{"id":79332,"date":"2026-03-01T19:33:25","date_gmt":"2026-03-01T11:33:25","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/79332.html"},"modified":"2026-03-01T19:33:25","modified_gmt":"2026-03-01T11:33:25","slug":"fedavg%ef%bc%9a%e5%9f%ba%e4%ba%8e%e5%8e%bb%e4%b8%ad%e5%bf%83%e5%8c%96%e6%95%b0%e6%8d%ae%e7%9a%84%e6%b7%b1%e5%ba%a6%e7%bd%91%e7%bb%9c%e9%80%9a%e4%bf%a1%e9%ab%98%e6%95%88%e5%ad%a6%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/79332.html","title":{"rendered":"FedAvg\uff1a\u57fa\u4e8e\u53bb\u4e2d\u5fc3\u5316\u6570\u636e\u7684\u6df1\u5ea6\u7f51\u7edc\u901a\u4fe1\u9ad8\u6548\u5b66\u4e60"},"content":{"rendered":"<h2>\u57fa\u4e8e\u53bb\u4e2d\u5fc3\u5316\u6570\u636e\u7684\u6df1\u5ea6\u7f51\u7edc\u901a\u4fe1\u9ad8\u6548\u5b66\u4e60<\/h2>\n<p>(Communication-Efficient Learning of Deep Networks from Decentralized Data)<\/p>\n<h4>\u6458\u8981 (Abstract)<\/h4>\n<p>\u73b0\u4ee3\u79fb\u52a8\u8bbe\u5907\u80fd\u591f\u8bbf\u95ee\u5927\u91cf\u9002\u5408\u7528\u4e8e\u8bad\u7ec3\u6a21\u578b\u7684\u6570\u636e&#xff0c;\u8fd9\u4e9b\u6a21\u578b\u53cd\u8fc7\u6765\u53c8\u80fd\u6781\u5927\u5730\u6539\u5584\u8bbe\u5907\u4e0a\u7684\u7528\u6237\u4f53\u9a8c\u3002\u4f8b\u5982&#xff0c;\u8bed\u8a00\u6a21\u578b\u53ef\u4ee5\u6539\u5584\u8bed\u97f3\u8bc6\u522b\u548c\u6587\u672c\u8f93\u5165&#xff0c;\u56fe\u50cf\u6a21\u578b\u53ef\u4ee5\u81ea\u52a8\u6311\u9009\u4f18\u8d28\u7167\u7247\u3002\u7136\u800c&#xff0c;\u8fd9\u4e9b\u4e30\u5bcc\u7684\u6570\u636e\u5f80\u5f80\u5177\u6709\u9690\u79c1\u654f\u611f\u6027\u3001\u6570\u91cf\u5e9e\u5927\u6216\u4e24\u8005\u517c\u5177&#xff0c;\u8fd9\u53ef\u80fd\u4f1a\u963b\u788d\u6211\u4eec\u5c06\u5176\u8bb0\u5f55\u5230\u6570\u636e\u4e2d\u5fc3\u5e76\u4f7f\u7528\u5e38\u89c4\u65b9\u6cd5\u5728\u90a3\u91cc\u8fdb\u884c\u8bad\u7ec3\u3002\u6211\u4eec\u63d0\u5021\u4e00\u79cd\u66ff\u4ee3\u65b9\u6848&#xff0c;\u5373\u8ba9\u8bad\u7ec3\u6570\u636e\u4fdd\u7559\u5728\u5206\u5e03\u5f0f\u7684\u79fb\u52a8\u8bbe\u5907\u4e0a&#xff0c;\u5e76\u901a\u8fc7\u805a\u5408\u672c\u5730\u8ba1\u7b97\u7684\u66f4\u65b0\u6765\u5b66\u4e60\u4e00\u4e2a\u5171\u4eab\u6a21\u578b\u3002\u6211\u4eec\u5c06\u8fd9\u79cd\u53bb\u4e2d\u5fc3\u5316\u7684\u65b9\u6cd5\u79f0\u4e3a\u8054\u90a6\u5b66\u4e60 (Federated Learning)\u3002<\/p>\n<p>\u6211\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u57fa\u4e8e\u8fed\u4ee3\u6a21\u578b\u5e73\u5747\u7684\u6df1\u5ea6\u7f51\u7edc\u8054\u90a6\u5b66\u4e60\u7684\u5b9e\u7528\u65b9\u6cd5&#xff0c;\u5e76\u8fdb\u884c\u4e86\u5e7f\u6cdb\u7684\u5b9e\u8bc1\u8bc4\u4f30&#xff0c;\u8003\u5bdf\u4e86\u4e94\u79cd\u4e0d\u540c\u7684\u6a21\u578b\u67b6\u6784\u548c\u56db\u4e2a\u6570\u636e\u96c6\u3002\u8fd9\u4e9b\u5b9e\u9a8c\u8868\u660e&#xff0c;\u8be5\u65b9\u6cd5\u5bf9\u4e0d\u5e73\u8861\u548c\u975e\u72ec\u7acb\u540c\u5206\u5e03&#xff08;non-IID&#xff09;\u7684\u6570\u636e\u5206\u5e03\u5177\u6709\u9c81\u68d2\u6027&#xff0c;\u800c\u8fd9\u4e9b\u6570\u636e\u5206\u5e03\u6b63\u662f\u6b64\u7c7b\u573a\u666f\u7684\u51b3\u5b9a\u6027\u7279\u5f81\u3002\u901a\u4fe1\u6210\u672c\u662f\u9996\u8981\u7684\u7ea6\u675f\u6761\u4ef6&#xff0c;\u6211\u4eec\u8bc1\u660e\u4e86\u4e0e\u540c\u6b65\u968f\u673a\u68af\u5ea6\u4e0b\u964d&#xff08;SGD&#xff09;\u76f8\u6bd4&#xff0c;\u8be5\u65b9\u6cd5\u5c06\u6240\u9700\u7684\u901a\u4fe1\u8f6e\u6570\u51cf\u5c11\u4e86 10 \u5230 100 \u500d\u3002<\/p>\n<hr \/>\n<h4>1 \u5f15\u8a00 (Introduction)<\/h4>\n<p>\u624b\u673a\u548c\u5e73\u677f\u7535\u8111\u65e5\u76ca\u6210\u4e3a\u8bb8\u591a\u4eba\u7684\u4e3b\u8981\u8ba1\u7b97\u8bbe\u5907 [30, 2]\u3002\u8fd9\u4e9b\u8bbe\u5907\u4e0a\u5f3a\u5927\u7684\u4f20\u611f\u5668&#xff08;\u5305\u62ec\u6444\u50cf\u5934\u3001\u9ea6\u514b\u98ce\u548c GPS&#xff09;&#xff0c;\u52a0\u4e0a\u5b83\u4eec\u7ecf\u5e38\u88ab\u968f\u8eab\u643a\u5e26\u7684\u4e8b\u5b9e&#xff0c;\u610f\u5473\u7740\u5b83\u4eec\u80fd\u591f\u83b7\u53d6\u524d\u6240\u672a\u6709\u7684\u5927\u91cf\u6570\u636e&#xff0c;\u5176\u4e2d\u5927\u90e8\u5206\u672c\u8d28\u4e0a\u662f\u79c1\u5bc6\u7684\u3002\u5728\u8fd9\u4e9b\u6570\u636e\u4e0a\u5b66\u4e60\u5230\u7684\u6a21\u578b\u6709\u671b\u901a\u8fc7\u9a71\u52a8\u66f4\u667a\u80fd\u7684\u5e94\u7528\u6765\u6781\u5927\u5730\u63d0\u9ad8\u53ef\u7528\u6027&#xff0c;\u4f46\u6570\u636e\u7684\u654f\u611f\u6027\u610f\u5473\u7740\u5c06\u5b83\u4eec\u96c6\u4e2d\u5b58\u50a8\u5b58\u5728\u7740\u98ce\u9669\u548c\u8d23\u4efb\u3002<\/p>\n<p>\u6211\u4eec\u7814\u7a76\u4e86\u4e00\u79cd\u5b66\u4e60\u6280\u672f&#xff0c;\u5b83\u5141\u8bb8\u7528\u6237\u5171\u540c\u4eab\u53d7\u4ece\u8fd9\u4e9b\u4e30\u5bcc\u6570\u636e\u4e2d\u8bad\u7ec3\u51fa\u7684\u5171\u4eab\u6a21\u578b\u7684\u597d\u5904&#xff0c;\u800c\u65e0\u9700\u96c6\u4e2d\u5b58\u50a8\u6570\u636e\u3002\u6211\u4eec\u5c06\u6211\u4eec\u7684\u65b9\u6cd5\u79f0\u4e3a\u8054\u90a6\u5b66\u4e60 (Federated Learning)&#xff0c;\u56e0\u4e3a\u5b66\u4e60\u4efb\u52a1\u662f\u7531\u4e00\u4e2a\u677e\u6563\u7684\u53c2\u4e0e\u8bbe\u5907\u8054\u90a6&#xff08;\u6211\u4eec\u79f0\u4e4b\u4e3a\u5ba2\u6237\u7aef (clients)&#xff09;\u6765\u89e3\u51b3\u7684&#xff0c;\u8fd9\u4e9b\u8bbe\u5907\u7531\u4e00\u4e2a\u4e2d\u592e\u670d\u52a1\u5668 (server)\u534f\u8c03\u3002\u6bcf\u4e2a\u5ba2\u6237\u7aef\u90fd\u6709\u4e00\u4e2a\u6c38\u8fdc\u4e0d\u4f1a\u4e0a\u4f20\u5230\u670d\u52a1\u5668\u7684\u672c\u5730\u8bad\u7ec3\u6570\u636e\u96c6\u3002\u76f8\u53cd&#xff0c;\u6bcf\u4e2a\u5ba2\u6237\u7aef\u4f1a\u8ba1\u7b97\u5bf9\u670d\u52a1\u5668\u7ef4\u62a4\u7684\u5f53\u524d\u5168\u5c40\u6a21\u578b\u7684\u4e00\u4e2a\u66f4\u65b0&#xff0c;\u5e76\u4e14\u4ec5\u4f20\u9012\u8fd9\u4e2a\u66f4\u65b0\u3002\u8fd9\u662f 2012 \u5e74\u767d\u5bab\u5173\u4e8e\u6d88\u8d39\u8005\u6570\u636e\u9690\u79c1\u62a5\u544a\u4e2d\u63d0\u51fa\u7684\u805a\u7126\u6536\u96c6 (focused collection) \u6216\u6570\u636e\u6700\u5c0f\u5316 (data minimization) \u539f\u5219\u7684\u76f4\u63a5\u5e94\u7528 [39]\u3002\u7531\u4e8e\u8fd9\u4e9b\u66f4\u65b0\u4ec5\u7528\u4e8e\u6539\u8fdb\u5f53\u524d\u6a21\u578b&#xff0c;\u56e0\u6b64\u4e00\u65e6\u5e94\u7528\u540e\u5c31\u6ca1\u6709\u7406\u7531\u518d\u5b58\u50a8\u5b83\u4eec\u3002<\/p>\n<p>\u8fd9\u79cd\u65b9\u6cd5\u7684\u4e00\u4e2a\u4e3b\u8981\u4f18\u52bf\u662f\u5c06\u6a21\u578b\u8bad\u7ec3\u4e0e\u76f4\u63a5\u8bbf\u95ee\u539f\u59cb\u8bad\u7ec3\u6570\u636e\u7684\u9700\u6c42\u89e3\u8026\u3002\u663e\u7136&#xff0c;\u4ecd\u7136\u9700\u8981\u5bf9\u534f\u8c03\u8bad\u7ec3\u7684\u670d\u52a1\u5668\u7ed9\u4e88\u4e00\u5b9a\u7684\u4fe1\u4efb\u3002\u7136\u800c&#xff0c;\u5bf9\u4e8e\u53ef\u4ee5\u6839\u636e\u6bcf\u4e2a\u5ba2\u6237\u7aef\u53ef\u7528\u6570\u636e\u6765\u6307\u5b9a\u8bad\u7ec3\u76ee\u6807\u7684\u5e94\u7528&#xff0c;\u8054\u90a6\u5b66\u4e60\u901a\u8fc7\u5c06\u653b\u51fb\u9762\u9650\u5236\u5728\u4ec5\u8bbe\u5907\u5c42\u9762&#xff0c;\u800c\u4e0d\u662f\u8bbe\u5907\u548c\u4e91\u7aef&#xff0c;\u53ef\u4ee5\u663e\u8457\u964d\u4f4e\u9690\u79c1\u548c\u5b89\u5168\u98ce\u9669\u3002<\/p>\n<p>\u6211\u4eec\u7684\u4e3b\u8981\u8d21\u732e\u6709&#xff1a;1) \u5c06\u79fb\u52a8\u8bbe\u5907\u4e0a\u57fa\u4e8e\u53bb\u4e2d\u5fc3\u5316\u6570\u636e\u7684\u8bad\u7ec3\u95ee\u9898\u786e\u7acb\u4e3a\u4e00\u4e2a\u91cd\u8981\u7684\u7814\u7a76\u65b9\u5411&#xff1b;2) \u9009\u62e9\u4e86\u4e00\u79cd\u53ef\u4ee5\u76f4\u63a5\u5e94\u7528\u4e8e\u6b64\u573a\u666f\u7684\u7b80\u5355\u5b9e\u7528\u7684\u7b97\u6cd5&#xff1b;3) \u5bf9\u6240\u63d0\u51fa\u7684\u65b9\u6cd5\u8fdb\u884c\u4e86\u5e7f\u6cdb\u7684\u5b9e\u8bc1\u8bc4\u4f30\u3002\u66f4\u5177\u4f53\u5730\u8bf4&#xff0c;\u6211\u4eec\u5f15\u5165\u4e86 FederatedAveraging \u7b97\u6cd5&#xff0c;\u5b83\u5c06\u6bcf\u4e2a\u5ba2\u6237\u7aef\u4e0a\u7684\u672c\u5730\u968f\u673a\u68af\u5ea6\u4e0b\u964d&#xff08;SGD&#xff09;\u4e0e\u6267\u884c\u6a21\u578b\u5e73\u5747\u7684\u670d\u52a1\u5668\u76f8\u7ed3\u5408\u3002\u6211\u4eec\u5bf9\u8be5\u7b97\u6cd5\u8fdb\u884c\u4e86\u5927\u91cf\u5b9e\u9a8c&#xff0c;\u8bc1\u660e\u5b83\u5bf9\u4e0d\u5e73\u8861\u548c\u975e\u72ec\u7acb\u540c\u5206\u5e03&#xff08;non-IID&#xff09;\u7684\u6570\u636e\u5206\u5e03\u5177\u6709\u9c81\u68d2\u6027&#xff0c;\u5e76\u4e14\u80fd\u591f\u5c06\u53bb\u4e2d\u5fc3\u5316\u6570\u636e\u4e0a\u8bad\u7ec3\u6df1\u5ea6\u7f51\u7edc\u6240\u9700\u7684\u901a\u4fe1\u8f6e\u6570\u51cf\u5c11\u6570\u4e2a\u6570\u91cf\u7ea7\u3002<\/p>\n<hr \/>\n<h4>\u8054\u90a6\u5b66\u4e60 (Federated