e3b\u8981\u4efb\u52a1\u5305\u62ec：<\/p>\n

                      \n
                    • \u5b9e\u4f53\u8bc6\u522b：\u8bc6\u522b\u6587\u672c\u4e2d\u7684\u5173\u952e\u5b9e\u4f53（\u5982\u5de5\u5177\u540d\u79f0\u3001\u6570\u636e\u683c\u5f0f\u3001\u7528\u6237\u504f\u597d）<\/li>\n
                    • \u5173\u7cfb\u62bd\u53d6：\u63d0\u53d6\u5b9e\u4f53\u4e4b\u95f4\u7684\u5173\u7cfb（\u5982"\u5de5\u5177A\u9002\u7528\u4e8e\u4efb\u52a1B"）<\/li>\n
                    • \u4e8b\u4ef6\u62bd\u53d6：\u8bc6\u522b\u91cd\u8981\u4e8b\u4ef6\u53ca\u5176\u53c2\u4e0e\u8005\u3001\u65f6\u95f4\u3001\u7ed3\u679c<\/li>\n
                    • \u6458\u8981\u751f\u6210：\u5c06\u957f\u6587\u672c\u538b\u7f29\u4e3a\u7b80\u6d01\u7684\u6458\u8981，\u4fdd\u7559\u6838\u5fc3\u4fe1\u606f<\/li>\n<\/ul>\n

                      \u5728Agent\u5de5\u4f5c\u6d41\u573a\u666f\u4e2d，\u4fe1\u606f\u62bd\u53d6\u53ef\u4ee5\u9488\u5bf9\u6027\u5730\u8bbe\u8ba1\u3002\u4f8b\u5982，\u4ece\u4e00\u6b21\u4ee3\u7801\u751f\u6210\u4efb\u52a1\u4e2d，\u53ef\u4ee5\u62bd\u53d6：\u4f7f\u7528\u7684\u7f16\u7a0b\u8bed\u8a00\u3001\u89e3\u51b3\u7684\u95ee\u9898\u7c7b\u578b\u3001\u8c03\u7528\u7684\u5e93\u51fd\u6570\u3001\u9047\u5230\u7684\u9519\u8bef\u53ca\u89e3\u51b3\u65b9\u6848\u7b49\u3002\u8fd9\u4e9b\u7ed3\u6784\u5316\u4fe1\u606f\u6bd4\u539f\u59cb\u5bf9\u8bdd\u8bb0\u5f55\u66f4\u6613\u4e8e\u68c0\u7d22\u548c\u590d\u7528[16]\u3002<\/p>\n

                      \u77e5\u8bc6\u84b8\u998f（Knowledge Distillation）\u662f\u53e6\u4e00\u79cd\u8bb0\u5fc6\u538b\u7f29\u6280\u672f\u3002\u5b83\u901a\u8fc7\u8bad\u7ec3\u4e00\u4e2a\u8f7b\u91cf\u7ea7\u6a21\u578b\u6765\u8fd1\u4f3c\u5927\u578b\u6a21\u578b\u7684\u884c\u4e3a，\u5c06\u5927\u578b\u6a21\u578b\u4e2d\u7684\u77e5\u8bc6\u8fc1\u79fb\u5230\u8f7b\u91cf\u7ea7\u6a21\u578b\u3002\u5728\u8bb0\u5fc6\u7cfb\u7edf\u4e2d，\u53ef\u4ee5\u4f7f\u7528\u77e5\u8bc6\u84b8\u998f\u8bad\u7ec3\u4e13\u95e8\u7684\u7f16\u7801\u5668，\u4f7f\u5176\u751f\u6210\u7684\u5d4c\u5165\u66f4\u597d\u5730\u6355\u6349\u8bb0\u5fc6\u7684\u5173\u952e\u7279\u5f81[56]\u3002<\/p>\n

                      6.2.2 \u5411\u91cf\u5d4c\u5165\u4e0e\u76f8\u4f3c\u5ea6\u68c0\u7d22<\/h4>\n

                      \u5411\u91cf\u5d4c\u5165（Vector Embedding）\u662f\u73b0\u4ee3\u8bb0\u5fc6\u7cfb\u7edf\u7684\u6838\u5fc3\u6280\u672f\u3002\u5b83\u5c06\u79bb\u6563\u7684\u8bb0\u5fc6\u5185\u5bb9\u6620\u5c04\u5230\u8fde\u7eed\u5411\u91cf\u7a7a\u95f4，\u4f7f\u5f97\u8bed\u4e49\u76f8\u4f3c\u7684\u8bb0\u5fc6\u5728\u5411\u91cf\u7a7a\u95f4\u4e2d\u8ddd\u79bb\u76f8\u8fd1[42]\u3002<\/p>\n

                      \u5d4c\u5165\u6a21\u578b\u901a\u5e38\u57fa\u4e8e\u9884\u8bad\u7ec3\u7684\u8bed\u8a00\u6a21\u578b（\u5982BERT\u3001Sentence-BERT），\u901a\u8fc7\u5bf9\u6bd4\u5b66\u4e60（Contrastive Learning）\u5fae\u8c03\u4ee5\u9002\u5e94\u7279\u5b9a\u9886\u57df\u7684\u8bed\u4e49\u76f8\u4f3c\u5ea6\u5224\u65ad\u3002\u5bf9\u6bd4\u5b66\u4e60\u7684\u76ee\u6807\u662f\u6700\u5c0f\u5316\u76f8\u4f3c\u6837\u672c\u95f4\u7684\u8ddd\u79bb，\u6700\u5927\u5316\u4e0d\u76f8\u4f3c\u6837\u672c\u95f4\u7684\u8ddd\u79bb：<\/p>\n

                      Lcontrastive=\u2212log\u2061exp\u2061(sim(x,x+)\/\u03c4)exp\u2061(sim(x,x+)\/\u03c4)+\u2211iexp\u2061(sim(x,xi\u2212)\/\u03c4)\\\\mathcal{L}_{contrastive} = -\\\\log \\\\frac{\\\\exp(\\\\text{sim}(x, x^+)\/\\\\tau)}{\\\\exp(\\\\text{sim}(x, x^+)\/\\\\tau) + \\\\sum_{i} \\\\exp(\\\\text{sim}(x, x_i^-)\/\\\\tau)}<\/span><\/span>L<\/span><\/span>co<\/span>n<\/span>t<\/span>r<\/span>a<\/span>s<\/span>t<\/span>i<\/span>v<\/span>e<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span>log<\/span><\/span><\/span><\/span><\/span>exp<\/span>(<\/span>sim<\/span><\/span>(<\/span>x<\/span>,<\/span><\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>\/<\/span>\u03c4<\/span>)<\/span><\/span>+<\/span><\/span>\u2211<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>exp<\/span>(<\/span>sim<\/span><\/span>(<\/span>x<\/span>,<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>\/<\/span>\u03c4<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>exp<\/span>(<\/span>sim<\/span><\/span>(<\/span>x<\/span>,<\/span><\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>\/<\/span>\u03c4<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                      \u5176\u4e2d xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u4e3a\u951a\u6837\u672c，x+x^+<\/span><\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u6b63\u6837\u672c（\u8bed\u4e49\u76f8\u4f3c），xi\u2212x_i^-<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u8d1f\u6837\u672c（\u8bed\u4e49\u4e0d\u76f8\u4f3c），sim\\\\text{sim}<\/span><\/span>sim<\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u76f8\u4f3c\u5ea6\u51fd\u6570（\u901a\u5e38\u7528\u4f59\u5f26\u76f8\u4f3c\u5ea6），\u03c4\\\\tau<\/span><\/span>\u03c4<\/span><\/span><\/span><\/span><\/span> \u4e3a\u6e29\u5ea6\u53c2\u6570[66]\u3002<\/p>\n

                      \u76f8\u4f3c\u5ea6\u68c0\u7d22\u7684\u6838\u5fc3\u662f\u6700\u8fd1\u90bb\u641c\u7d22\u3002\u7ed9\u5b9a\u67e5\u8be2\u5411\u91cf qq<\/span><\/span>q<\/span><\/span><\/span><\/span><\/span>，\u5728\u8bb0\u5fc6\u5411\u91cf\u96c6\u5408 {v1,v2,…,vN}\\\\{v_1, v_2, …, v_N\\\\}<\/span><\/span>{<\/span>v<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>v<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>v<\/span><\/span>N<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>}<\/span><\/span><\/span><\/span><\/span> \u4e2d\u627e\u5230\u6700\u76f8\u4f3c\u7684 KK<\/span><\/span>K<\/span><\/span><\/span><\/span><\/span> \u4e2a\u5411\u91cf：<\/p>\n

                      TopK(q)=arg\u2061TopKi\u2009sim(q,vi)\\\\text{TopK}(q) = \\\\arg\\\\text{TopK}_{i} \\\\, \\\\text{sim}(q, v_i)<\/span><\/span>TopK<\/span><\/span>(<\/span>q<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>arg<\/span><\/span><\/span>TopK<\/span><\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>sim<\/span><\/span>(<\/span>q<\/span>,<\/span><\/span>v<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                      \u7cbe\u786e\u6700\u8fd1\u90bb\u641c\u7d22\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(Nd)O(Nd)<\/span><\/span>O<\/span>(<\/span>N<\/span>d<\/span>)<\/span><\/span><\/span><\/span><\/span>（dd<\/span><\/span>d<\/span><\/span><\/span><\/span><\/span> \u4e3a\u5411\u91cf\u7ef4\u5ea6），\u5bf9\u4e8e\u5927\u89c4\u6a21\u8bb0\u5fc6\u5e93\u4e0d\u53ef\u884c\u3002\u8fd1\u4f3c\u6700\u8fd1\u90bb\u7b97\u6cd5\u901a\u8fc7\u727a\u7272\u5c11\u91cf\u7cbe\u5ea6\u6362\u53d6\u6570\u91cf\u7ea7\u52a0\u901f，\u5982HNSW\u7b97\u6cd5\u7684\u67e5\u8be2\u590d\u6742\u5ea6\u4ec5\u4e3a O(log\u2061N)O(\\\\log N)<\/span><\/span>O<\/span>(<\/span>log<\/span><\/span><\/span>N<\/span>)<\/span><\/span><\/span><\/span><\/span>[61]\u3002<\/p>\n

                      6.2.3 \u8bb0\u5fc6\u7684\u9057\u5fd8\u4e0e\u66f4\u65b0\u7b56\u7565<\/h4>\n

                      \u8bb0\u5fc6\u7cfb\u7edf\u9700\u8981\u5904\u7406\u4fe1\u606f\u7684\u52a8\u6001\u53d8\u5316：\u65b0\u77e5\u8bc6\u4e0d\u65ad\u4ea7\u751f，\u65e7\u77e5\u8bc6\u53ef\u80fd\u8fc7\u65f6\u3002\u6709\u6548\u7684\u9057\u5fd8（Forgetting）\u548c\u66f4\u65b0（Updating）\u7b56\u7565\u786e\u4fdd\u8bb0\u5fc6\u5e93\u4fdd\u6301\u65f6\u6548\u6027\u548c\u51c6\u786e\u6027[62]\u3002<\/p>\n

                      \u65f6\u95f4\u8870\u51cf\u662f\u6700\u7b80\u5355\u7684\u9057\u5fd8\u7b56\u7565\u3002\u6bcf\u6761\u8bb0\u5fc6\u5173\u8054\u4e00\u4e2a\u65f6\u95f4\u6233，\u68c0\u7d22\u65f6\u6839\u636e\u65f6\u95f4\u8870\u51cf\u51fd\u6570\u964d\u4f4e\u65e7\u8bb0\u5fc6\u7684\u6743\u91cd：<\/p>\n

                      w(m)=exp\u2061(\u2212\u03bb(tcurrent\u2212tm))w(m) = \\\\exp(-\\\\lambda (t_{current} – t_m))<\/span><\/span>w<\/span>(<\/span>m<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>exp<\/span>(<\/span>\u2212<\/span>\u03bb<\/span>(<\/span>t<\/span><\/span>c<\/span>u<\/span>rre<\/span>n<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>t<\/span><\/span>m<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>))<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                      \u5176\u4e2d tmt_m<\/span><\/span>t<\/span><\/span>m<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u8bb0\u5fc6 mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u7684\u521b\u5efa\u65f6\u95f4，\u03bb\\\\lambda<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span> \u4e3a\u8870\u51cf\u7387\u3002\u8be5\u7b56\u7565\u5047\u8bbe\u65b0\u4fe1\u606f\u901a\u5e38\u66f4\u76f8\u5173，\u4f46\u53ef\u80fd\u8bef\u5220\u957f\u671f\u6709\u6548\u7684\u77e5\u8bc6\u3002<\/p>\n

                      \u8bbf\u95ee\u9891\u7387\u662f\u53e6\u4e00\u79cd\u9057\u5fd8\u4f9d\u636e\u3002\u9891\u7e41\u8bbf\u95ee\u7684\u8bb0\u5fc6\u88ab\u8ba4\u4e3a\u66f4\u6709\u4ef7\u503c，\u5e94\u4fdd\u7559；\u957f\u671f\u672a\u8bbf\u95ee\u7684\u8bb0\u5fc6\u53ef\u80fd\u88ab\u9057\u5fd8\u3002LFU（Least Frequently Used）\u548cLRU（Least Recently Used）\u662f\u7ecf\u5178\u7684\u7f13\u5b58\u6dd8\u6c70\u7b56\u7565，\u53ef\u4ee5\u5e94\u7528\u4e8e\u8bb0\u5fc6\u7ba1\u7406[16]\u3002<\/p>\n

                      \u4e00\u81f4\u6027\u66f4\u65b0\u5904\u7406\u77e5\u8bc6\u51b2\u7a81\u3002\u5f53\u65b0\u83b7\u53d6\u7684\u4fe1\u606f\u4e0e\u5df2\u6709\u8bb0\u5fc6\u77db\u76fe\u65f6，\u9700\u8981\u5224\u65ad\u54ea\u4e2a\u66f4\u53ef\u9760\u3002\u53ef\u4ee5\u57fa\u4e8e\u4fe1\u606f\u6765\u6e90\u7684\u53ef\u4fe1\u5ea6\u3001\u652f\u6301\u8bc1\u636e\u7684\u6570\u91cf\u3001\u4e0e\u5176\u4ed6\u77e5\u8bc6\u7684\u4e00\u81f4\u6027\u7b49\u56e0\u7d20\u7efc\u5408\u5224\u65ad\u3002\u8d1d\u53f6\u65af\u66f4\u65b0\u63d0\u4f9b\u4e86\u4e00\u79cd\u5f62\u5f0f\u5316\u6846\u67b6：\u5c06\u65b0\u65e7\u4fe1\u606f\u89c6\u4e3a\u89c2\u6d4b，\u6839\u636e\u8d1d\u53f6\u65af\u89c4\u5219\u66f4\u65b0\u5bf9\u77e5\u8bc6\u771f\u5b9e\u6027\u7684\u4fe1\u5ff5[56]\u3002<\/p>\n

                      6.3 \u8bb0\u5fc6\u9a71\u52a8\u7684SOP\u5b66\u4e60\u4e0e\u4f18\u5316<\/h3>\n

                      6.3.1 \u4ece\u7ecf\u9a8c\u4e2d\u63d0\u53d6\u64cd\u4f5c\u6a21\u5f0f<\/h4>\n

                      Agent\u7684\u5386\u53f2\u6267\u884c\u8bb0\u5f55\u8574\u542b\u4e86\u4e30\u5bcc\u7684\u64cd\u4f5c\u6a21\u5f0f，\u901a\u8fc7\u5206\u6790\u8fd9\u4e9b\u8bb0\u5f55\u53ef\u4ee5\u81ea\u52a8\u53d1\u73b0\u6709\u6548\u7684SOP\u3002\u8fd9\u79cd\u4ece\u7ecf\u9a8c\u4e2d\u5b66\u4e60SOP\u7684\u65b9\u6cd5\u907f\u514d\u4e86\u4eba\u5de5\u8bbe\u8ba1\u7684\u5c40\u9650\u6027，\u80fd\u591f\u53d1\u73b0\u975e\u76f4\u89c2\u4f46\u9ad8\u6548\u7684\u64cd\u4f5c\u5e8f\u5217[42]\u3002<\/p>\n

                      \u9891\u7e41\u6a21\u5f0f\u6316\u6398（Frequent Pattern Mining）\u662f\u63d0\u53d6\u64cd\u4f5c\u6a21\u5f0f\u7684\u57fa\u672c\u6280\u672f\u3002\u7ed9\u5b9a\u4e00\u7ec4\u6210\u529f\u7684\u5de5\u4f5c\u6d41\u8f68\u8ff9，\u7b97\u6cd5\u627e\u51fa\u9891\u7e41\u51fa\u73b0\u7684\u52a8\u4f5c\u5b50\u5e8f\u5217\u3002\u5f62\u5f0f\u5316\u5730，\u8bbe\u52a8\u4f5c\u5e8f\u5217\u6570\u636e\u5e93\u4e3a D={\u03c41,\u03c42,…,\u03c4N}\\\\mathcal{D} = \\\\{\\\\tau_1, \\\\tau_2, …, \\\\tau_N\\\\}<\/span><\/span>D<\/span><\/span>=<\/span><\/span><\/span><\/span>{<\/span>\u03c4<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u03c4<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>\u03c4<\/span><\/span>N<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>}<\/span><\/span><\/span><\/span><\/span>，\u6a21\u5f0f pp<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span> \u7684\u652f\u6301\u5ea6\u4e3a\u5305\u542b pp<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span> \u7684\u5e8f\u5217\u6bd4\u4f8b：<\/p>\n

                      support(p)=\u2223{\u03c4\u2208D:p\u2286\u03c4}\u2223\u2223D\u2223\\\\text{support}(p) = \\\\frac{|\\\\{\\\\tau \\\\in \\\\mathcal{D} : p \\\\subseteq \\\\tau\\\\}|}{|\\\\mathcal{D}|}<\/span><\/span>support<\/span><\/span>(<\/span>p<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>D<\/span>\u2223<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>{<\/span>\u03c4<\/span><\/span>\u2208<\/span><\/span>D<\/span><\/span>:<\/span><\/span>p<\/span><\/span>\u2286<\/span><\/span>\u03c4<\/span>}<\/span>\u2223<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                      \u9891\u7e41\u6a21\u5f0f\u662f\u652f\u6301\u5ea6\u8d85\u8fc7\u9608\u503c \u03b8\\\\theta<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span><\/span> \u7684\u6a21\u5f0f：{p:support(p)\u2265\u03b8}\\\\{p : \\\\text{support}(p) \\\\geq \\\\theta\\\\}<\/span><\/span>{<\/span>p<\/span><\/span>:<\/span><\/span><\/span><\/span>support<\/span><\/span>(<\/span>p<\/span>)<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>\u03b8<\/span>}<\/span><\/span><\/span><\/span><\/span>\u3002Apriori\u548cFP-Growth\u662f\u7ecf\u5178\u7684\u9891\u7e41\u6a21\u5f0f\u6316\u6398\u7b97\u6cd5[66]\u3002<\/p>\n

                      \u5e8f\u5217\u805a\u7c7b（Sequence Clustering）\u53ef\u4ee5\u53d1\u73b0\u4e0d\u540c\u7c7b\u578b\u7684SOP\u6a21\u677f\u3002\u5c06\u76f8\u4f3c\u7684\u5de5\u4f5c\u6d41\u8f68\u8ff9\u805a\u4e3a\u4e00\u7c7b，\u6bcf\u7c7b\u4ee3\u8868\u89e3\u51b3\u7279\u5b9a\u7c7b\u578b\u4efb\u52a1\u7684\u6807\u51c6\u65b9\u6cd5\u3002\u65b0\u4efb\u52a1\u5230\u6765\u65f6，\u9996\u5148\u5224\u65ad\u5176\u6240\u5c5e\u7c7b\u522b，\u7136\u540e\u590d\u7528\u5bf9\u5e94\u7c7b\u522b\u7684SOP\u3002\u8fd9\u79cd\u57fa\u4e8e\u6848\u4f8b\u7684\u63a8\u7406（Case-Based Reasoning）\u65b9\u6cd5\u5728\u5b9e\u8df5\u4e2d\u975e\u5e38\u6709\u6548[61]\u3002<\/p>\n

                      6.3.2 \u6848\u4f8b\u5e93\u6784\u5efa\u4e0e\u76f8\u4f3c\u5ea6\u5339\u914d<\/h4>\n

                      \u6848\u4f8b\u5e93（Case Library）\u662f\u8bb0\u5fc6\u9a71\u52a8\u7684SOP\u5b66\u4e60\u7684\u6838\u5fc3\u7ec4\u4ef6\u3002\u6bcf\u4e2a\u6848\u4f8b\u5305\u542b\u95ee\u9898\u63cf\u8ff0\u3001\u89e3\u51b3\u65b9\u6848\u548c\u6267\u884c\u7ed3\u679c\u4e09\u90e8\u5206\u3002\u6848\u4f8b\u5e93\u7684\u6784\u5efa\u9700\u8981\u89e3\u51b3\u6848\u4f8b\u8868\u793a\u3001\u7d22\u5f15\u548c\u68c0\u7d22\u7b49\u5173\u952e\u95ee\u9898[62]\u3002<\/p>\n

                      \u6848\u4f8b\u8868\u793a\u5c06\u539f\u59cb\u4efb\u52a1\u4fe1\u606f\u7f16\u7801\u4e3a\u7ed3\u6784\u5316\u683c\u5f0f\u3002\u5bf9\u4e8e\u6587\u672c\u578b\u4efb\u52a1，\u53ef\u4ee5\u4f7f\u7528TF-IDF\u6216BERT\u5d4c\u5165\u8868\u793a\u95ee\u9898；\u5bf9\u4e8e\u7ed3\u6784\u5316\u4efb\u52a1，\u53ef\u4ee5\u4f7f\u7528\u7279\u5f81\u5411\u91cf\u7f16\u7801\u5173\u952e\u5c5e\u6027\u3002\u89e3\u51b3\u65b9\u6848\u90e8\u5206\u9700\u8981\u8bb0\u5f55\u5b8c\u6574\u7684\u64cd\u4f5c\u5e8f\u5217，\u5305\u62ec\u8c03\u7528\u7684\u5de5\u5177\u3001\u751f\u6210\u7684\u63a8\u7406\u3001\u8bbe\u7f6e\u7684\u53c2\u6570\u7b49[16]\u3002<\/p>\n

                      \u6848\u4f8b\u7d22\u5f15\u652f\u6301\u5feb\u901f\u68c0\u7d22\u3002\u5e38\u7528\u65b9\u6cd5\u662f\u5c06\u6848\u4f8b\u8868\u793a\u4e3a\u5411\u91cf，\u4f7f\u7528\u5411\u91cf\u6570\u636e\u5e93\u5b58\u50a8\u548c\u7d22\u5f15\u3002\u5bf9\u4e8e\u5927\u89c4\u6a21\u6848\u4f8b\u5e93，\u53ef\u4ee5\u5efa\u7acb\u5c42\u6b21\u5316\u7d22\u5f15：\u5148\u7528\u7c97\u7c92\u5ea6\u5206\u7c7b（\u5982\u4efb\u52a1\u9886\u57df\u3001\u96be\u5ea6\u7ea7\u522b）\u7f29\u5c0f\u641c\u7d22\u8303\u56f4，\u518d\u5728\u5019\u9009\u96c6\u5185\u8fdb\u884c\u7cbe\u7ec6\u5339\u914d[56]\u3002<\/p>\n

                      \u76f8\u4f3c\u5ea6\u5339\u914d\u5ea6\u91cf\u65b0\u4efb\u52a1\u4e0e\u5386\u53f2\u6848\u4f8b\u7684\u76f8\u4f3c\u6027\u3002\u5e38\u7528\u7684\u76f8\u4f3c\u5ea6\u5ea6\u91cf\u5305\u62ec：<\/p>\n

                        \n
                      • \u4f59\u5f26\u76f8\u4f3c\u5ea6：simcos(x,y)=x\u22c5y\u2225x\u2225\u2225y\u2225\\\\text{sim}_{cos}(x, y) = \\\\frac{x \\\\cdot y}{\\\\|x\\\\| \\\\|y\\\\|}<\/span><\/span>sim<\/span><\/span><\/span>cos<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span>,<\/span><\/span>y<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2225<\/span>x<\/span>\u2225\u2225<\/span>y<\/span>\u2225<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span>\u22c5<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n
                      • \u6b27\u6c0f\u8ddd\u79bb：simeuclid(x,y)=\u2225x\u2212y\u2225\\\\text{sim}_{euclid}(x, y) = \\\\|x – y\\\\|<\/span><\/span>sim<\/span><\/span><\/span>e<\/span>u<\/span>c<\/span>l<\/span>i<\/span>d<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span>,<\/span><\/span>y<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2225<\/span>x<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>y<\/span>\u2225<\/span><\/span><\/span><\/span><\/span><\/li>\n
                      • \u7f16\u8f91\u8ddd\u79bb：\u9002\u7528\u4e8e\u5e8f\u5217\u578b\u8868\u793a，\u5ea6\u91cf\u5c06\u4e00\u4e2a\u5e8f\u5217\u53d8\u4e3a\u53e6\u4e00\u4e2a\u6240\u9700\u7684\u6700\u5c11\u64cd\u4f5c\u6570<\/li>\n<\/ul>\n

                        \u68c0\u7d22\u5230\u76f8\u4f3c\u6848\u4f8b\u540e，Agent\u53ef\u4ee5\u590d\u7528\u5176\u89e3\u51b3\u65b9\u6848，\u6216\u5728\u5176\u57fa\u7840\u4e0a\u8fdb\u884c\u9002\u5e94\u6027\u4fee\u6539[42]\u3002<\/p>\n

                        6.3.3 \u8bb0\u5fc6\u5f15\u5bfc\u7684\u63a2\u7d22\u7b56\u7565<\/h4>\n

                        \u8bb0\u5fc6\u4e0d\u4ec5\u53ef\u4ee5\u7528\u4e8e\u89e3\u51b3\u65b9\u6848\u590d\u7528，\u8fd8\u53ef\u4ee5\u6307\u5bfc\u63a2\u7d22\u8fc7\u7a0b\u3002\u5f53Agent\u9762\u5bf9\u65b0\u4efb\u52a1\u65f6，\u53ef\u4ee5\u57fa\u4e8e\u8bb0\u5fc6\u5224\u65ad\u54ea\u4e9b\u64cd\u4f5c\u66f4\u6709\u53ef\u80fd\u6210\u529f，\u4f18\u5148\u5c1d\u8bd5\u9ad8\u6f5c\u529b\u9009\u9879，\u907f\u514d\u76f2\u76ee\u63a2\u7d22[66]\u3002<\/p>\n

                        \u4e0a\u7f6e\u4fe1\u754c（Upper Confidence Bound, UCB）\u7b97\u6cd5\u5c06\u8bb0\u5fc6\u4f5c\u4e3a\u5148\u9a8c\u77e5\u8bc6\u878d\u5165\u591a\u81c2 bandit \u95ee\u9898\u3002\u6bcf\u4e2a\u52a8\u4f5c aa<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span> \u7ef4\u62a4\u4e00\u4e2a\u4ef7\u503c\u4f30\u8ba1 Q(a)Q(a)<\/span><\/span>Q<\/span>(<\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span> \u548c\u8bbf\u95ee\u8ba1\u6570 N(a)N(a)<\/span><\/span>N<\/span>(<\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002\u52a8\u4f5c\u9009\u62e9\u51c6\u5219\u4e3a：<\/p>\n

                        a\u2217=arg\u2061max\u2061a[Q(a)+cln\u2061TN(a)]a^* = \\\\arg\\\\max_a \\\\left[ Q(a) + c \\\\sqrt{\\\\frac{\\\\ln T}{N(a)}} \\\\right]<\/span><\/span>a<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>arg<\/span><\/span><\/span><\/span>a<\/span><\/span><\/span><\/span>max<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span>Q<\/span>(<\/span>a<\/span>)<\/span><\/span>+<\/span><\/span>c<\/span><\/span><\/span><\/span>N<\/span>(<\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>ln<\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                        \u5176\u4e2d TT<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span> \u4e3a\u603b\u5c1d\u8bd5\u6b21\u6570，cc<\/span><\/span>c<\/span><\/span><\/span><\/span><\/span> \u63a7\u5236\u63a2\u7d22\u7a0b\u5ea6\u3002\u8bb0\u5fc6\u53ef\u4ee5\u521d\u59cb\u5316 Q(a)Q(a)<\/span><\/span>Q<\/span>(<\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u4f7fAgent\u4f18\u5148\u5c1d\u8bd5\u5386\u53f2\u4e0a\u8868\u73b0\u597d\u7684\u52a8\u4f5c[61]\u3002<\/p>\n