Learning)<\/h4>\n<p>\u975e\u5e38\u9002\u5408\u8054\u90a6\u5b66\u4e60\u7684\u95ee\u9898\u5177\u6709\u4ee5\u4e0b\u5c5e\u6027&#xff1a;1) \u4f7f\u7528\u79fb\u52a8\u8bbe\u5907\u4e0a\u7684\u771f\u5b9e\u4e16\u754c\u6570\u636e\u8fdb\u884c\u8bad\u7ec3&#xff0c;\u76f8\u6bd4\u4e8e\u4f7f\u7528\u6570\u636e\u4e2d\u5fc3\u4e2d\u901a\u5e38\u53ef\u7528\u7684\u4ee3\u7406\u6570\u636e&#xff0c;\u5177\u6709\u660e\u663e\u7684\u4f18\u52bf\u30022) \u8fd9\u4e9b\u6570\u636e\u5177\u6709\u9690\u79c1\u654f\u611f\u6027\u6216\u4f53\u91cf\u5e9e\u5927&#xff08;\u76f8\u5bf9\u4e8e\u6a21\u578b\u5927\u5c0f\u800c\u8a00&#xff09;&#xff0c;\u56e0\u6b64\u4ec5\u4e3a\u4e86\u6a21\u578b\u8bad\u7ec3\u7684\u76ee\u7684\u5c06\u5176\u8bb0\u5f55\u5230\u6570\u636e\u4e2d\u5fc3\u662f\u4e0d\u53ef\u53d6\u7684&#xff08;\u8fd9\u7b26\u5408\u805a\u7126\u6536\u96c6\u539f\u5219&#xff09;\u30023) \u5bf9\u4e8e\u76d1\u7763\u5b66\u4e60\u4efb\u52a1&#xff0c;\u6570\u636e\u4e0a\u7684\u6807\u7b7e\u53ef\u4ee5\u4ece\u7528\u6237\u4ea4\u4e92\u4e2d\u81ea\u7136\u5730\u63a8\u65ad\u51fa\u6765\u3002<\/p>\n<p>\u8bb8\u591a\u9a71\u52a8\u79fb\u52a8\u8bbe\u5907\u667a\u80fd\u884c\u4e3a\u7684\u6a21\u578b\u90fd\u7b26\u5408\u4e0a\u8ff0\u6807\u51c6\u3002\u4e3e\u4e24\u4e2a\u4f8b\u5b50&#xff1a;\u4e00\u662f\u56fe\u50cf\u5206\u7c7b (image classification)&#xff0c;\u4f8b\u5982\u9884\u6d4b\u54ea\u4e9b\u7167\u7247\u5c06\u6765\u6700\u6709\u53ef\u80fd\u88ab\u591a\u6b21\u67e5\u770b\u6216\u5206\u4eab&#xff1b;\u4e8c\u662f\u8bed\u8a00\u6a21\u578b (language models)&#xff0c;\u53ef\u901a\u8fc7\u6539\u8fdb\u89e3\u7801\u3001\u4e0b\u4e00\u4e2a\u8bcd\u9884\u6d4b\u751a\u81f3\u9884\u6d4b\u5b8c\u6574\u56de\u590d\u6765\u6539\u5584\u89e6\u6478\u5c4f\u952e\u76d8\u4e0a\u7684\u8bed\u97f3\u8bc6\u522b\u548c\u6587\u672c\u8f93\u5165 [10]\u3002\u8fd9\u4e24\u4e2a\u4efb\u52a1\u7684\u6f5c\u5728\u8bad\u7ec3\u6570\u636e&#xff08;\u7528\u6237\u62cd\u6444\u7684\u6240\u6709\u7167\u7247&#xff0c;\u4ee5\u53ca\u4ed6\u4eec\u5728\u79fb\u52a8\u952e\u76d8\u4e0a\u8f93\u5165\u7684\u6240\u6709\u5185\u5bb9&#xff0c;\u5305\u62ec\u5bc6\u7801\u3001URL\u3001\u6d88\u606f\u7b49&#xff09;\u90fd\u53ef\u80fd\u662f\u9690\u79c1\u654f\u611f\u7684\u3002\u5f97\u51fa\u8fd9\u4e9b\u6837\u672c\u7684\u5206\u5e03\u4e5f\u53ef\u80fd\u4e0e\u5bb9\u6613\u83b7\u5f97\u7684\u4ee3\u7406\u6570\u636e\u96c6\u5927\u76f8\u5f84\u5ead&#xff1a;\u804a\u5929\u548c\u77ed\u4fe1\u4e2d\u7684\u8bed\u8a00\u4f7f\u7528\u901a\u5e38\u4e0e\u6807\u51c6\u8bed\u8a00\u8bed\u6599\u5e93&#xff08;\u5982\u7ef4\u57fa\u767e\u79d1\u548c\u5176\u4ed6\u7f51\u7edc\u6587\u6863&#xff09;\u5927\u4e0d\u76f8\u540c&#xff1b;\u4eba\u4eec\u7528\u624b\u673a\u62cd\u6444\u7684\u7167\u7247\u53ef\u80fd\u4e0e\u5178\u578b\u7684 Flickr \u7167\u7247\u5b8c\u5168\u4e0d\u540c\u3002\u6700\u540e&#xff0c;\u8fd9\u4e9b\u95ee\u9898\u7684\u6807\u7b7e\u662f\u76f4\u63a5\u53ef\u7528\u7684&#xff1a;\u8f93\u5165\u7684\u6587\u672c\u5c31\u662f\u8bed\u8a00\u6a21\u578b\u81ea\u6807\u6ce8\u7684\u6807\u7b7e&#xff0c;\u800c\u7167\u7247\u6807\u7b7e\u53ef\u4ee5\u901a\u8fc7\u7528\u6237\u4e0e\u5176\u7167\u7247\u5e94\u7528\u7684\u81ea\u7136\u4ea4\u4e92\u6765\u5b9a\u4e49&#xff08;\u54ea\u4e9b\u7167\u7247\u88ab\u5220\u9664\u3001\u5206\u4eab\u6216\u67e5\u770b&#xff09;\u3002<\/p>\n<p>\u8fd9\u4e24\u9879\u4efb\u52a1\u90fd\u975e\u5e38\u9002\u5408\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc\u3002\u5bf9\u4e8e\u56fe\u50cf\u5206\u7c7b&#xff0c;\u524d\u9988\u6df1\u5ea6\u7f51\u7edc&#xff0c;\u7279\u522b\u662f\u5377\u79ef\u795e\u7ecf\u7f51\u7edc (CNN)&#xff0c;\u4f17\u6240\u5468\u77e5\u80fd\u63d0\u4f9b\u6700\u5148\u8fdb\u7684\u7ed3\u679c [26, 25]\u3002\u5bf9\u4e8e\u8bed\u8a00\u5efa\u6a21\u4efb\u52a1&#xff0c;\u5faa\u73af\u795e\u7ecf\u7f51\u7edc&#xff0c;\u7279\u522b\u662f LSTM&#xff0c;\u4e5f\u53d6\u5f97\u4e86\u6700\u5148\u8fdb\u7684\u7ed3\u679c [20, 5, 22]\u3002<\/p>\n<h4>\u9690\u79c1 (Privacy)<\/h4>\n<p>\u4e0e\u6301\u4e45\u5316\u6570\u636e\u4e0a\u7684\u6570\u636e\u4e2d\u5fc3\u8bad\u7ec3\u76f8\u6bd4&#xff0c;\u8054\u90a6\u5b66\u4e60\u5177\u6709\u660e\u663e\u7684\u9690\u79c1\u4f18\u52bf\u3002\u54ea\u6015\u6301\u6709\u7684\u662f\u201c\u533f\u540d\u5316\u201d\u7684\u6570\u636e\u96c6&#xff0c;\u4f9d\u7136\u53ef\u80fd\u901a\u8fc7\u4e0e\u5176\u4ed6\u6570\u636e\u7684\u7ed3\u5408&#xff08;joins&#xff09;\u4f7f\u7528\u6237\u9690\u79c1\u53d7\u5230\u5a01\u80c1 [37]\u3002\u76f8\u6bd4\u4e4b\u4e0b&#xff0c;\u8054\u90a6\u5b66\u4e60\u4f20\u8f93\u7684\u4fe1\u606f\u662f\u6539\u5584\u7279\u5b9a\u6a21\u578b\u6240\u9700\u7684\u6700\u5c0f\u66f4\u65b0&#xff08;\u81ea\u7136\u5730&#xff0c;\u9690\u79c1\u6536\u76ca\u7684\u5f3a\u5ea6\u53d6\u51b3\u4e8e\u66f4\u65b0\u7684\u5185\u5bb9&#xff09;\u3002\u00b9 \u8fd9\u4e9b\u66f4\u65b0\u672c\u8eab\u53ef\u4ee5\u662f&#xff08;\u4e5f\u5e94\u8be5\u662f&#xff09;\u77ed\u6682\u7684 (ephemeral)\u3002\u6839\u636e\u6570\u636e\u5904\u7406\u4e0d\u7b49\u5f0f&#xff0c;\u5b83\u4eec\u5305\u542b\u7684\u4fe1\u606f\u6c38\u8fdc\u4e0d\u4f1a\u591a\u4e8e\u539f\u59cb\u8bad\u7ec3\u6570\u636e&#xff0c;\u800c\u4e14\u901a\u5e38\u5305\u542b\u5f97\u5c11\u5f97\u591a\u3002\u6b64\u5916&#xff0c;\u805a\u5408\u7b97\u6cd5\u4e0d\u9700\u8981\u77e5\u9053\u66f4\u65b0\u7684\u6765\u6e90&#xff0c;\u56e0\u6b64\u8fd9\u4e9b\u66f4\u65b0\u53ef\u4ee5\u901a\u8fc7 Tor \u7b49\u6df7\u5408\u7f51\u7edc [7] \u6216\u53d7\u4fe1\u4efb\u7684\u7b2c\u4e09\u65b9\u8fdb\u884c\u4f20\u8f93&#xff0c;\u800c\u65e0\u9700\u8bc6\u522b\u5143\u6570\u636e\u3002\u5728\u672c\u6587\u672b\u5c3e&#xff0c;\u6211\u4eec\u5c06\u7b80\u8981\u8ba8\u8bba\u5c06\u8054\u90a6\u5b66\u4e60\u4e0e\u5b89\u5168\u591a\u65b9\u8ba1\u7b97\u548c\u5dee\u5206\u9690\u79c1\u76f8\u7ed3\u5408\u7684\u53ef\u80fd\u6027\u3002<\/p>\n<p>\u00b9 \u4f8b\u5982&#xff0c;\u5982\u679c\u66f4\u65b0\u662f\u6240\u6709\u672c\u5730\u6570\u636e\u7684\u635f\u5931\u603b\u68af\u5ea6&#xff0c;\u800c\u7279\u5f81\u662f\u7a00\u758f\u7684\u8bcd\u888b&#xff0c;\u90a3\u4e48\u975e\u96f6\u68af\u5ea6\u4f1a\u51c6\u786e\u5730\u63ed\u793a\u7528\u6237\u5728\u8bbe\u5907\u4e0a\u8f93\u5165\u4e86\u54ea\u4e9b\u8bcd\u3002\u76f8\u6bd4\u4e4b\u4e0b&#xff0c;\u5bf9\u4e8e CNN \u8fd9\u6837\u7684\u5bc6\u96c6\u6a21\u578b&#xff0c;\u8bb8\u591a\u68af\u5ea6\u7684\u603b\u548c\u4e3a\u8bd5\u56fe\u5bfb\u6c42\u5355\u4e2a\u8bad\u7ec3\u5b9e\u4f8b\u4fe1\u606f\u7684\u653b\u51fb\u8005\u63d0\u4f9b\u4e86\u4e00\u4e2a\u66f4\u96be\u653b\u7834\u7684\u76ee\u6807&#xff08;\u5c3d\u7ba1\u653b\u51fb\u4ecd\u7136\u53ef\u80fd\u53d1\u751f&#xff09;\u3002<\/p>\n<h4>\u8054\u90a6\u4f18\u5316 (Federated Optimization)<\/h4>\n<p>\u6211\u4eec\u5c06\u8054\u90a6\u5b66\u4e60\u4e2d\u9690\u542b\u7684\u4f18\u5316\u95ee\u9898\u79f0\u4e3a\u8054\u90a6\u4f18\u5316 (federated optimization)&#xff0c;\u4ee5\u5efa\u7acb\u5176\u4e0e\u5206\u5e03\u5f0f\u4f18\u5316 (distributed optimization) \u7684\u8054\u7cfb&#xff08;\u53ca\u5bf9\u6bd4&#xff09;\u3002\u8054\u90a6\u4f18\u5316\u5177\u6709\u51e0\u4e2a\u533a\u522b\u4e8e\u5178\u578b\u5206\u5e03\u5f0f\u4f18\u5316\u95ee\u9898\u7684\u5173\u952e\u5c5e\u6027&#xff1a;<\/p>\n<ul>\n<li>\u975e\u72ec\u7acb\u540c\u5206\u5e03 (Non-IID)&#xff1a;\u7ed9\u5b9a\u5ba2\u6237\u7aef\u4e0a\u7684\u8bad\u7ec3\u6570\u636e\u901a\u5e38\u57fa\u4e8e\u7279\u5b9a\u7528\u6237\u5bf9\u79fb\u52a8\u8bbe\u5907\u7684\u4f7f\u7528\u60c5\u51b5&#xff0c;\u56e0\u6b64&#xff0c;\u4efb\u4f55\u7279\u5b9a\u7528\u6237\u7684\u672c\u5730\u6570\u636e\u96c6\u90fd\u4e0d\u80fd\u4ee3\u8868\u603b\u4f53\u4eba\u53e3\u5206\u5e03\u3002<\/li>\n<li>\u4e0d\u5e73\u8861 (Unbalanced)&#xff1a;\u540c\u6837\u5730&#xff0c;\u4e00\u4e9b\u7528\u6237\u4f7f\u7528\u670d\u52a1\u6216\u5e94\u7528\u7a0b\u5e8f\u7684\u9891\u7387\u8fdc\u9ad8\u4e8e\u5176\u4ed6\u7528\u6237&#xff0c;\u5bfc\u81f4\u4e0d\u540c\u8bbe\u5907\u7684\u672c\u5730\u8bad\u7ec3\u6570\u636e\u91cf\u5404\u4e0d\u76f8\u540c\u3002<\/li>\n<li>\u5927\u89c4\u6a21\u5206\u5e03\u5f0f (Massively distributed)&#xff1a;\u6211\u4eec\u9884\u671f\u53c2\u4e0e\u4f18\u5316\u7684\u5ba2\u6237\u7aef\u6570\u91cf\u8fdc\u8fdc\u5927\u4e8e\u6bcf\u4e2a\u5ba2\u6237\u7aef\u5e73\u5747\u7684\u6837\u672c\u6570\u91cf\u3002<\/li>\n<li>\u6709\u9650\u7684\u901a\u4fe1 (Limited communication)&#xff1a;\u79fb\u52a8\u8bbe\u5907\u7ecf\u5e38\u5904\u4e8e\u79bb\u7ebf\u72b6\u6001&#xff0c;\u6216\u8005\u8fde\u63a5\u5728\u7f13\u6162\u3001\u6602\u8d35\u7684\u7f51\u7edc\u4e0a\u3002<\/li>\n<\/ul>\n<p>\u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d&#xff0c;\u6211\u4eec\u7684\u91cd\u70b9\u662f\u4f18\u5316\u7684\u975e\u72ec\u7acb\u540c\u5206\u5e03\u548c\u4e0d\u5e73\u8861\u5c5e\u6027&#xff0c;\u4ee5\u53ca\u901a\u4fe1\u7ea6\u675f\u7684\u5173\u952e\u6027\u8d28\u3002\u4e00\u4e2a\u90e8\u7f72\u7684\u8054\u90a6\u4f18\u5316\u7cfb\u7edf\u8fd8\u5fc5\u987b\u89e3\u51b3\u65e0\u6570\u5b9e\u9645\u95ee\u9898&#xff1a;\u968f\u7740\u6570\u636e\u7684\u6dfb\u52a0\u548c\u5220\u9664&#xff0c;\u5ba2\u6237\u7aef\u6570\u636e\u96c6\u4f1a\u53d1\u751f\u53d8\u5316&#xff1b;\u5ba2\u6237\u7aef\u7684\u53ef\u7528\u6027\u4ee5\u590d\u6742\u7684\u65b9\u5f0f\u4e0e\u672c\u5730\u6570\u636e\u5206\u5e03\u76f8\u5173\u8054&#xff08;\u4f8b\u5982&#xff0c;\u8bb2\u7f8e\u5f0f\u82f1\u8bed\u7684\u7