                        \u8d1d\u53f6\u65af\u4f18\u5316（Bayesian Optimization）\u63d0\u4f9b\u4e86\u66f4\u590d\u6742\u7684\u8bb0\u5fc6\u5f15\u5bfc\u63a2\u7d22\u6846\u67b6\u3002\u5b83\u7ef4\u62a4\u4e00\u4e2a\u5173\u4e8e\u52a8\u4f5c\u4ef7\u503c\u7684\u9ad8\u65af\u8fc7\u7a0b（Gaussian Process）\u5148\u9a8c，\u6839\u636e\u89c2\u6d4b\u4e0d\u65ad\u66f4\u65b0\u540e\u9a8c\u3002\u8bb0\u5fc6\u63d0\u4f9b\u4e86\u5148\u9a8c\u5206\u5e03\u7684\u521d\u59cb\u53c2\u6570，\u52a0\u901f\u6536\u655b\u3002\u8d1d\u53f6\u65af\u4f18\u5316\u7279\u522b\u9002\u7528\u4e8e\u8bc4\u4f30\u4ee3\u4ef7\u9ad8\u7684\u573a\u666f，\u5982\u9700\u8981\u8c03\u7528\u6602\u8d35API\u7684\u52a8\u4f5c\u9009\u62e9[62]\u3002<\/p>\n

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                        \u8bb0\u5fc6\u68c0\u7d22\u6d41\u7a0b<\/p>\n

                        <\/span><\/p>\n

                        \u7f16\u7801<\/p>\n

                        <\/span><\/p>\n

                        ANN\u641c\u7d22<\/p>\n

                        <\/span><\/p>\n

                        \u91cd\u6392\u5e8f<\/p>\n

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                        \u67e5\u8be2<\/p>\n

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                        \u5411\u91cf\u8868\u793a<\/p>\n

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                        \u5019\u9009\u8bb0\u5fc6<\/p>\n

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                        \u68c0\u7d22\u7ed3\u679c<\/p>\n

                        <\/span><\/p>\n

                        \u8bb0\u5fc6\u5c42\u6b21\u7ed3\u6784<\/p>\n

                        <\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                        \u8f93\u5165\u4fe1\u606f<\/p>\n

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                        \u77ed\u671f\u8bb0\u5fc6<\/p>\n

                        <\/span><\/p>\n

                        \u4fe1\u606f\u7b5b\u9009<\/p>\n

                        <\/span><\/p>\n

                        \u60c5\u666f\u8bb0\u5fc6<\/p>\n

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                        \u8bed\u4e49\u8bb0\u5fc6<\/p>\n

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                        \u7a0b\u5e8f\u8bb0\u5fc6<\/p>\n

                        <\/span><\/p>\n

                        7 \u63a2\u7d22-\u5229\u7528\u6743\u8861\u4e0e\u7b56\u7565\u4f18\u5316<\/h2>\n

                        7.1 \u63a2\u7d22-\u5229\u7528\u56f0\u5883\u7684\u7406\u8bba\u5206\u6790<\/h3>\n

                        7.1.1 \u591a\u81c2Bandit\u95ee\u9898\u7684\u542f\u793a<\/h4>\n

                        \u63a2\u7d22-\u5229\u7528\u6743\u8861（Exploration-Exploitation Tradeoff）\u662f\u5f3a\u5316\u5b66\u4e60\u7684\u6838\u5fc3\u56f0\u5883，\u4e5f\u662fAgent\u5de5\u4f5c\u6d41\u4f18\u5316\u5fc5\u987b\u9762\u5bf9\u7684\u57fa\u672c\u95ee\u9898\u3002\u591a\u81c2Bandit\u95ee\u9898（Multi-Armed Bandit Problem）\u662f\u7814\u7a76\u8fd9\u4e00\u95ee\u9898\u7684\u7ecf\u5178\u6a21\u578b[16]\u3002<\/p>\n

                        \u5728\u591a\u81c2Bandit\u95ee\u9898\u4e2d，Agent\u9762\u4e34 KK<\/span><\/span>K<\/span><\/span><\/span><\/span><\/span> \u4e2a\u52a8\u4f5c\u9009\u9879（\u81c2），\u6bcf\u4e2a\u81c2\u7684\u5956\u52b1\u670d\u4ece\u672a\u77e5\u5206\u5e03\u3002Agent\u7684\u76ee\u6807\u662f\u901a\u8fc7\u6709\u9650\u6b21\u5c1d\u8bd5\u6700\u5927\u5316\u7d2f\u79ef\u5956\u52b1\u3002\u6bcf\u6b21\u5c1d\u8bd5\u65f6，Agent\u9762\u4e34\u4e24\u96be\u9009\u62e9：\u5229\u7528（Exploitation）\u5f53\u524d\u4f30\u8ba1\u5956\u52b1\u6700\u9ad8\u7684\u81c2\u4ee5\u83b7\u5f97\u5373\u65f6\u6536\u76ca，\u6216\u63a2\u7d22（Exploration）\u5176\u4ed6\u81c2\u4ee5\u83b7\u53d6\u66f4\u51c6\u786e\u7684\u4fe1\u606f[14]\u3002<\/p>\n

                        \u5f62\u5f0f\u5316\u5730，\u8bbe\u81c2 ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u7684\u771f\u5b9e\u671f\u671b\u5956\u52b1\u4e3a \u03bci\\\\mu_i<\/span><\/span>\u03bc<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，Agent\u5728\u65f6\u523b tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u9009\u62e9\u81c2 ItI_t<\/span><\/span>I<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u83b7\u5f97\u5956\u52b1 rt\u223cN(\u03bcIt,\u03c32)r_t \\\\sim \\\\mathcal{N}(\\\\mu_{I_t}, \\\\sigma^2)<\/span><\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u223c<\/span><\/span><\/span><\/span>N<\/span>(<\/span>\u03bc<\/span><\/span>I<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002\u7d2f\u79ef\u9057\u61be（Cumulative Regret）\u5b9a\u4e49\u4e3a：<\/p>\n

                        RT=T\u22c5max\u2061i\u03bci\u2212\u2211t=1T\u03bcItR_T = T \\\\cdot \\\\max_i \\\\mu_i – \\\\sum_{t=1}^T \\\\mu_{I_t}<\/span><\/span>R<\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>T<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>max<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03bc<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>t<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03bc<\/span><\/span>I<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                        \u9057\u61be\u5ea6\u91cf\u4e86Agent\u4e0e\u59cb\u7ec8\u9009\u62e9\u6700\u4f18\u81c2\u7684\u7406\u60f3\u7b56\u7565\u4e4b\u95f4\u7684\u5dee\u8ddd\u3002\u4f18\u79c0\u7684\u7b97\u6cd5\u5e94\u4fdd\u8bc1\u9057\u61be\u6b21\u7ebf\u6027\u589e\u957f，\u5373 lim\u2061T\u2192\u221eRT\/T=0\\\\lim_{T \\\\rightarrow \\\\infty} R_T \/ T = 0<\/span><\/span>lim<\/span><\/span>T<\/span>\u2192<\/span>\u221e<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>R<\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span>T<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>[56]\u3002<\/p>\n

                        7.1.2 \u4fe1\u606f\u589e\u76ca\u4e0e\u4e0d\u786e\u5b9a\u6027\u91cf\u5316<\/h4>\n

                        \u4ece\u4fe1\u606f\u8bba\u89c6\u89d2，\u63a2\u7d22\u7684\u4ef7\u503c\u5728\u4e8e\u51cf\u5c11\u4e0d\u786e\u5b9a\u6027\u3002\u4fe1\u606f\u589e\u76ca（Information Gain）\u5ea6\u91cf\u4e86\u6267\u884c\u67d0\u52a8\u4f5c\u540e\u5bf9\u73af\u5883\u8ba4\u77e5\u7684\u6539\u8fdb\u7a0b\u5ea6\u3002\u9009\u62e9\u4fe1\u606f\u589e\u76ca\u9ad8\u7684\u52a8\u4f5c，\u5373\u4f7f\u5176\u5373\u65f6\u5956\u52b1\u4e0d\u9ad8，\u4e5f\u53ef\u80fd\u5e26\u6765\u957f\u671f\u6536\u76ca[42]\u3002<\/p>\n

                        \u8d1d\u53f6\u65af\u6846\u67b6\u4e0b，Agent\u7ef4\u62a4\u5bf9\u6bcf\u4e2a\u52a8\u4f5c\u4ef7\u503c\u5206\u5e03\u7684\u4fe1\u5ff5 P(\u03bci\u2223Ht)P(\\\\mu_i | \\\\mathcal{H}_t)<\/span><\/span>P<\/span>(<\/span>\u03bc<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>H<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>，\u5176\u4e2d Ht\\\\mathcal{H}_t<\/span><\/span>H<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u5386\u53f2\u89c2\u6d4b\u3002\u4fe1\u606f\u589e\u76ca\u5b9a\u4e49\u4e3a\u6267\u884c\u52a8\u4f5c aa<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span> \u524d\u540e\u4fe1\u5ff5\u5206\u5e03\u7684KL\u6563\u5ea6\u671f\u671b：<\/p>\n

                        IG(a)=Er\u2223a,Ht[DKL(P(\u03bc\u2223Ht,a,r)\u2225P(\u03bc\u2223Ht))]IG(a) = \\\\mathbb{E}_{r | a, \\\\mathcal{H}_t} [D_{KL}(P(\\\\mu | \\\\mathcal{H}_t, a, r) \\\\| P(\\\\mu | \\\\mathcal{H}_t))]<\/span><\/span>I<\/span>G<\/span>(<\/span>a<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>E<\/span><\/span>r<\/span>\u2223<\/span>a<\/span>,<\/span>H<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>D<\/span><\/span>K<\/span>L<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>P<\/span>(<\/span>\u03bc<\/span>\u2223<\/span>H<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span>,<\/span><\/span>r<\/span>)<\/span>\u2225<\/span>P<\/span>(<\/span>\u03bc<\/span>\u2223<\/span>H<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>))]<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                        \u4fe1\u606f\u589e\u76ca\u5f15\u5bfc\u7684\u63a2\u7d22\u7b56\u7565\u4f18\u5148\u9009\u62e9\u80fd\u591f\u6700\u5927\u7a0b\u5ea6\u51cf\u5c11\u4ef7\u503c\u4e0d\u786e\u5b9a\u6027\u7684\u52a8\u4f5c\u3002Thompson Sampling\u548cInformation-Directed Sampling\u662f\u57fa\u4e8e\u4fe1\u606f\u589e\u76ca\u7684\u4ee3\u8868\u6027\u7b97\u6cd5[66]\u3002<\/p>\n

                        \u4e0d\u786e\u5b9a\u6027\u91cf\u5316（Uncertainty Quantification）\u662f\u6307\u5bfc\u63a2\u7d22\u7684\u5173\u952e\u3002\u5bf9\u4e8e\u795e\u7ecf\u7f51\u7edc\u7b56\u7565，\u5e38\u7528\u7684\u4e0d\u786e\u5b9a\u6027\u4f30\u8ba1\u65b9\u6cd5\u5305\u62ec：<\/p>\n

                          \n
                        • \u96c6\u6210\u65b9\u6cd5：\u8bad\u7ec3\u591a\u4e2a\u7f51\u7edc，\u7528\u9884\u6d4b\u65b9\u5dee\u4f30\u8ba1\u4e0d\u786e\u5b9a\u6027<\/li>\n
                        • Dropout\u91c7\u6837：\u5728\u524d\u5411\u4f20\u64ad\u65f6\u542f\u7528Dropout，\u591a\u6b21\u91c7\u6837\u83b7\u5f97\u9884\u6d4b\u5206\u5e03<\/li>\n
                        • \u8d1d\u53f6\u65af\u795e\u7ecf\u7f51\u7edc：\u5c06\u6743\u91cd\u89c6\u4e3a\u968f\u673a\u53d8\u91cf，\u901a\u8fc7\u540e\u9a8c\u63a8\u65ad\u83b7\u5f97\u9884\u6d4b\u4e0d\u786e\u5b9a\u6027<\/li>\n<\/ul>\n

                          \u5728\u5de5\u4f5c\u6d41\u4f18\u5316\u4e2d，\u4e0d\u786e\u5b9a\u6027\u9ad8\u7684\u6b65\u9aa4\u5e94\u83b7\u5f97\u66f4\u591a\u63a2\u7d22\u673a\u4f1a，\u4ee5\u9a8c\u8bc1\u5176\u771f\u5b9e\u6548\u679c[61]\u3002<\/p>\n

                          7.1.3 \u4e50\u89c2\u9762\u5bf9\u4e0d\u786e\u5b9a\u6027\u7684\u539f\u5219<\/h4>\n

                          \u4e50\u89c2\u9762\u5bf9\u4e0d\u786e\u5b9a\u6027（Optimism in the Face of Uncertainty）\u662f\u8bbe\u8ba1\u9ad8\u6548\u63a2\u7d22\u7b56\u7565\u7684\u6838\u5fc3\u539f\u5219\u3002\u8be5\u539f\u5219\u4e3b\u5f20：\u5bf9\u4e8e\u4e0d\u786e\u5b9a\u6027\u9ad8\u7684\u9009\u9879，\u5e94\u4e50\u89c2\u5730\u5047\u8bbe\u5176\u53ef\u80fd\u5177\u6709\u9ad8\u6536\u76ca，\u4ece\u800c\u7ed9\u4e88\u63a2\u7d22\u673a\u4f1a[62]\u3002<\/p>\n

                          \u4e0a\u7f6e\u4fe1\u754c（UCB）\u7b97\u6cd5\u662f\u4e50\u89c2\u539f\u5219\u7684\u7ecf\u5178\u5b9e\u73b0\u3002UCB\u4e3a\u6bcf\u4e2a\u52a8\u4f5c\u7ef4\u62a4\u4e00\u4e2a\u7f6e\u4fe1\u533a\u95f4，\u9009\u62e9\u7f6e\u4fe1\u4e0a\u754c\u6700\u9ad8\u7684\u52a8\u4f5c：<\/p>\n

                          at=arg\u2061max\u2061a[\u03bc^a+cln\u2061tNa]a_t = \\\\arg\\\\max_a \\\\left[ \\\\hat{\\\\mu}_a + c \\\\sqrt{\\\\frac{\\\\ln t}{N_a}} \\\\right]<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>arg<\/span><\/span><\/span><\/span>a<\/span><\/span><\/span><\/span>max<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>\u03bc<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>c<\/span><\/span><\/span><\/span>N<\/span><\/span>a<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>ln<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u5176\u4e2d \u03bc^a\\\\hat{\\\\mu}_a<\/span><\/span><\/span>\u03bc<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u52a8\u4f5c aa<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span> \u7684\u7ecf\u9a8c\u5e73\u5747\u5956\u52b1，NaN_a<\/span><\/span>N<\/span><\/span>a<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u9009\u62e9\u6b21\u6570\u3002\u7b2c\u4e8c\u9879\u4e3a\u7f6e\u4fe1\u533a\u95f4\u5bbd\u5ea6，\u968f\u7740\u5c1d\u8bd5\u6b21\u6570\u589e\u52a0\u800c\u51cf\u5c0f\u3002\u8be5\u516c\u5f0f\u5b9e\u73b0\u4e86\u81ea\u52a8\u7684\u63a2\u7d22-\u5229\u7528\u5e73\u8861：\u5bf9\u5c1d\u8bd5\u5c11\u7684\u52a8\u4f5c（NaN_a<\/span><\/span>N<\/span><\/span>a<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5c0f），\u63a2\u7d22\u9879\u5360\u4e3b\u5bfc；\u5bf9\u5c1d\u8bd5\u591a\u7684\u52a8\u4f5c，\u5229\u7528\u9879\u5360\u4e3b\u5bfc[16]\u3002<\/p>\n

                          UCB\u7b97\u6cd5\u7684\u9057\u61be\u4e0a\u754c\u4e3a O(KTln\u2061T)O(\\\\sqrt{KT \\\\ln T})<\/span><\/span>O<\/span>(<\/span><\/span>K<\/span>T<\/span><\/span>ln<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>，\u63a5\u8fd1\u7406\u8bba\u4e0b\u754c\u3002\u5728Agent\u5de5\u4f5c\u6d41\u4f18\u5316\u4e2d，UCB\u53ef\u4ee5\u5e94\u7528\u4e8e\u5de5\u5177\u9009\u62e9\u3001\u63a8\u7406\u7b56\u7565\u9009\u62e9\u7b49\u591a\u4e2a\u5c42\u9762，\u5b9e\u73b0\u9ad8\u6548\u7684\u63a2\u7d22[124]\u3002<\/p>\n

                          7.2 \u63a2\u7d22\u7b56\u7565\u7684\u8bbe\u8ba1\u4e0e\u5b9e\u73b0<\/h3>\n

                          7.2.1 Epsilon-\u8d2a\u5a6a\u4e0e\u8870\u51cf\u7b56\u7565<\/h4>\n

                          Epsilon-\u8d2a\u5a6a（\u03f5\\\\epsilon<\/span><\/span>\u03f5<\/span><\/span><\/span><\/span><\/span>-Greedy）\u662f\u6700\u7b80\u5355\u7684\u63a2\u7d22\u7b56\u7565，\u4ee5\u6982\u7387 \u03f5\\\\epsilon<\/span><\/span>\u03f5<\/span><\/span><\/span><\/span><\/span> \u968f\u673a\u63a2\u7d22，\u4ee5\u6982\u7387 1\u2212\u03f51-\\\\epsilon<\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03f5<\/span><\/span><\/span><\/span><\/span> \u9009\u62e9\u5f53\u524d\u6700\u4f18\u52a8\u4f5c\u3002\u5f62\u5f0f\u5316\u5730，\u7b56\u7565\u4e3a[56]：<\/p>\n

                          \u03c0(a\u2223s)={1\u2212\u03f5+\u03f5\u2223A\u2223if\u00a0a=arg\u2061max\u2061a\u2032Q(s,a\u2032)\u03f5\u2223A\u2223otherwise\\\\pi(a|s) = \\\\begin{cases} 1 – \\\\epsilon + \\\\frac{\\\\epsilon}{|\\\\mathcal{A}|} & \\\\text{if } a = \\\\arg\\\\max_{a'} Q(s, a') \\\\\\\\ \\\\frac{\\\\epsilon}{|\\\\mathcal{A}|} & \\\\text{otherwise} \\\\end{cases}<\/span><\/span>\u03c0<\/span>(<\/span>a<\/span>\u2223<\/span>s<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>{<\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span>\u03f5<\/span><\/span>+<\/span><\/span><\/span><\/span>\u2223<\/span>A<\/span>\u2223<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03f5<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>A<\/span>\u2223<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03f5<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>if\u00a0<\/span><\/span>a<\/span><\/span>=<\/span><\/span>arg<\/span><\/span><\/span>max<\/span><\/span>a<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>Q<\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>otherwise<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u03f5\\\\epsilon<\/span><\/span>\u03f5<\/span><\/span><\/span><\/span><\/span>-\u8d2a\u5a6a\u7684\u4f18\u70b9\u662f\u5b9e\u73b0\u7b80\u5355\u3001\u8ba1\u7b97\u5f00\u9500\u5c0f；\u7f3a\u70b9\u662f\u63a2\u7d22\u5b8c\u5168\u968f\u673a，\u53ef\u80fd\u5c1d\u8bd5\u660e\u663e\u52a3\u8d28\u7684\u52a8\u4f5c，\u6d6a\u8d39\u6837\u672c\u3002<\/p>\n

                          \u8870\u51cf\u03f5\\\\epsilon<\/span><\/span>\u03f5<\/span><\/span><\/span><\/span><\/span>-\u8d2a\u5a6a（Decaying \u03f5\\\\epsilon<\/span><\/span>\u03f5<\/span><\/span><\/span><\/span><\/span>-Greedy）\u968f\u7740\u65f6\u95f4\u9010\u6b65\u964d\u4f4e\u63a2\u7d22\u7387，\u5b9e\u73b0\u4ece\u63a2\u7d22\u5230\u5229\u7528\u7684\u8fc7\u6e21：<\/p>\n

                          \u03f5t=\u03f50\u22c5\u03b3t\\\\epsilon_t = \\\\epsilon_0 \\\\cdot \\\\gamma^t<\/span><\/span>\u03f5<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u03f5<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>\u03b3<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u6216<\/p>\n

                          \u03f5t=\u03f501+\u03b2t\\\\epsilon_t = \\\\frac{\\\\epsilon_0}{1 + \\\\beta t}<\/span><\/span>\u03f5<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>+<\/span><\/span>\u03b2t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03f5<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u5176\u4e2d \u03f50\\\\epsilon_0<\/span><\/span>\u03f5<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u521d\u59cb\u63a2\u7d22\u7387，\u03b3\u2208(0,1)\\\\gamma \\\\in (0,1)<\/span><\/span>\u03b3<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>(<\/span>0<\/span>,<\/span><\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u8870\u51cf\u56e0\u5b50，\u03b2\\\\beta<\/span><\/span>\u03b2<\/span><\/span><\/span><\/span><\/span> \u63a7\u5236\u8870\u51cf\u901f\u5ea6\u3002\u8870\u51cf\u7b56\u7565\u7b26\u5408\u76f4\u89c9：\u521d\u671f\u9700\u8981\u5927\u91cf\u63a2\u7d22\u5efa\u7acb\u4ef7\u503c\u4f30\u8ba1，\u540e\u671f\u5e94\u66f4\u591a\u5229\u7528\u5df2\u77e5\u4fe1\u606f[42]\u3002<\/p>\n

                          7.2.2 \u73bb\u5c14\u5179\u66fc\u63a2\u7d22\u4e0e\u71b5\u6b63\u5219\u5316<\/h4>\n

                          \u73bb\u5c14\u5179\u66fc\u63a2\u7d22（Boltzmann Exploration）\u6839\u636e\u52a8\u4f5c\u4ef7\u503c\u7684softmax\u5206\u5e03\u8fdb\u884c\u91c7\u6837，\u4ef7\u503c\u9ad8\u7684\u52a8\u4f5c\u88ab\u9009\u4e2d\u7684\u6982\u7387\u5927，\u4f46\u6240\u6709\u52a8\u4f5c\u90fd\u6709\u975e\u96f6\u6982\u7387：<\/p>\n

                          \u03c0(a\u2223s)=exp\u2061(Q(s,a)\/\u03c4)\u2211a\u2032exp\u2061(Q(s,a\u2032)\/\u03c4)\\\\pi(a|s) = \\\\frac{\\\\exp(Q(s,a)\/\\\\tau)}{\\\\sum_{a'} \\\\exp(Q(s,a')\/\\\\tau)}<\/span><\/span>\u03c0<\/span>(<\/span>a<\/span>\u2223<\/span>s<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>a<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>exp<\/span>(<\/span>Q<\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>\/<\/span>\u03c4<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>exp<\/span>(<\/span>Q<\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span>\/<\/span>\u03c4<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u5176\u4e2d \u03c4\\\\tau<\/span><\/span>\u03c4<\/span><\/span><\/span><\/span><\/span> \u4e3a\u6e29\u5ea6\u53c2\u6570\u3002\u9ad8\u6e29（\u03c4\u2192\u221e\\\\tau \\\\rightarrow \\\\infty<\/span><\/span>\u03c4<\/span><\/span>\u2192<\/span><\/span><\/span><\/span>\u221e<\/span><\/span><\/span><\/span><\/span>）\u65f6\u5206\u5e03\u8d8b\u4e8e\u5747\u5300，\u5b8c\u5168\u63a2\u7d22；\u4f4e\u6e29（\u03c4\u21920\\\\tau \\\\rightarrow 0<\/span><\/span>\u03c4<\/span><\/span>\u2192<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>）\u65f6\u5206\u5e03\u8d8b\u4e8e\u5c16\u9510，\u8d2a\u5a6a\u5229\u7528[66]\u3002<\/p>\n

                          \u71b5\u6b63\u5219\u5316（Entropy Regularization）\u5c06\u7b56\u7565\u71b5\u4f5c\u4e3a\u5956\u52b1\u7684\u4e00\u90e8\u5206，\u9f13\u52b1\u63a2\u7d22：<\/p>\n

                          J(\u03b8)=E\u03c4\u223c\u03c0\u03b8[R(\u03c4)]+\u03b1\u22c5H(\u03c0\u03b8(\u22c5\u2223s))J(\\\\theta) = \\\\mathbb{E}_{\\\\tau \\\\sim \\\\pi_\\\\theta} [R(\\\\tau)] + \\\\alpha \\\\cdot H(\\\\pi_\\\\theta(\\\\cdot|s))<\/span><\/span>J<\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>E<\/span><\/span>\u03c4<\/span>\u223c<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>R<\/span>(<\/span>\u03c4<\/span>)]<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b1<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>H<\/span>(<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u22c5<\/span>\u2223<\/span>s<\/span>))<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u5176\u4e2d H(\u03c0)=\u2212\u2211a\u03c0(a)log\u2061\u03c0(a)H(\\\\pi) = -\\\\sum_a \\\\pi(a) \\\\log \\\\pi(a)<\/span><\/span>H<\/span>(<\/span>\u03c0<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span>\u2211<\/span><\/span>a<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c0<\/span>(<\/span>a<\/span>)<\/span><\/span>log<\/span><\/span><\/span>\u03c0<\/span>(<\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7b56\u7565\u71b5，\u03b1\\\\alpha<\/span><\/span>\u03b1<\/span><\/span><\/span><\/span><\/span> \u63a7\u5236\u6b63\u5219\u5316\u5f3a\u5ea6\u3002Soft Actor-Critic（SAC）\u7b97\u6cd5\u57fa\u4e8e\u6700\u5927\u71b5\u6846\u67b6，\u5728\u673a\u5668\u4eba\u63a7\u5236\u3001\u6e38\u620f\u7b49\u4efb\u52a1\u4e2d\u8868\u73b0\u51fa\u8272[61]\u3002<\/p>\n

                          7.2.3 \u57fa\u4e8e\u597d\u5947\u5fc3\u7684\u5185\u5728\u52a8\u673a<\/h4>\n

                          \u5916\u5728\u5956\u52b1（Extrinsic Reward）\u7a00\u758f\u65f6，\u5185\u5728\u52a8\u673a（Intrinsic Motivation）\u53ef\u4ee5\u9a71\u52a8\u63a2\u7d22\u3002\u597d\u5947\u5fc3（Curiosity）\u662f\u4e00\u79cd\u91cd\u8981\u7684\u5185\u5728\u52a8\u673a，\u9f13\u52b1Agent\u63a2\u7d22\u65b0\u5947\u3001\u4e0d\u786e\u5b9a\u7684\u72b6\u6001[62]\u3002<\/p>\n

                          \u5185\u5728\u597d\u5947\u5fc3\u6a21\u5757（Intrinsic Curiosity Module, ICM）\u901a\u8fc7\u9884\u6d4b\u4e0b\u4e00\u4e2a\u72b6\u6001\u7684\u8868\u5f81\u6765\u5ea6\u91cf\u597d\u5947\u5fc3\u3002\u8bbe\u5f53\u524d\u72b6\u6001\u4e3a sts_t<\/span><\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u6267\u884c\u52a8\u4f5c ata_t<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u540e\u89c2\u6d4b\u5230 st+1s_{t+1}<\/span><\/span>s<\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002ICM\u5b66\u4e60\u4e00\u4e2a\u524d\u5411\u6a21\u578b\u9884\u6d4b\u4e0b\u4e00\u72b6\u6001\u8868\u5f81：<\/p>\n

                          \u03d5^(st+1)=f(\u03d5(st),at;\u03b8F)\\\\hat{\\\\phi}(s_{t+1}) = f(\\\\phi(s_t), a_t; \\\\theta_F)<\/span><\/span><\/span>\u03d5<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>f<\/span>(<\/span>\u03d5<\/span>(<\/span>s<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>,<\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>;<\/span><\/span>\u03b8<\/span><\/span>F<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u5185\u5728\u5956\u52b1\u5b9a\u4e49\u4e3a\u9884\u6d4b\u8bef\u5dee：<\/p>\n