528\u6237\u7684\u624b\u673a\u63d2\u7535\u5145\u7535\u7684\u65f6\u95f4&#xff0c;\u53ef\u80fd\u4e0e\u8bb2\u82f1\u5f0f\u82f1\u8bed\u7684\u7528\u6237\u4e0d\u540c&#xff09;&#xff1b;\u4ee5\u53ca\u6709\u4e9b\u5ba2\u6237\u7aef\u53ef\u80fd\u4ece\u4e0d\u54cd\u5e94\u6216\u53d1\u9001\u635f\u574f\u7684\u66f4\u65b0\u3002<\/p>\n<p>\u8fd9\u4e9b\u95ee\u9898\u8d85\u51fa\u4e86\u5f53\u524d\u5de5\u4f5c\u7684\u8303\u56f4&#xff1b;\u76f8\u53cd&#xff0c;\u6211\u4eec\u4f7f\u7528\u9002\u5408\u5b9e\u9a8c\u7684\u53d7\u63a7\u73af\u5883&#xff0c;\u4f46\u4ecd\u7136\u89e3\u51b3\u4e86\u5ba2\u6237\u7aef\u53ef\u7528\u6027\u4ee5\u53ca\u4e0d\u5e73\u8861\u548c\u975e\u72ec\u7acb\u540c\u5206\u5e03\u6570\u636e\u7684\u5173\u952e\u95ee\u9898\u3002\u6211\u4eec\u5047\u8bbe\u4e00\u79cd\u5206\u6b65\u901a\u4fe1\u8f6e\u6b21\u7684\u540c\u6b65\u66f4\u65b0\u65b9\u6848\u3002\u6709\u4e00\u7ec4\u56fa\u5b9a\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">KK<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><\/span> \u4e2a\u5ba2\u6237\u7aef&#xff0c;\u6bcf\u4e2a\u90fd\u6709\u4e00\u4e2a\u56fa\u5b9a\u7684\u672c\u5730\u6570\u636e\u96c6\u3002\u5728\u6bcf\u8f6e\u5f00\u59cb\u65f6&#xff0c;\u968f\u673a\u9009\u62e9\u4e00\u90e8\u5206\u6bd4\u4f8b\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span> \u7684\u5ba2\u6237\u7aef&#xff0c;\u670d\u52a1\u5668\u5c06\u5f53\u524d\u7684\u5168\u5c40\u7b97\u6cd5\u72b6\u6001&#xff08;\u4f8b\u5982&#xff0c;\u5f53\u524d\u6a21\u578b\u53c2\u6570&#xff09;\u53d1\u9001\u7ed9\u8fd9\u4e9b\u5ba2\u6237\u7aef\u4e2d\u7684\u6bcf\u4e00\u4e2a\u3002\u6211\u4eec\u4ec5\u9009\u62e9\u90e8\u5206\u5ba2\u6237\u7aef\u662f\u4e3a\u4e86\u63d0\u9ad8\u6548\u7387&#xff0c;\u56e0\u4e3a\u6211\u4eec\u7684\u5b9e\u9a8c\u8868\u660e&#xff0c;\u589e\u52a0\u5ba2\u6237\u7aef\u6570\u91cf\u8d85\u8fc7\u4e00\u5b9a\u7a0b\u5ea6\u540e\u4f1a\u5e26\u6765\u6536\u76ca\u9012\u51cf\u3002\u7136\u540e&#xff0c;\u6bcf\u4e2a\u9009\u5b9a\u7684\u5ba2\u6237\u7aef\u6839\u636e\u5168\u5c40\u72b6\u6001\u548c\u5176\u672c\u5730\u6570\u636e\u96c6\u8fdb\u884c\u672c\u5730\u8ba1\u7b97&#xff0c;\u5e76\u5c06\u66f4\u65b0\u53d1\u9001\u5230\u670d\u52a1\u5668\u3002\u63a5\u7740&#xff0c;\u670d\u52a1\u5668\u5c06\u8fd9\u4e9b\u66f4\u65b0\u5e94\u7528\u5230\u5176\u5168\u5c40\u72b6\u6001&#xff0c;\u7136\u540e\u91cd\u590d\u6b64\u8fc7\u7a0b\u3002<\/p>\n<hr \/>\n<p>\u867d\u7136\u6211\u4eec\u91cd\u70b9\u5173\u6ce8\u975e\u51f8\u7684\u795e\u7ecf\u7f51\u7edc\u76ee\u6807&#xff0c;\u4f46\u6211\u4eec\u8003\u8651\u7684\u7b97\u6cd5\u9002\u7528\u4e8e\u4efb\u4f55\u5f62\u5f0f\u7684\u6709\u9650\u548c (finite-sum) \u76ee\u6807&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">min\u2061w\u2208Rdf(w)\u5176\u4e2df(w)&#061;def1n\u2211i&#061;1nfi(w).(1) \\\\min_{w \\\\in \\\\mathbb{R}^d} f(w) \\\\quad \\\\text{\u5176\u4e2d} \\\\quad f(w) \\\\stackrel{\\\\text{def}}{&#061;} \\\\frac{1}{n} \\\\sum_{i&#061;1}^n f_i(w). \\\\quad (1) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.9938em;vertical-align: -0.8408em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6679em\"><span class=\"\" style=\"top: -2.2866em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mrel mtight\">\u2208<\/span><span class=\"mord mtight\"><span class=\"mord mathbb mtight\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.782em\"><span class=\"\" style=\"top: -2.786em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"\"><span class=\"mop\">min<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8408em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u5176\u4e2d<\/span><\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\"><span class=\"mop op-limits\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.153em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"\"><span class=\"mop\">&#061;<\/span><\/span><\/span><span class=\"\" style=\"top: -3.5669em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">def<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.9291em;vertical-align: -1.2777em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.6514em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">.