                          rtint=\u2225\u03d5(st+1)\u2212\u03d5^(st+1)\u22252r_t^{int} = \\\\|\\\\phi(s_{t+1}) – \\\\hat{\\\\phi}(s_{t+1})\\\\|^2<\/span><\/span>r<\/span><\/span>t<\/span><\/span><\/span><\/span>in<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2225<\/span>\u03d5<\/span>(<\/span>s<\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>\u03d5<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>\u2225<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u9884\u6d4b\u8bef\u5dee\u5927\u7684\u72b6\u6001\u88ab\u8ba4\u4e3a\u662f"\u65b0\u5947\u7684"，Agent\u88ab\u6fc0\u52b1\u53bb\u63a2\u7d22\u3002ICM\u907f\u514d\u4e86\u5728\u539f\u59cb\u89c2\u6d4b\u7a7a\u95f4\u9884\u6d4b，\u800c\u662f\u5728\u5b66\u4e60\u5230\u7684\u8868\u5f81\u7a7a\u95f4\u9884\u6d4b，\u8fc7\u6ee4\u4e86\u4e0e\u51b3\u7b56\u65e0\u5173\u7684\u566a\u58f0[66]\u3002<\/p>\n

                          \u5728\u5de5\u4f5c\u6d41\u4f18\u5316\u4e2d，\u597d\u5947\u5fc3\u53ef\u4ee5\u5f15\u5bfcAgent\u5c1d\u8bd5\u65b0\u9896\u7684\u64cd\u4f5c\u7ec4\u5408，\u53d1\u73b0\u975e\u4f20\u7edf\u7684\u89e3\u51b3\u65b9\u6848\u3002\u7814\u7a76\u8868\u660e，\u7ed3\u5408\u5185\u5728\u5956\u52b1\u7684\u8bad\u7ec3\u80fd\u591f\u53d1\u73b0\u66f4\u9c81\u68d2\u3001\u66f4\u901a\u7528\u7684SOP[16]\u3002<\/p>\n

                          7.3 \u7b56\u7565\u4f18\u5316\u7684\u7a33\u5b9a\u6027\u4e0e\u6536\u655b\u6027<\/h3>\n

                          7.3.1 \u7b56\u7565\u66f4\u65b0\u7684\u6b65\u957f\u63a7\u5236<\/h4>\n

                          \u7b56\u7565\u68af\u5ea6\u65b9\u6cd5\u4e2d，\u6b65\u957f（Step Size）\u7684\u9009\u62e9\u81f3\u5173\u91cd\u8981\u3002\u6b65\u957f\u8fc7\u5927\u5bfc\u81f4\u7b56\u7565\u5267\u70c8\u53d8\u5316，\u53ef\u80fd\u5d29\u6e83\u5230\u6b21\u4f18\u89e3；\u6b65\u957f\u8fc7\u5c0f\u5219\u6536\u655b\u7f13\u6162，\u4e14\u5bb9\u6613\u9677\u5165\u5c40\u90e8\u6700\u4f18[124]\u3002<\/p>\n

                          \u4fe1\u4efb\u57df\u65b9\u6cd5\u901a\u8fc7\u7ea6\u675f\u7b56\u7565\u66f4\u65b0\u7684\u5e45\u5ea6\u6765\u4fdd\u8bc1\u7a33\u5b9a\u6027\u3002TRPO\u4f7f\u7528KL\u6563\u5ea6\u7ea6\u675f：<\/p>\n

                          max\u2061\u03b8E[\u03c0\u03b8(a\u2223s)\u03c0\u03b8old(a\u2223s)A\u03c0\u03b8old(s,a)]\\\\max_\\\\theta \\\\mathbb{E} \\\\left[ \\\\frac{\\\\pi_\\\\theta(a|s)}{\\\\pi_{\\\\theta_{old}}(a|s)} A^{\\\\pi_{\\\\theta_{old}}}(s,a) \\\\right]<\/span><\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>max<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>E<\/span><\/span>[<\/span><\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span>\u2223<\/span>s<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span>\u2223<\/span>s<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span>)<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          s.t.\u00a0E[DKL(\u03c0\u03b8old(\u22c5\u2223s)\u2225\u03c0\u03b8(\u22c5\u2223s))]\u2264\u03b4\\\\text{s.t. } \\\\mathbb{E}[D_{KL}(\\\\pi_{\\\\theta_{old}}(\\\\cdot|s) \\\\| \\\\pi_\\\\theta(\\\\cdot|s))] \\\\leq \\\\delta<\/span><\/span>s.t.\u00a0<\/span><\/span>E<\/span>[<\/span>D<\/span><\/span>K<\/span>L<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span>o<\/span>l<\/span>d<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u22c5<\/span>\u2223<\/span>s<\/span>)<\/span>\u2225<\/span>\u03c0<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u22c5<\/span>\u2223<\/span>s<\/span>))]<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>\u03b4<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u8be5\u7ea6\u675f\u786e\u4fdd\u65b0\u7b56\u7565\u4e0e\u65e7\u7b56\u7565\u8db3\u591f\u63a5\u8fd1，\u907f\u514d\u707e\u96be\u6027\u9057\u5fd8（Catastrophic Forgetting）[56]\u3002<\/p>\n

                          PPO\u901a\u8fc7\u88c1\u526a\u76ee\u6807\u51fd\u6570\u8fd1\u4f3c\u5b9e\u73b0\u4fe1\u4efb\u57df\u7ea6\u675f，\u907f\u514d\u4e86\u6602\u8d35\u7684\u7ea6\u675f\u4f18\u5316\u3002\u88c1\u526a\u673a\u5236\u81ea\u52a8\u9650\u5236\u6982\u7387\u6bd4\u7684\u8303\u56f4，\u5f53\u6982\u7387\u6bd4\u8d85\u51fa [1\u2212\u03f5,1+\u03f5][1-\\\\epsilon, 1+\\\\epsilon]<\/span><\/span>[<\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03f5<\/span>,<\/span><\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03f5<\/span>]<\/span><\/span><\/span><\/span><\/span> \u533a\u95f4\u65f6，\u68af\u5ea6\u4e3a\u96f6，\u963b\u6b62\u8fdb\u4e00\u6b65\u66f4\u65b0[16]\u3002<\/p>\n

                          7.3.2 \u7ecf\u9a8c\u56de\u653e\u4e0e\u6837\u672c\u6548\u7387<\/h4>\n

                          \u7ecf\u9a8c\u56de\u653e（Experience Replay）\u662f\u63d0\u5347\u6837\u672c\u6548\u7387\u7684\u5173\u952e\u6280\u672f\u3002\u5b83\u5c06Agent\u7684\u7ecf\u9a8c (s,a,r,s\u2032)(s, a, r, s')<\/span><\/span>(<\/span>s<\/span>,<\/span><\/span>a<\/span>,<\/span><\/span>r<\/span>,<\/span><\/span>s<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u5b58\u50a8\u5728\u56de\u653e\u7f13\u51b2\u533a（Replay Buffer）\u4e2d，\u8bad\u7ec3\u65f6\u968f\u673a\u91c7\u6837\u5c0f\u6279\u91cf\u6570\u636e\u3002\u8fd9\u79cd\u65b9\u6cd5\u6253\u7834\u4e86\u6837\u672c\u95f4\u7684\u65f6\u95f4\u76f8\u5173\u6027，\u63d0\u9ad8\u4e86\u6570\u636e\u5229\u7528\u6548\u7387[42]\u3002<\/p>\n

                          \u4f18\u5148\u7ecf\u9a8c\u56de\u653e（Prioritized Experience Replay）\u6839\u636eTD\u8bef\u5dee\u4e3a\u7ecf\u9a8c\u5206\u914d\u4f18\u5148\u7ea7，\u4f18\u5148\u91c7\u6837\u5b66\u4e60\u4ef7\u503c\u9ad8\u7684\u7ecf\u9a8c\u3002\u91c7\u6837\u6982\u7387\u4e3a：<\/p>\n

                          P(i)=\u2223\u03b4i\u2223\u03b1\u2211j\u2223\u03b4j\u2223\u03b1P(i) = \\\\frac{|\\\\delta_i|^\\\\alpha}{\\\\sum_j |\\\\delta_j|^\\\\alpha}<\/span><\/span>P<\/span>(<\/span>i<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>\u03b4<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span>\u03b1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>\u03b4<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span>\u03b1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u5176\u4e2d \u03b4i\\\\delta_i<\/span><\/span>\u03b4<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u7b2c ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u6761\u7ecf\u9a8c\u7684TD\u8bef\u5dee，\u03b1\\\\alpha<\/span><\/span>\u03b1<\/span><\/span><\/span><\/span><\/span> \u63a7\u5236\u4f18\u5148\u7ea7\u7a0b\u5ea6\u3002\u4f18\u5148\u56de\u653e\u4f7f\u5f97Agent\u66f4\u5173\u6ce8"\u4ee4\u4eba\u60ca\u8bb6"\u7684\u7ecf\u9a8c，\u52a0\u901f\u5b66\u4e60[66]\u3002<\/p>\n

                          \u5728\u5de5\u4f5c\u6d41\u4f18\u5316\u4e2d，\u7ecf\u9a8c\u56de\u653e\u8fd8\u53ef\u4ee5\u5b9e\u73b0\u8de8\u4efb\u52a1\u5b66\u4e60\u3002\u4e0d\u540c\u4efb\u52a1\u7684\u7ecf\u9a8c\u5b58\u50a8\u5728\u540c\u4e00\u7f13\u51b2\u533a，Agent\u53ef\u4ee5\u4ece\u591a\u6837\u5316\u7684\u7ecf\u9a8c\u4e2d\u5b66\u4e60\u901a\u7528\u7684\u64cd\u4f5c\u6a21\u5f0f，\u63d0\u5347\u6cdb\u5316\u80fd\u529b[61]\u3002<\/p>\n

                          7.3.3 \u591a\u8f6e\u8fed\u4ee3\u4e2d\u7684\u7b56\u7565\u9000\u5316\u95ee\u9898<\/h4>\n

                          \u591a\u8f6e\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\u4e2d，\u7b56\u7565\u9000\u5316（Policy Degradation）\u662f\u5e38\u89c1\u95ee\u9898\u3002Agent\u53ef\u80fd\u5728\u8bad\u7ec3\u521d\u671f\u8868\u73b0\u826f\u597d，\u4f46\u968f\u7740\u8bad\u7ec3\u8fdb\u884c，\u7b56\u7565\u8d28\u91cf\u53cd\u800c\u4e0b\u964d\u3002\u8fd9\u79cd\u73b0\u8c61\u88ab\u79f0\u4e3a"\u56de\u58f0\u9677\u9631"（Echo Trap）[16]\u3002<\/p>\n

                          \u56de\u58f0\u9677\u9631\u7684\u4ea7\u751f\u673a\u5236\u662f：Agent\u5728\u65e9\u671f\u63a2\u7d22\u4e2d\u53d1\u73b0\u4e86\u67d0\u4e9b\u9ad8\u5956\u52b1\u8f68\u8ff9，\u968f\u7740\u8bad\u7ec3\u8fdb\u884c，\u7b56\u7565\u8fc7\u5ea6\u62df\u5408\u8fd9\u4e9b\u8f68\u8ff9，\u5931\u53bb\u4e86\u591a\u6837\u6027\u3002\u5f53\u8fd9\u4e9b\u8f68\u8ff9\u5b9e\u9645\u4e0a\u662f\u6b21\u4f18\u7684\u6216\u4f9d\u8d56\u4e8e\u7279\u5b9a\u6761\u4ef6\u65f6，\u7b56\u7565\u6027\u80fd\u5c31\u4f1a\u4e0b\u964d\u3002<\/p>\n

                          \u9632\u6b62\u7b56\u7565\u9000\u5316\u7684\u7b56\u7565\u5305\u62ec：<\/p>\n

                            \n
                          • \u65e9\u505c（Early Stopping）：\u76d1\u63a7\u9a8c\u8bc1\u96c6\u6027\u80fd，\u5f53\u6027\u80fd\u4e0d\u518d\u63d0\u5347\u65f6\u505c\u6b62\u8bad\u7ec3<\/li>\n
                          • \u53c2\u8003\u7b56\u7565\u7ea6\u675f（Reference Policy Constraint）：\u901a\u8fc7KL\u6563\u5ea6\u7ea6\u675f\u65b0\u7b56\u7565\u4e0e\u521d\u59cb\u53c2\u8003\u7b56\u7565\u7684\u8ddd\u79bb，\u9632\u6b62\u504f\u79bb\u592a\u8fdc<\/li>\n
                          • \u591a\u6837\u6027\u5956\u52b1（Diversity Reward）：\u5956\u52b1\u751f\u6210\u591a\u6837\u5316\u8f68\u8ff9\u7684\u884c\u4e3a，\u9f13\u52b1\u63a2\u7d22<\/li>\n
                          • \u96c6\u6210\u7b56\u7565（Ensemble Policy）：\u7ef4\u62a4\u591a\u4e2a\u7b56\u7565，\u901a\u8fc7\u6295\u7968\u6216\u5e73\u5747\u964d\u4f4e\u5355\u4e00\u7b56\u7565\u9000\u5316\u7684\u98ce\u9669<\/li>\n<\/ul>\n

                            \u5728Agent\u5de5\u4f5c\u6d41\u4f18\u5316\u4e2d，\u7b56\u7565\u9000\u5316\u8868\u73b0\u4e3a\u5de5\u4f5c\u6d41\u591a\u6837\u6027\u7684\u4e27\u5931\u2014\u2014Agent\u53cd\u590d\u4f7f\u7528\u76f8\u540c\u7684\u64cd\u4f5c\u5e8f\u5217，\u5373\u4f7f\u9762\u5bf9\u4e0d\u540c\u7c7b\u578b\u7684\u4efb\u52a1\u3002\u4fdd\u6301\u7b56\u7565\u591a\u6837\u6027\u5bf9\u4e8e\u53d1\u73b0\u9c81\u68d2\u7684SOP\u81f3\u5173\u91cd\u8981[62]\u3002<\/p>\n

                            #mermaid-svg-9SiUdYMNH32xXSk3{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-9SiUdYMNH32xXSk3 .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-9SiUdYMNH32xXSk3 .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-9SiUdYMNH32xXSk3 .error-icon{fill:#552222;}#mermaid-svg-9SiUdYMNH32xXSk3 .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-9SiUdYMNH32xXSk3 .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-9SiUdYMNH32xXSk3 .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-9SiUdYMNH32xXSk3 .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-9SiUdYMNH32xXSk3 .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-9SiUdYMNH32xXSk3 .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-9SiUdYMNH32xXSk3 .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-9SiUdYMNH32xXSk3 .marker{fill:#333333;stroke:#333333;}#mermaid-svg-9SiUdYMNH32xXSk3 .marker.cross{stroke:#333333;}#mermaid-svg-9SiUdYMNH32xXSk3 svg{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-9SiUdYMNH32xXSk3 p{margin:0;}#mermaid-svg-9SiUdYMNH32xXSk3 .label{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;color:#333;}#mermaid-svg-9SiUdYMNH32xXSk3 .cluster-label text{fill:#333;}#mermaid-svg-9SiUdYMNH32xXSk3 .cluster-label span{color:#333;}#mermaid-svg-9SiUdYMNH32xXSk3 .cluster-label span p{background-color:transparent;}#mermaid-svg-9SiUdYMNH32xXSk3 .label text,#mermaid-svg-9SiUdYMNH32xXSk3 span{fill:#333;color:#333;}#mermaid-svg-9SiUdYMNH32xXSk3 .node rect,#mermaid-svg-9SiUdYMNH32xXSk3 .node circle,#mermaid-svg-9SiUdYMNH32xXSk3 .node ellipse,#mermaid-svg-9SiUdYMNH32xXSk3 .node polygon,#mermaid-svg-9SiUdYMNH32xXSk3 .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-9SiUdYMNH32xXSk3 .rough-node .label text,#mermaid-svg-9SiUdYMNH32xXSk3 .node .label text,#mermaid-svg-9SiUdYMNH32xXSk3 .image-shape .label,#mermaid-svg-9SiUdYMNH32xXSk3 .icon-shape .label{text-anchor:middle;}#mermaid-svg-9SiUdYMNH32xXSk3 .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-9SiUdYMNH32xXSk3 .rough-node .label,#mermaid-svg-9SiUdYMNH32xXSk3 .node .label,#mermaid-svg-9SiUdYMNH32xXSk3 .image-shape .label,#mermaid-svg-9SiUdYMNH32xXSk3 .icon-shape .label{text-align:center;}#mermaid-svg-9SiUdYMNH32xXSk3 .node.clickable{cursor:pointer;}#mermaid-svg-9SiUdYMNH32xXSk3 .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-9SiUdYMNH32xXSk3 .arrowheadPath{fill:#333333;}#mermaid-svg-9SiUdYMNH32xXSk3 .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-9SiUdYMNH32xXSk3 .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-9SiUdYMNH32xXSk3 .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-9SiUdYMNH32xXSk3 .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-9SiUdYMNH32xXSk3 .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-9SiUdYMNH32xXSk3 .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-9SiUdYMNH32xXSk3 .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-9SiUdYMNH32xXSk3 .cluster text{fill:#333;}#mermaid-svg-9SiUdYMNH32xXSk3 .cluster span{color:#333;}#mermaid-svg-9SiUdYMNH32xXSk3 div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-9SiUdYMNH32xXSk3 .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-9SiUdYMNH32xXSk3 rect.text{fill:none;stroke-width:0;}#mermaid-svg-9SiUdYMNH32xXSk3 .icon-shape,#mermaid-svg-9SiUdYMNH32xXSk3 .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-9SiUdYMNH32xXSk3 .icon-shape p,#mermaid-svg-9SiUdYMNH32xXSk3 .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-9SiUdYMNH32xXSk3 .icon-shape rect,#mermaid-svg-9SiUdYMNH32xXSk3 .image-shape rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-9SiUdYMNH32xXSk3 .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-9SiUdYMNH32xXSk3 .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-9SiUdYMNH32xXSk3 :root{–mermaid-font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;}<\/p>\n

                            \u7a33\u5b9a\u6027\u4fdd\u969c<\/p>\n

                            <\/span><\/span><\/span><\/span><\/p>\n

                            \u7b56\u7565\u4f18\u5316<\/p>\n

                            <\/span><\/p>\n

                            \u4fe1\u4efb\u57df\u7ea6\u675f<\/p>\n

                            <\/span><\/p>\n

                            \u7ecf\u9a8c\u56de\u653e<\/p>\n

                            <\/span><\/p>\n

                            \u65e9\u505c\u673a\u5236<\/p>\n

                            <\/span><\/p>\n

                            \u63a2\u7d22-\u5229\u7528\u7b56\u7565<\/p>\n

                            <\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                            \u63a2\u7d22\u7b56\u7565<\/p>\n

                            <\/span><\/p>\n

                            Epsilon-\u8d2a\u5a6a<\/p>\n

                            <\/span><\/p>\n

                            UCB<\/p>\n

                            <\/span><\/p>\n

                            \u73bb\u5c14\u5179\u66fc<\/p>\n

                            <\/span><\/p>\n

                            \u597d\u5947\u5fc3\u9a71\u52a8<\/p>\n

                            <\/span><\/p>\n

                            \u8870\u51cfepsilon<\/p>\n

                            <\/span><\/p>\n

                            \u4e50\u89c2\u539f\u5219<\/p>\n

                            <\/span><\/p>\n

                            \u6e29\u5ea6\u8c03\u8282<\/p>\n

                            <\/span><\/p>\n

                            \u9884\u6d4b\u8bef\u5dee<\/p>\n

                            <\/span><\/p>\n

                            8 \u672a\u6765\u5c55\u671b\u4e0e\u6311\u6218<\/h2>\n

                            8.1 \u5f53\u524d\u7814\u7a76\u7684\u5c40\u9650\u6027<\/h3>\n

                            8.1.1 \u6837\u672c\u6548\u7387\u4e0e\u8ba1\u7b97\u6210\u672c<\/h4>\n

                            \u5c3d\u7ba1\u5f3a\u5316\u5b66\u4e60\u5728Agent\u5de5\u4f5c\u6d41\u4f18\u5316\u4e2d\u5c55\u73b0\u51fa\u5de8\u5927\u6f5c\u529b，\u4f46\u6837\u672c\u6548\u7387\u4f4e\u4e0b\u4ecd\u662f\u5236\u7ea6\u5176\u5b9e\u9645\u5e94\u7528\u7684\u4e3b\u8981\u74f6\u9888\u3002\u8bad\u7ec3\u4e00\u4e2a\u80fd\u591f\u5904\u7406\u590d\u6742\u4efb\u52a1\u7684Agent\u5f80\u5f80\u9700\u8981\u6570\u767e\u4e07\u751a\u81f3\u6570\u5343\u4e07\u6b21\u4ea4\u4e92，\u8fd9\u5728\u771f\u5b9e\u73af\u5883\u4e2d\u662f\u4e0d\u53ef\u63a5\u53d7\u7684[137]\u3002<\/p>\n

                            \u8ba1\u7b97\u6210\u672c\u540c\u6837\u662f\u4e00\u4e2a\u4e25\u5cfb\u6311\u6218\u3002\u5927\u578b\u8bed\u8a00\u6a21\u578b\u4f5c\u4e3aAgent\u7684\u63a8\u7406\u5f15\u64ce，\u6bcf\u6b21\u524d\u5411\u4f20\u64ad\u90fd\u9700\u8981\u5927\u91cf\u8ba1\u7b97\u8d44\u6e90\u3002\u7ed3\u5408\u5f3a\u5316\u5b66\u4e60\u7684\u591a\u8f6e\u8fed\u4ee3\u8bad\u7ec3，\u603b\u4f53\u8ba1\u7b97\u6210\u672c\u53ef\u80fd\u8fbe\u5230\u6570\u767e\u4e07\u7f8e\u5143\u3002\u8fd9\u79cd\u9ad8\u6210\u672c\u9650\u5236\u4e86\u7814\u7a76\u7684\u666e\u53ca\u548c\u6280\u672f\u7684 democratization[16]\u3002<\/p>\n

                            \u63d0\u5347\u6837\u672c\u6548\u7387\u7684\u53ef\u80fd\u65b9\u5411\u5305\u62ec：<\/p>\n

                              \n
                            • \u6a21\u578b-based RL：\u5b66\u4e60\u73af\u5883\u6a21\u578b，\u901a\u8fc7\u89c4\u5212\u51cf\u5c11\u771f\u5b9e\u4ea4\u4e92\u9700\u6c42<\/li>\n
                            • \u8fc1\u79fb\u5b66\u4e60：\u5c06\u5728\u76f8\u4f3c\u4efb\u52a1\u4e0a\u5b66\u5230\u7684\u77e5\u8bc6\u8fc1\u79fb\u5230\u65b0\u4efb\u52a1<\/li>\n
                            • \u5143\u5b66\u4e60：\u5b66\u4e60\u5982\u4f55\u5feb\u901f\u5b66\u4e60，\u4f7fAgent\u80fd\u591f\u8fc5\u901f\u9002\u5e94\u65b0\u73af\u5883<\/li>\n
                            • \u8bfe\u7a0b\u5b66\u4e60：\u4ece\u7b80\u5355\u4efb\u52a1\u5f00\u59cb，\u9010\u6b65\u589e\u52a0\u96be\u5ea6，\u52a0\u901f\u5b66\u4e60\u8fdb\u7a0b<\/li>\n<\/ul>\n

                              8.1.2 \u5956\u52b1\u8bbe\u8ba1\u7684\u5de5\u7a0b\u4f9d\u8d56<\/h4>\n

                              \u5f3a\u5316\u5b66\u4e60\u7684\u6027\u80fd\u5f88\u5927\u7a0b\u5ea6\u4e0a\u4f9d\u8d56\u4e8e\u5956\u52b1\u51fd\u6570\u7684\u8bbe\u8ba1\u3002\u5728Agent\u5de5\u4f5c\u6d41\u573a\u666f\u4e2d，\u5b9a\u4e49\u4e00\u4e2a\u65e2\u80fd\u51c6\u786e\u53cd\u6620\u4efb\u52a1\u76ee\u6807\u3001\u53c8\u80fd\u5f15\u5bfc\u6709\u6548\u5b66\u4e60\u7684\u5956\u52b1\u51fd\u6570\u6781\u5177\u6311\u6218\u6027[124]\u3002<\/p>\n

                              \u5956\u52b1\u8bbe\u8ba1\u9762\u4e34\u7684\u4e3b\u8981\u56f0\u96be\u5305\u62ec：<\/p>\n

                                \n
                              • \u7a00\u758f\u5956\u52b1：\u5927\u591a\u6570\u4e2d\u95f4\u6b65\u9aa4\u6ca1\u6709\u660e\u786e\u7684\u53cd\u9988，\u5bfc\u81f4\u5b66\u4e60\u4fe1\u53f7\u5f31<\/li>\n
                              • \u5956\u52b1\u4f5c\u5f0a（Reward Hacking）：Agent\u53ef\u80fd\u627e\u5230\u5956\u52b1\u51fd\u6570\u7684\u6f0f\u6d1e，\u4ee5\u975e\u9884\u671f\u65b9\u5f0f\u83b7\u5f97\u9ad8\u5956\u52b1<\/li>\n
                              • \u591a\u76ee\u6807\u6743\u8861：\u5b9e\u9645\u4efb\u52a1\u5f80\u5f80\u6d89\u53ca\u591a\u4e2a\u76ee\u6807，\u5982\u4f55\u5e73\u8861\u8fd9\u4e9b\u76ee\u6807\u7f3a\u4e4f\u7edf\u4e00\u6807\u51c6<\/li>\n
                              • \u9886\u57df\u7279\u5f02\u6027：\u4e0d\u540c\u4efb\u52a1\u9700\u8981\u4e0d\u540c\u7684\u5956\u52b1\u8bbe\u8ba1，\u96be\u4ee5\u901a\u7528\u5316<\/li>\n<\/ul>\n

                                \u8fc7\u7a0b\u5956\u52b1\u6a21\u578b（PRM）\u4e3a\u81ea\u52a8\u5956\u52b1\u5b66\u4e60\u63d0\u4f9b\u4e86\u65b9\u5411，\u4f46PRM\u672c\u8eab\u7684\u8bad\u7ec3\u4ecd\u9700\u8981\u5927\u91cf\u6807\u6ce8\u6570\u636e\u3002\u5f00\u53d1\u80fd\u591f\u4ece\u5c11\u91cf\u793a\u8303\u6216\u81ea\u7136\u8bed\u8a00\u6307\u4ee4\u4e2d\u81ea\u52a8\u63a8\u65ad\u5956\u52b1\u7684\u65b9\u6cd5，\u662f\u964d\u4f4e\u5de5\u7a0b\u4f9d\u8d56\u7684\u5173\u952e[56]\u3002<\/p>\n

                                8.1.3 \u6cdb\u5316\u80fd\u529b\u4e0e\u5206\u5e03\u5916\u573a\u666f<\/h4>\n

                                \u5f53\u524dAgent\u5de5\u4f5c\u6d41\u4f18\u5316\u65b9\u6cd5\u5728\u8bad\u7ec3\u5206\u5e03\u5185\u8868\u73b0\u826f\u597d，\u4f46\u9762\u5bf9\u5206\u5e03\u5916（Out-of-Distribution, OOD）\u573a\u666f\u65f6\u5f80\u5f80\u5931\u6548\u3002\u8fd9\u79cd\u6cdb\u5316\u80fd\u529b\u7684\u7f3a\u5931\u9650\u5236\u4e86Agent\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u7684\u53ef\u9760\u6027[141]\u3002<\/p>\n

                                \u6cdb\u5316\u80fd\u529b\u4e0d\u8db3\u7684\u539f\u56e0\u5305\u62ec：<\/p>\n

                                  \n
                                • \u8fc7\u62df\u5408\u8bad\u7ec3\u4efb\u52a1：Agent\u53ef\u80fd\u8bb0\u4f4f\u4e86\u8bad\u7ec3\u4efb\u52a1\u7684\u7279\u5b9a\u6a21\u5f0f，\u800c\u975e\u5b66\u4e60\u901a\u7528\u539f\u7406<\/li>\n
                                • \u7f3a\u4e4f\u7ec4\u5408\u6cdb\u5316：\u9762\u5bf9\u8bad\u7ec3\u65f6\u672a\u89c1\u8fc7\u7684\u64cd\u4f5c\u7ec4\u5408，Agent\u96be\u4ee5\u6709\u6548\u5e94\u5bf9<\/li>\n
                                • \u5bf9\u566a\u58f0\u654f\u611f：\u771f\u5b9e\u73af\u5883\u4e2d\u7684\u89c2\u6d4b\u566a\u58f0\u3001\u5de5\u5177\u6545\u969c\u7b49\u53ef\u80fd\u5bfc\u81f4Agent\u884c\u4e3a\u5f02\u5e38<\/li>\n<\/ul>\n

                                  \u63d0\u5347\u6cdb\u5316\u80fd\u529b\u9700\u8981：\u66f4\u4e30\u5bcc\u7684\u8bad\u7ec3\u6570\u636e\u3001\u66f4\u5f3a\u7684\u6b63\u5219\u5316\u6280\u672f\u3001\u663e\u5f0f\u7684\u56e0\u679c\u63a8\u7406\u80fd\u529b，\u4ee5\u53ca\u66f4\u9c81\u68d2\u7684\u7b56\u7565\u8868\u793a[42]\u3002<\/p>\n

                                  8.2 \u524d\u6cbf\u7814\u7a76\u65b9\u5411<\/h3>\n

                                  8.2.1 \u4e16\u754c\u6a21\u578b\u4e0e\u6a21\u578b\u9884\u6d4b\u63a7\u5236<\/h4>\n

                                  \u4e16\u754c\u6a21\u578b（World Model）\u662f\u5f3a\u5316\u5b66\u4e60\u7684\u524d\u6cbf\u65b9\u5411，\u5b83\u4f7fAgent\u80fd\u591f\u5b66\u4e60\u73af\u5883\u52a8\u6001，\u5728\u5185\u90e8\u6a21\u62df\u4e2d\u8fdb\u884c\u89c4\u5212\u548c\u51b3\u7b56\u3002\u4e0e\u5b66\u4e60\u5230\u7684\u7b56\u7565\u76f8\u6bd4，\u57fa\u4e8e\u4e16\u754c\u6a21\u578b\u7684\u89c4\u5212\u5177\u6709\u66f4\u597d\u7684\u6cdb\u5316\u80fd\u529b\u548c\u53ef\u89e3\u91ca\u6027[66]\u3002<\/p>\n

                                  \u4e16\u754c\u6a21\u578b\u7684\u6838\u5fc3\u7ec4\u4ef6\u5305\u62ec：<\/p>\n

                                    \n
                                  • \u72b6\u6001\u8868\u5f81\u6a21\u578b：\u5c06\u9ad8\u7ef4\u89c2\u6d4b\u538b\u7f29\u4e3a\u7d27\u51d1\u7684\u6f5c\u5728\u72b6\u6001<\/li>\n
                                  • \u8f6c\u79fb\u6a21\u578b：\u9884\u6d4b\u7ed9\u5b9a\u52a8\u4f5c\u540e\u7684\u4e0b\u4e00\u72b6\u6001<\/li>\n
                                  • \u5956\u52b1\u6a21\u578b：\u9884\u6d4b\u72b6\u6001-\u52a8\u4f5c\u5bf9\u7684\u5373\u65f6\u5956\u52b1<\/li>\n<\/ul>\n

                                    \u6709\u4e86\u4e16\u754c\u6a21\u578b，Agent\u53ef\u4ee5\u4f7f\u7528\u6a21\u578b\u9884\u6d4b\u63a7\u5236（Model Predictive Control, MPC）\u8fdb\u884c\u89c4\u5212\u3002MPC\u901a\u8fc7\u8499\u7279\u5361\u6d1b\u6811\u641c\u7d22（MCTS）\u6216\u4ea4\u53c9\u71b5\u65b9\u6cd5（CEM）\u5728\u6a21\u578b\u4e2d\u6a21\u62df\u591a\u6761\u8f68\u8ff9，\u9009\u62e9\u6700\u4f18\u52a8\u4f5c\u3002\u8fd9\u79cd\u65b9\u6cd5\u5c06\u5b66\u4e60\u4e0e\u89c4\u5212\u5206\u79bb，\u7b56\u7565\u53ef\u4ee5\u66f4\u7075\u6d3b\u5730\u9002\u5e94\u65b0\u76ee\u6807[61]\u3002<\/p>\n

                                    \u5728Agent\u5de5\u4f5c\u6d41\u573a\u666f\u4e2d，\u4e16\u754c\u6a21\u578b\u53ef\u4ee5\u9884\u6d4b\u4e0d\u540c\u64cd\u4f5c\u7684\u6548\u679c，\u5e2e\u52a9Agent\u8fdb\u884c\u524d\u77bb\u6027\u7684\u5de5\u4f5c\u6d41\u89c4\u5212\u3002\u4f8b\u5982，\u5728\u6267\u884c\u590d\u6742\u6570\u636e\u5206\u6790\u524d，Agent\u53ef\u4ee5\u5728\u4e16\u754c\u6a21\u578b\u4e2d\u6a21\u62df\u4e0d\u540c\u5206\u6790\u8def\u5f84，\u9009\u62e9\u6700\u53ef\u80fd\u6210\u529f\u7684\u65b9\u6848[145]\u3002<\/p>\n

                                    8.2.2 \u795e\u7ecf\u7b26\u53f7\u7ed3\u5408\u4e0e\u53ef\u89e3\u91ca\u6027<\/h4>\n

                                    \u7eaf\u795e\u7ecf\u7f51\u7edc\u65b9\u6cd5\u867d\u7136\u5728\u6a21\u5f0f\u8bc6\u522b\u65b9\u9762\u8868\u73b0\u51fa\u8272，\u4f46\u5728\u903b\u8f91\u63a8\u7406\u548c\u53ef\u89e3\u91ca\u6027\u65b9\u9762\u5b58\u5728\u4e0d\u8db3\u3002\u795e\u7ecf\u7b26\u53f7\u7ed3\u5408（Neuro-Symbolic Integration）\u65e8\u5728\u878d\u5408\u795e\u7ecf\u7f51\u7edc\u7684\u5b66\u4e60\u80fd\u529b\u548c\u7b26\u53f7\u7cfb\u7edf\u7684\u63a8\u7406\u80fd\u529b[62]\u3002<\/p>\n

                                    \u795e\u7ecf\u7b26\u53f7Agent\u7684\u5178\u578b\u67b6\u6784\u5305\u62ec：<\/p>\n

                                      \n
                                    • \u611f\u77e5\u6a21\u5757：\u795e\u7ecf\u7f51\u7edc\u5904\u7406\u539f\u59cb\u8f93\u5165，\u63d0\u53d6\u7ed3\u6784\u5316\u4fe1\u606f<\/li>\n
                                    • \u7b26\u53f7\u63a8\u7406\u5f15\u64ce：\u57fa\u4e8e\u903b\u8f91\u89c4\u5219\u8fdb\u884c\u663e\u5f0f\u63a8\u7406<\/li>\n
                                    • \u795e\u7ecf-\u7b26\u53f7\u63a5\u53e3：\u5c06\u795e\u7ecf\u8f93\u51fa\u8f6c\u6362\u4e3a\u7b26\u53f7\u8868\u793a，\u6216\u5c06\u7b26\u53f7\u89c4\u5219\u5d4c\u5165\u795e\u7ecf\u7f51\u7edc<\/li>\n<\/ul>\n

                                      \u53ef\u89e3\u91ca\u6027（Interpretability）\u662fAgent\u5de5\u4f5c\u6d41\u5728\u5b9e\u9645\u90e8\u7f72\u4e2d\u7684\u5173\u952e\u9700\u6c42\u3002\u7528\u6237\u9700\u8981\u7406\u89e3Agent\u7684\u51b3\u7b56\u4f9d\u636e，\u624d\u80fd\u4fe1\u4efb\u5e76\u6709\u6548\u76d1\u7763\u5176\u884c\u4e3a\u3002\u7b26\u53f7\u5316\u7684\u5de5\u4f5c\u6d41\u8868\u793a（\u5982\u6761\u4ef6-\u52a8\u4f5c\u89c4\u5219）\u6bd4\u795e\u7ecf\u7f51\u7edc\u6743\u91cd\u66f4\u5bb9\u6613\u7406\u89e3\u548c\u9a8c\u8bc1[137]\u3002<\/p>\n

                                      \u8fc7\u7a0b\u5956\u52b1\u6a21\u578b\u672c\u8eab\u5c31\u5177\u6709\u53ef\u89e3\u91ca\u6027\u4f18\u52bf\u2014\u2014\u5b83\u660e\u786e\u6307\u51fa\u4e86\u6bcf\u4e2a\u6b65\u9aa4\u7684\u8d28\u91cf\u8bc4\u4f30，\u5e2e\u52a9\u7528\u6237\u7406\u89e3Agent\u7684\u63a8\u7406\u8fc7\u7a0b\u3002\u672a\u6765\u7814\u7a76\u53ef\u4ee5\u8fdb\u4e00\u6b65\u63a2\u7d22\u5982\u4f55\u5c06PRM\u4e0e\u7b26\u53f7\u63a8\u7406\u7ed3\u5408，\u751f\u6210\u4eba\u7c7b\u53ef\u7406\u89e3\u7684\u5de5\u4f5c\u6d41\u89e3\u91ca[16]\u3002<\/p>\n

                                      8.2.3 \u6301\u7eed\u5b66\u4e60\u4e0e\u707e\u96be\u6027\u9057\u5fd8<\/h4>\n

                                      \u6301\u7eed\u5b66\u4e60（Continual Learning）\u7814\u7a76\u5982\u4f55\u4f7fAgent\u5728\u5b66\u4e60\u65b0\u4efb\u52a1\u7684\u540c\u65f6\u4fdd\u6301\u65e7\u4efb\u52a1\u7684\u80fd\u529b\u3002\u8fd9\u662f\u5b9e\u73b0\u771f\u6b63\u81ea\u4e3b\u8fdb\u5316\u7684\u5173\u952e\u2014\u2014Agent\u9700\u8981\u5728\u6574\u4e2a\u751f\u547d\u5468\u671f\u4e2d\u4e0d\u65ad\u79ef\u7d2f\u77e5\u8bc6，\u800c\u975e\u9488\u5bf9\u6bcf\u4e2a\u4efb\u52a1\u4ece\u5934\u8bad\u7ec3[124]\u3002<\/p>\n

                                      \u707e\u96be\u6027\u9057\u5fd8（Catastrophic Forgetting）\u662f\u6301\u7eed\u5b66\u4e60\u7684\u4e3b\u8981\u969c\u788d\u3002\u5f53\u795e\u7ecf\u7f51\u7edc\u9488\u5bf9\u65b0\u4efb\u52a1\u8bad\u7ec3\u65f6，\u53ef\u80fd\u8986\u76d6\u65e7\u4efb\u52a1\u7684\u6743\u91cd，\u5bfc\u81f4\u65e7\u4efb\u52a1\u6027\u80fd\u6025\u5267\u4e0b\u964d\u3002\u89e3\u51b3\u9057\u5fd8\u95ee\u9898\u7684\u4e3b\u8981\u7b56\u7565\u5305\u62ec：<\/p>\n

                                        \n
                                      • \u6b63\u5219\u5316\u65b9\u6cd5：\u9650\u5236\u91cd\u8981\u53c2\u6570\u7684\u53d8\u5316，\u5982EWC（Elastic Weight Consolidation）<\/li>\n
                                      • \u56de\u653e\u65b9\u6cd5：\u4fdd\u7559\u65e7\u4efb\u52a1\u6837\u672c，\u4e0e\u65b0\u4efb\u52a1\u4e00\u8d77\u8bad\u7ec3<\/li>\n
                                      • \u6a21\u5757\u5316\u67b6\u6784：\u4e3a\u4e0d\u540c\u4efb\u52a1\u4f7f\u7528\u4e0d\u540c\u5b50\u7f51\u7edc，\u907f\u514d\u5e72\u6270<\/li>\n
                                      • \u5143\u5b66\u4e60\u65b9\u6cd5：\u5b66\u4e60\u4e0d\u6613\u9057\u5fd8\u7684\u8868\u793a<\/li>\n<\/ul>\n

                                        \u5728Agent\u5de5\u4f5c\u6d41\u4f18\u5316\u4e2d，\u6301\u7eed\u5b66\u4e60\u610f\u5473\u7740Agent\u80fd\u591f\u4ece\u6bcf\u4e2a\u65b0\u4efb\u52a1\u4e2d\u5b66\u4e60，\u4e0d\u65ad\u6539\u8fdb\u5176SOP\u5e93\u3002\u6709\u6548\u7684\u6301\u7eed\u5b66\u4e60\u673a\u5236\u5c06\u4f7fAgent\u8d8a\u7528\u8d8a\u806a\u660e，\u771f\u6b63\u5b9e\u73b0\u81ea\u6211\u8fdb\u5316[56]\u3002<\/p>\n

                                        8.3 \u5e94\u7528\u524d\u666f\u4e0e\u793e\u4f1a\u5f71\u54cd<\/h3>\n

                                        8.3.1 \u81ea\u52a8\u5316\u5de5\u4f5c\u6d41\u7f16\u6392\u7684\u5de5\u4e1a\u5e94\u7528<\/h4>\n

                                        Agent\u5de5\u4f5c\u6d41\u81ea\u6211\u8fdb\u5316\u6280\u672f\u5728\u5de5\u4e1a\u9886\u57df\u5177\u6709\u5e7f\u9614\u7684\u5e94\u7528\u524d\u666f\u3002\u5728\u8f6f\u4ef6\u5f00\u53d1\u4e2d，\u80fd\u591f\u81ea\u4e3b\u89c4\u5212\u3001\u7f16\u7801\u3001\u6d4b\u8bd5\u3001\u90e8\u7f72\u7684AI\u5de5\u7a0b\u5e08\u5c06\u5927\u5e45\u63d0\u5347\u5f00\u53d1\u6548\u7387；\u5728\u5ba2\u6237\u670d\u52a1\u4e2d，\u80fd\u591f\u52a8\u6001\u8c03\u6574\u7b56\u7565\u7684\u667a\u80fd\u5ba2\u670d\u5c06\u63d0\u4f9b\u66f4\u4f18\u8d28\u7684\u7528\u6237\u4f53\u9a8c；\u5728\u79d1\u5b66\u7814\u7a76\u4e2d，\u80fd\u591f\u81ea\u4e3b\u8bbe\u8ba1\u5b9e\u9a8c\u3001\u5206\u6790\u6570\u636e\u7684AI\u52a9\u624b\u5c06\u52a0\u901f\u53d1\u73b0\u8fdb\u7a0b[141]\u3002<\/p>\n

                                        \u88683 Agent\u5de5\u4f5c\u6d41\u81ea\u6211\u8fdb\u5316\u6280\u672f\u7684\u6f5c\u5728\u5e94\u7528\u9886\u57df<\/p>\n\n\u5e94\u7528\u9886\u57df\u5f53\u524d\u75db\u70b9Agent\u89e3\u51b3\u65b9\u6848\u9884\u671f\u6548\u76ca<\/tr>\n\n\n\n\n\n\n
                                        \u8f6f\u4ef6\u5f00\u53d1<\/td>\n\u91cd\u590d\u6027\u7f16\u7801\u4efb\u52a1\u8017\u65f6\u3001\u4eba\u5de5\u6d4b\u8bd5\u8986\u76d6\u4e0d\u5168<\/td>\n\u81ea\u52a8\u751f\u6210\u4ee3\u7801\u3001\u81ea\u4e3b\u6d4b\u8bd5\u4fee\u590d<\/td>\n\u5f00\u53d1\u6548\u7387\u63d0\u534750%+，\u7f3a\u9677\u7387\u964d\u4f4e30%<\/td>\n<\/tr>\n
                                        \u5ba2\u6237\u670d\u52a1<\/td>\n\u4eba\u5de5\u5ba2\u670d\u6210\u672c\u9ad8\u3001\u54cd\u5e94\u6162\u3001\u8d28\u91cf\u4e0d\u7a33\u5b9a<\/td>\n7×24\u5c0f\u65f6\u667a\u80fd\u670d\u52a1\u3001\u4e2a\u6027\u5316\u5e94\u7b54<\/td>\n\u6210\u672c\u964d\u4f4e60%，\u6ee1\u610f\u5ea6\u63d0\u534720%<\/td>\n<\/tr>\n
                                        \u6570\u636e\u5206\u6790<\/td>\n\u6570\u636e\u6e05\u6d17\u7e41\u7410\u3001\u5206\u6790\u6a21\u578b\u9009\u62e9\u56f0\u96be<\/td>\n\u81ea\u52a8\u6570\u636e\u9884\u5904\u7406\u3001\u6a21\u578b\u81ea\u52a8\u8c03\u4f18<\/td>\n\u5206\u6790\u5468\u671f\u7f29\u77ed70%<\/td>\n<\/tr>\n
                                        \u5185\u5bb9\u521b\u4f5c<\/td>\n\u521b\u610f\u67af\u7aed\u3001\u98ce\u683c\u4e00\u81f4\u6027\u96be\u4fdd\u8bc1<\/td>\n\u8f85\u52a9\u521b\u610f\u751f\u6210\u3001\u98ce\u683c\u81ea\u52a8\u9002\u914d<\/td>\n\u4ea7\u51fa\u6548\u7387\u63d0\u53473-5\u500d<\/td>\n<\/tr>\n
                                        \u6559\u80b2\u57f9\u8bad<\/td>\n\u4e2a\u6027\u5316\u6559\u5b66\u96be\u4ee5\u89c4\u6a21\u5316<\/td>\n\u81ea\u9002\u5e94\u5b66\u4e60\u8def\u5f84\u3001\u667a\u80fd\u7b54\u7591<\/td>\n\u5b66\u4e60\u6548\u679c\u63d0\u534740%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                                        8.3.2 \u4eba\u673a\u534f\u4f5c\u7684\u65b0\u8303\u5f0f<\/h4>\n

                                        Agent\u5de5\u4f5c\u6d41\u81ea\u6211\u8fdb\u5316\u5c06\u91cd\u5851\u4eba\u673a\u534f\u4f5c\u6a21\u5f0f\u3002\u4f20\u7edf\u7684\u4eba\u673a\u4ea4\u4e92\u662f\u547d\u4ee4-\u54cd\u5e94\u5f0f\u7684：\u4eba\u53d1\u51fa\u6307\u4ee4，\u673a\u5668\u6267\u884c\u3002\u672a\u6765\u7684\u534f\u4f5c\u5c06\u66f4\u52a0\u5bf9\u7b49\u548c\u52a8\u6001：\u4eba\u4e0eAgent\u5171\u540c\u89c4\u5212\u4efb\u52a1\u3001\u5206\u5de5\u6267\u884c\u3001\u76f8\u4e92\u5b66\u4e60[42]\u3002<\/p>\n

                                        \u5728\u4eba\u673a\u534f\u4f5c\u4e2d，Agent\u9700\u8981\u5177\u5907\u4ee5\u4e0b\u80fd\u529b：<\/p>\n

                                          \n
                                        • \u610f\u56fe\u7406\u89e3：\u51c6\u786e\u7406\u89e3\u4eba\u7c7b\u7684\u76ee\u6807\u548c\u7ea6\u675f<\/li>\n
                                        • \u4e3b\u52a8\u6c9f\u901a：\u5728\u4e0d\u786e\u5b9a\u65f6\u4e3b\u52a8\u8be2\u95ee，\u5728\u6267\u884c\u4e2d\u4e3b\u52a8\u6c47\u62a5<\/li>\n
                                        • \u9002\u5e94\u6027：\u6839\u636e\u4eba\u7c7b\u53cd\u9988\u5feb\u901f\u8c03\u6574\u884c\u4e3a<\/li>\n
                                        • \u53ef\u6559\u6027：\u80fd\u591f\u4ece\u4eba\u7c7b\u793a\u8303\u548c\u7ea0\u6b63\u4e2d\u5b66\u4e60<\/li>\n<\/ul>\n

                                          \u5f3a\u5316\u5b66\u4e60\u4e3a\u8bad\u7ec3\u534f\u4f5c\u578bAgent\u63d0\u4f9b\u4e86\u6846\u67b6\u3002\u901a\u8fc7\u5c06\u4eba\u7c7b\u5efa\u6a21\u4e3a\u73af\u5883\u7684\u4e00\u90e8\u5206，Agent\u53ef\u4ee5\u5b66\u4e60\u6700\u5927\u5316\u8054\u5408\u4efb\u52a1\u6210\u529f\u7387\u7684\u6700\u4f18\u7b56\u7565\u3002\u9006\u5f3a\u5316\u5b66\u4e60（Inverse RL）\u8fd8\u53ef\u4ee5\u4ece\u4eba\u7c7b\u884c\u4e3a\u4e2d\u63a8\u65ad\u5956\u52b1\u51fd\u6570，\u4f7fAgent\u66f4\u597d\u5730\u5bf9\u9f50\u4eba\u7c7b\u610f\u56fe[66]\u3002<\/p>\n

                                          8.3.3 \u5b89\u5168\u5bf9\u9f50\u4e0e\u4ef7\u503c\u7ea6\u675f<\/h4>\n

                                          \u968f\u7740Agent\u81ea\u4e3b\u6027\u7684\u63d0\u5347，\u5b89\u5168\u5bf9\u9f50（Safety Alignment）\u6210\u4e3a\u4e0d\u53ef\u5ffd\u89c6\u7684\u95ee\u9898\u3002\u81ea\u6211\u8fdb\u5316\u7684Agent\u53ef\u80fd\u53d1\u73b0\u4eba\u7c7b\u672a\u9884\u671f\u5230\u7684\u7b56\u7565，\u5176\u4e2d\u4e00\u4e9b\u53ef\u80fd\u662f\u6709\u5bb3\u7684\u6216\u8fdd\u80cc\u4eba\u7c7b\u4ef7\u503c\u89c2\u7684[61]\u3002<\/p>\n

                                          \u786e\u4fddAgent\u5b89\u5168\u7684\u5173\u952e\u63aa\u65bd\u5305\u62ec：<\/p>\n

                                            \n
                                          • \u4ef7\u503c\u5bf9\u9f50：\u5c06\u4eba\u7c7b\u4ef7\u503c\u89c2\u7f16\u7801\u4e3a\u7ea6\u675f\u6761\u4ef6\u6216\u5956\u52b1\u51fd\u6570\u7684\u4e00\u90e8\u5206<\/li>\n
                                          • \u80fd\u529b\u63a7\u5236：\u9650\u5236Agent\u7684\u884c\u52a8\u8303\u56f4，\u9632\u6b62\u5176\u83b7\u5f97\u5371\u9669\u80fd\u529b<\/li>\n
                                          • \u53ef\u4e2d\u65ad\u6027：\u786e\u4fdd\u4eba\u7c7b\u53ef\u4ee5\u968f\u65f6\u63a5\u7ba1\u6216\u505c\u6b62Agent<\/li>\n
                                          • \u900f\u660e\u6027：Agent\u80fd\u591f\u89e3\u91ca\u5176\u884c\u4e3a\u4f9d\u636e，\u63a5\u53d7\u4eba\u7c7b\u5ba1\u67e5<\/li>\n<\/ul>\n

                                            Constitutional AI\u7b49\u65b9\u6cd5\u5c1d\u8bd5\u901a\u8fc7\u539f\u5219\u7ea6\u675f\u5f15\u5bfcAgent\u884c\u4e3a\u3002Agent\u5728\u8bad\u7ec3\u65f6\u4e0d\u4ec5\u6700\u5927\u5316\u4efb\u52a1\u5956\u52b1，\u8fd8\u9700\u9075\u5b88\u9884\u5b9a\u4e49\u7684\u884c\u4e3a\u51c6\u5219\u3002\u5f3a\u5316\u5b66\u4e60\u4e2d\u7684\u7ea6\u675fMDP（Constrained MDP）\u6846\u67b6\u4e3a\u5f62\u5f0f\u5316\u5b89\u5168\u7ea6\u675f\u63d0\u4f9b\u4e86\u6570\u5b66\u5de5\u5177[145]\u3002<\/p>\n

                                            Agent\u5de5\u4f5c\u6d41\u81ea\u6211\u8fdb\u5316\u6280\u672f\u7684\u53d1\u5c55\u5fc5\u987b\u4e0e\u5b89\u5168\u7814\u7a76\u540c\u6b65\u63a8\u8fdb\u3002\u53ea\u6709\u5728\u786e\u4fdd\u53ef\u63a7\u3001\u53ef\u4fe1\u7684\u524d\u63d0\u4e0b，\u8fd9\u9879\u6280\u672f\u624d\u80fd\u771f\u6b63\u9020\u798f\u793e\u4f1a\u3002<\/p>\n

                                            #mermaid-svg-MSZpvMoWBHaPfPcC{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-MSZpvMoWBHaPfPcC .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-MSZpvMoWBHaPfPcC .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-MSZpvMoWBHaPfPcC .error-icon{fill:#552222;}#mermaid-svg-MSZpvMoWBHaPfPcC .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-MSZpvMoWBHaPfPcC .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-MSZpvMoWBHaPfPcC .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-MSZpvMoWBHaPfPcC .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-MSZpvMoWBHaPfPcC .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-MSZpvMoWBHaPfPcC .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-MSZpvMoWBHaPfPcC .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-MSZpvMoWBHaPfPcC .marker{fill:#333333;stroke:#333333;}#mermaid-svg-MSZpvMoWBHaPfPcC .marker.cross{stroke:#333333;}#mermaid-svg-MSZpvMoWBHaPfPcC svg{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-MSZpvMoWBHaPfPcC p{margin:0;}#mermaid-svg-MSZpvMoWBHaPfPcC .label{font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;color:#333;}#mermaid-svg-MSZpvMoWBHaPfPcC .cluster-label text{fill:#333;}#mermaid-svg-MSZpvMoWBHaPfPcC .cluster-label span{color:#333;}#mermaid-svg-MSZpvMoWBHaPfPcC .cluster-label span p{background-color:transparent;}#mermaid-svg-MSZpvMoWBHaPfPcC .label text,#mermaid-svg-MSZpvMoWBHaPfPcC span{fill:#333;color:#333;}#mermaid-svg-MSZpvMoWBHaPfPcC .node rect,#mermaid-svg-MSZpvMoWBHaPfPcC .node circle,#mermaid-svg-MSZpvMoWBHaPfPcC .node ellipse,#mermaid-svg-MSZpvMoWBHaPfPcC .node polygon,#mermaid-svg-MSZpvMoWBHaPfPcC .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-MSZpvMoWBHaPfPcC .rough-node .label text,#mermaid-svg-MSZpvMoWBHaPfPcC .node .label text,#mermaid-svg-MSZpvMoWBHaPfPcC .image-shape .label,#mermaid-svg-MSZpvMoWBHaPfPcC .icon-shape .label{text-anchor:middle;}#mermaid-svg-MSZpvMoWBHaPfPcC .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-MSZpvMoWBHaPfPcC .rough-node .label,#mermaid-svg-MSZpvMoWBHaPfPcC .node .label,#mermaid-svg-MSZpvMoWBHaPfPcC .image-shape .label,#mermaid-svg-MSZpvMoWBHaPfPcC .icon-shape .label{text-align:center;}#mermaid-svg-MSZpvMoWBHaPfPcC .node.clickable{cursor:pointer;}#mermaid-svg-MSZpvMoWBHaPfPcC .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-MSZpvMoWBHaPfPcC .arrowheadPath{fill:#333333;}#mermaid-svg-MSZpvMoWBHaPfPcC .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-MSZpvMoWBHaPfPcC .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-MSZpvMoWBHaPfPcC .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-MSZpvMoWBHaPfPcC .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-MSZpvMoWBHaPfPcC .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-MSZpvMoWBHaPfPcC .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-MSZpvMoWBHaPfPcC .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-MSZpvMoWBHaPfPcC .cluster text{fill:#333;}#mermaid-svg-MSZpvMoWBHaPfPcC .cluster span{color:#333;}#mermaid-svg-MSZpvMoWBHaPfPcC div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-MSZpvMoWBHaPfPcC .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-MSZpvMoWBHaPfPcC rect.text{fill:none;stroke-width:0;}#mermaid-svg-MSZpvMoWBHaPfPcC .icon-shape,#mermaid-svg-MSZpvMoWBHaPfPcC .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-MSZpvMoWBHaPfPcC .icon-shape p,#mermaid-svg-MSZpvMoWBHaPfPcC .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-MSZpvMoWBHaPfPcC .icon-shape rect,#mermaid-svg-MSZpvMoWBHaPfPcC .image-shape rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-MSZpvMoWBHaPfPcC .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-MSZpvMoWBHaPfPcC .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-MSZpvMoWBHaPfPcC :root{–mermaid-font-family:\\”trebuchet ms\\”,verdana,arial,sans-serif;}<\/p>\n

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                                            \u53c2\u8003\u6587\u732e<\/h2>\n

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