<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5bf9\u4e8e\u673a\u5668\u5b66\u4e60\u95ee\u9898&#xff0c;\u6211\u4eec\u901a\u5e38\u8bbe\u5b9a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">fi(w)&#061;\u2113(xi,yi;w)f_i(w) &#061; \\\\ell(x_i, y_i; w)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2113<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">;<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4e5f\u5c31\u662f\u8bf4&#xff0c;\u662f\u7528\u6a21\u578b\u53c2\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u5bf9\u6837\u672c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">(xi,yi)(x_i, y_i)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u8fdb\u884c\u9884\u6d4b\u65f6\u7684\u635f\u5931\u3002\u6211\u4eec\u5047\u8bbe\u6570\u636e\u88ab\u5212\u5206\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">KK<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><\/span> \u4e2a\u5ba2\u6237\u7aef\u4e0a&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Pk\\\\mathcal{P}_k<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\" style=\"margin-right: 0.0822em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0822em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u5ba2\u6237\u7aef <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">kk<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span> \u4e0a\u7684\u6570\u636e\u70b9\u7d22\u5f15\u96c6\u5408&#xff0c;\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">nk&#061;\u2223Pk\u2223n_k &#061; |\\\\mathcal{P}_k|<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathcal\" style=\"margin-right: 0.0822em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0822em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span>\u3002\u56e0\u6b64&#xff0c;\u6211\u4eec\u53ef\u4ee5\u5c06\u76ee\u6807\u65b9\u7a0b (1) \u91cd\u5199\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">f(w)&#061;\u2211k&#061;1KnknFk(w)\u5176\u4e2dFk(w)&#061;1nk\u2211i\u2208Pkfi(w). f(w) &#061; \\\\sum_{k&#061;1}^K \\\\frac{n_k}{n} F_k(w) \\\\quad \\\\text{\u5176\u4e2d} \\\\quad F_k(w) &#061; \\\\frac{1}{n_k} \\\\sum_{i \\\\in \\\\mathcal{P}_k} f_i(w). <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.1304em;vertical-align: -1.3021em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8283em\"><span class=\"\" style=\"top: -1.8479em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3021em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1076em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u5176\u4e2d<\/span><\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.7216em;vertical-align: -1.4002em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.836em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05em\"><span class=\"\" style=\"top: -1.8557em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">\u2208<\/span><span class=\"mord mtight\"><span class=\"mord mathcal mtight\" style=\"margin-right: 0.0822em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0822em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.4002em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">.<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5982\u679c\u5212\u5206 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Pk\\\\mathcal{P}_k<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\" style=\"margin-right: 0.0822em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0822em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u901a\u8fc7\u5c06\u8bad\u7ec3\u6837\u672c\u5747\u5300\u968f\u673a\u5730\u5206\u5e03\u5728\u5404\u4e2a\u5ba2\u6237\u7aef\u4e0a\u5f62\u6210\u7684&#xff0c;\u90a3\u4e48\u6211\u4eec\u5c06\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EPk[Fk(w)]&#061;f(w)\\\\mathbb{E}_{\\\\mathcal{P}_k}[F_k(w)] &#061; f(w)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0059em;vertical-align: -0.2559em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathcal mtight\" style=\"margin-right: 0.0822em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0822em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2559em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)]<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5176\u4e2d\u671f\u671b\u662f\u57fa\u4e8e\u5206\u914d\u7ed9\u56fa\u5b9a\u5ba2\u6237\u7aef <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">kk<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span> \u7684\u6837\u672c\u96c6\u8ba1\u7b97\u7684\u3002\u8fd9\u662f\u5206\u5e03\u5f0f\u4f18\u5316\u7b97\u6cd5\u901a\u5e38\u505a\u51fa\u7684\u72ec\u7acb\u540c\u5206\u5e03&#xff08;IID&#xff09;\u5047\u8bbe&#xff1b;\u6211\u4eec\u5c06\u8fd9\u79cd\u60c5\u51b5\u4e0d\u6210\u7acb\u7684\u573a\u666f&#xff08;\u5373 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">FkF_k<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u53ef\u80fd\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ff<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><\/span> \u7684\u4efb\u610f\u7cdf\u7cd5\u7684\u8fd1\u4f3c\u503c&#xff09;\u79f0\u4e3a\u975e\u72ec\u7acb\u540c\u5206\u5e03 (non-IID) \u573a\u666f\u3002<\/p>\n<p>\u5728\u6570\u636e\u4e2d\u5fc3\u4f18\u5316\u4e2d&#xff0c;\u901a\u4fe1\u6210\u672c\u76f8\u5bf9\u8f83\u5c0f&#xff0c;\u800c\u8ba1\u7b97\u6210\u672c\u5360\u4e3b\u5bfc\u5730\u4f4d&#xff0c;\u6700\u8fd1\u8bb8\u591a\u91cd\u70b9\u653e\u5728\u4f7f\u7528 GPU \u6765\u964d\u4f4e\u8fd9\u4e9b\u6210\u672c\u3002\u76f8\u53cd&#xff0c;\u5728\u8054\u90a6\u4f18\u5316\u4e2d&#xff0c;\u901a\u4fe1\u6210\u672c\u5360\u4e3b\u5bfc\u5730\u4f4d\u2014\u2014\u6211\u4eec\u901a\u5e38\u4f1a\u53d7\u9650\u4e8e 1 MB\/s \u6216\u66f4\u4f4e\u7684\u4e0a\u4f20\u5e26\u5bbd\u3002\u6b64\u5916&#xff0c;\u5ba2\u6237\u7aef\u901a\u5e38\u53ea\u4f1a\u5728\u5145\u7535\u3001\u63d2\u7535\u4e14\u8fde\u63a5\u5230\u4e0d\u9650\u6d41\u91cf\u7684 Wi-Fi \u65f6\u624d\u81ea\u613f\u53c2\u4e0e\u4f18\u5316\u3002\u53e6\u5916&#xff0c;\u6211\u4eec\u9884\u8ba1\u6bcf\u4e2a\u5ba2\u6237\u7aef\u6bcf\u5929\u53ea\u4f1a\u53c2\u4e0e\u5c11\u91cf\u7684\u66f4\u65b0\u8f6e\u6b21\u3002\u53e6\u4e00\u65b9\u9762&#xff0c;\u7531\u4e8e\u5355\u4e2a\u8bbe\u5907\u4e0a\u7684\u6570\u636e\u96c6\u89c4\u6a21\u76f8\u5bf9\u4e8e\u603b\u6570\u636e\u96c6\u8f83\u5c0f&#xff0c;\u4e14\u73b0\u4ee3\u667a\u80fd\u624b\u673a\u62e5\u6709\u76f8\u5bf9\u8f83\u5feb\u7684\u5904\u7406\u5668&#xff08;\u5305\u62ec GPU&#xff09;&#xff0c;\u5bf9\u4e8e\u8bb8\u591a\u6a21\u578b\u7c7b\u578b\u800c\u8a00&#xff0c;\u76f8\u6bd4\u4e8e\u901a\u4fe1\u6210\u672c&#xff0c;\u8ba1\u7b97\u51e0\u4e4e\u662f\u514d\u8d39\u7684\u3002\u56e0\u6b64&#xff0c;\u6211\u4eec\u7684\u76ee\u6807\u662f\u4f7f\u7528\u989d\u5916\u7684\u8ba1\u7b97\u91cf\u6765\u51cf\u5c11\u8bad\u7ec3\u6a21\u578b\u6240\u9700\u7684\u901a\u4fe1\u8f6e\u6570\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e24\u79cd\u4e3b\u8981\u65b9\u5f0f\u589e\u52a0\u8ba1\u7b97\u91cf&#xff1a;1) \u589e\u52a0\u5e76\u884c\u5ea6&#xff0c;\u5728\u6bcf\u4e2a\u901a\u4fe1\u8f6e\u6b21\u4e4b\u95f4\u8ba9\u66f4\u591a\u5ba2\u6237\u7aef\u72ec\u7acb\u5de5\u4f5c&#xff1b;2) \u589e\u52a0\u6bcf\u4e2a\u5ba2\u6237\u7aef\u7684\u8ba1\u7b97\u91cf&#xff0c;\u4e0d\u662f\u6267\u884c\u50cf\u8ba1\u7b97\u4e00\u6b21\u68af\u5ea6\u8fd9\u6837\u7b80\u5355\u7684\u8ba1\u7b97&#xff0c;\u800c\u662f\u6bcf\u4e2a\u5ba2\u6237\u7aef\u5728\u6bcf\u6b21\u901a\u4fe1\u8f6e\u6b21\u4e4b\u95f4\u6267\u884c\u66f4\u590d\u6742\u7684\u8ba1\u7b97\u3002\u6211\u4eec\u5bf9\u8fd9\u4e24\u79cd\u65b9\u6cd5\u90fd\u8fdb\u884c\u4e86\u7814\u7a76&#xff0c;\u4f46\u5728\u8fbe\u5230\u5ba2\u6237\u7aef\u4e4b\u95f4\u6700\u4f4e\u7ea7\u522b\u7684\u5e76\u884c\u5ea6\u540e&#xff0c;\u6211\u4eec\u53d6\u5f97\u7684\u52a0\u901f\u6548\u679c\u4e3b\u8981\u5f52\u529f\u4e8e\u5728\u6bcf\u4e2a\u5ba2\u6237\u7aef\u4e0a\u589e\u52a0\u4e86\u66f4\u591a\u7684\u8ba1\u7b97\u91cf\u3002<\/p>\n<h4>\u76f8\u5173\u5de5\u4f5c (Related Work)<\/h4>\n<p>\u901a\u8fc7\u8fed\u4ee3\u5e73\u5747\u672c\u5730\u8bad\u7ec3\u6a21\u578b\u6765\u5b9e\u73b0\u5206\u5e03\u5f0f\u8bad\u7ec3&#xff0c;\u5df2\u7ecf\u88ab McDonald \u7b49\u4eba [28] (\u5bf9\u4e8e\u611f\u77e5\u673a) \u548c Povey \u7b49\u4eba [31] (\u5bf9\u4e8e\u8bed\u97f3\u8bc6\u522b DNN) \u7814\u7a76\u8fc7\u3002Zhang \u7b49\u4eba [42] \u7814\u7a76\u4e86\u4e00\u79cd\u91c7\u7528\u201c\u8f6f(soft)\u201d\u5e73\u5747\u7684\u5f02\u6b65\u65b9\u6cd5\u3002\u8fd9\u4e9b\u5de5\u4f5c\u4ec5\u8003\u8651\u4e86\u96c6\u7fa4\/\u6570\u636e\u4e2d\u5fc3\u573a\u666f&#xff08;\u6700\u591a16\u4e2a\u5de5\u4f5c\u8282\u70b9&#xff0c;\u57fa\u4e8e\u9ad8\u901f\u7f51\u7edc\u7684\u6302\u949f\u65f6\u95f4&#xff09;&#xff0c;\u5e76\u4e14\u6ca1\u6709\u8003\u8651\u4e0d\u5e73\u8861\u548c\u975e\u72ec\u7acb\u540c\u5206\u5e03&#xff08;non-IID&#xff09;\u7684\u6570\u636e\u96c6&#xff0c;\u800c\u8fd9\u4e9b\u5c5e\u6027\u5bf9\u8054\u90a6\u5b66\u4e60\u573a\u666f\u81f3\u5173\u91cd\u8981\u3002\u6211\u4eec\u5c06\u8fd9\u79cd\u98ce\u683c\u7684\u7b97\u6cd5\u8c03\u6574\u5230\u8054\u90a6\u8bbe\u7f6e\u4e2d&#xff0c;\u5e76\u8fdb\u884c\u4e86\u9002\u5f53\u7684\u5b9e\u8bc1\u8bc4\u4f30&#xff0c;\u8fd9\u63d0\u51fa\u4e86\u4e0e\u6570\u636e\u4e2d\u5fc3\u8bbe\u7f6e\u76f8\u5173\u95ee\u9898\u4e0d\u540c\u7684\u65b0\u95ee\u9898&#xff0c;\u5e76\u9700\u8981\u4e0d\u540c\u7684\u65b9\u6cd5\u8bba\u3002<\/p>\n<p>\u51fa\u4e8e\u4e0e\u6211\u4eec\u76f8\u4f3c\u7684\u52a8\u673a&#xff0c;Neverova \u7b49\u4eba [29] \u4e5f\u8ba8\u8bba\u4e86\u5c06\u654f\u611f\u7528\u6237\u6570\u636e\u4fdd\u7559\u5728\u8bbe\u5907\u4e0a\u7684\u4f18\u52bf\u3002Shokri \u548c Shmatikov [35] \u7684\u5de5\u4f5c\u5728\u51e0\u4e2a\u65b9\u9762\u4e0e\u6211\u4eec\u76f8\u5173&#xff1a;\u4ed6\u4eec\u4e13\u6ce8\u4e8e\u8bad\u7ec3\u6df1\u5ea6\u7f51\u7edc&#xff0c;\u5f3a\u8c03\u9690\u79c1\u7684\u91cd\u8981\u6027&#xff0c;\u5e76\u901a\u8fc7\u5728\u6bcf\u8f6e\u901a\u4fe1\u4e2d\u4ec5\u5171\u4eab\u90e8\u5206\u53c2\u6570\u6765\u89e3\u51b3\u901a\u4fe1\u6210\u672c\u95ee\u9898&#xff1b;\u7136\u800c&#xff0c;\u4ed6\u4eec\u540c\u6837\u6ca1\u6709\u8003\u8651\u4e0d\u5e73\u8861\u548c\u975e\u72ec\u7acb\u540c\u5206\u5e03\u7684\u6570\u636e&#xff0c;\u5e76\u4e14\u5176\u5b9e\u8bc1\u8bc4\u4f30\u8f83\u4e3a\u6709\u9650\u3002<\/p>\n<p>\u5728\u51f8\u4f18\u5316\u7684\u80cc\u666f\u4e0b&#xff0c;\u5206\u5e03\u5f0f\u4f18\u5316\u548c\u4f30\u8ba1\u95ee\u9898\u5df2\u5f15\u8d77\u4e86\u6781\u5927\u7684\u5173\u6ce8 [4, 15, 33]&#xff0c;\u4e00\u4e9b\u7b97\u6cd5\u786e\u5b9e\u4e13\u95e8\u9488\u5bf9\u901a\u4fe1\u6548\u7387\u8fdb\u884c\u4e86\u4f18\u5316 [45, 34, 40, 27, 43]\u3002\u9664\u4e86\u5047\u8bbe\u76ee\u6807\u662f\u51f8\u7684\u4e4b\u5916&#xff0c;\u73b0\u6709\u7684\u8fd9\u9879\u5de5\u4f5c\u901a\u5e38\u8fd8\u8981\u6c42\u5ba2\u6237\u7aef\u7684\u6570\u91cf\u8fdc\u5c11\u4e8e\u6bcf\u4e2a\u5ba2\u6237\u7aef\u7684\u6837\u672c\u6570&#xff0c;\u8981\u6c42\u6570\u636e\u4ee5 IID \u65b9\u5f0f\u5206\u5e03\u5728\u5404\u4e2a\u5ba2\u6237\u7aef\u4e0a&#xff0c;\u5e76\u4e14\u8981\u6c42\u6bcf\u4e2a\u8282\u70b9\u62e5\u6709\u5b8c\u5168\u76f8\u540c\u6570\u91cf\u7684\u6570\u636e\u70b9\u2014\u2014\u6240\u6709\u8fd9\u4e9b\u5047\u8bbe\u5728\u8054\u90a6\u4f18\u5316\u573a\u666f\u4e2d\u90fd\u88ab\u6253\u7834\u4e86\u3002\u5f02\u6b65\u5206\u5e03\u5f0f\u5f62\u5f0f\u7684 SGD \u4e5f\u88ab\u5e94\u7528\u4e8e\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u4e2d&#xff0c;\u4f8b\u5982 Dean \u7b49\u4eba [12]&#xff0c;\u4f46\u8fd9\u4e9b\u65b9\u6cd5\u5728\u8054\u90a6\u8bbe\u7f6e\u4e2d\u9700\u8981\u6781\u5176\u5de8\u5927\u7684\u66f4\u65b0\u6b21\u6570&#xff0c;\u8fd9\u662f\u4e0d\u53ef\u63a5\u53d7\u7684\u3002\u5206\u5e03\u5f0f\u5171\u8bc6\u7b97\u6cd5&#xff08;\u5982 [41]&#xff09;\u653e\u5bbd\u4e86 IID \u5047\u8bbe&#xff0c;\u4f46\u4ecd\u7136\u4e0d\u9002\u5408\u5177\u6709\u6781\u5927\u6570\u91cf\u5ba2\u6237\u7aef\u7684\u901a\u4fe1\u53d7\u9650\u7684\u4f18\u5316\u95ee\u9898\u3002<\/p>\n<p>\u6211\u4eec\u8003\u8651\u7684&#xff08;\u53c2\u6570\u5316&#xff09;\u7b97\u6cd5\u7cfb\u5217\u7684\u4e00\u4e2a\u6781\u7aef\u60c5\u51b5\u662f\u7b80\u5355\u7684\u5355\u6b21\u5e73\u5747&#xff08;one-shot averaging&#xff09;&#xff0c;\u5373\u6bcf\u4e2a\u5ba2\u6237\u7aef\u5728\u5176\u672c\u5730\u6570\u636e\u4e0a\u6c42\u89e3\u6700\u5c0f\u5316&#xff08;\u53ef\u80fd\u5177\u6709\u6b63\u5219\u5316\u9879\u7684&#xff09;\u635f\u5931\u7684\u6a21\u578b&#xff0c;\u7136\u540e\u5c06\u8fd9\u4e9b\u6a21\u578b\u5e73\u5747\u5316\u4ee5\u4ea7\u751f\u6700\u7ec8\u7684\u5168\u5c40\u6a21\u578b\u3002\u8fd9\u79cd\u65b9\u6cd5\u5728\u5177\u6709 IID \u6570\u636e\u7684\u51f8\u60c5\u51b5\u4e0b\u5df2\u7ecf\u88ab\u5e7f\u6cdb\u7814\u7a76&#xff0c;\u5e76\u4e14\u5df2\u77e5\u5728\u6700\u574f\u7684\u60c5\u51b5\u4e0b&#xff0c;\u4ea7\u751f\u7684\u5168\u5c40\u6a21\u578b\u5e76\u4e0d\u6bd4\u5728\u5355\u4e2a\u5ba2\u6237\u7aef\u4e0a\u8bad\u7ec3\u6a21\u578b\u66f4\u597d [44, 3, 46]\u3002<\/p>\n<hr \/>\n<h4>2 FederatedAveraging \u7b97\u6cd5 (The FederatedAveraging Algorithm)<\/h4>\n<p>\u8fd1\u671f\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\u7684\u5927\u91cf\u6210\u529f\u5e94\u7528\u51e0\u4e4e\u90fd\u4f9d\u8d56\u4e8e\u968f\u673a\u68af\u5ea6\u4e0b\u964d&#xff08;SGD&#xff09;\u7684\u53d8\u4f53\u8fdb\u884c\u4f18\u5316&#xff1b;\u4e8b\u5b9e\u4e0a&#xff0c;\u8bb8\u591a\u8fdb\u5c55\u90fd\u53ef\u4ee5\u7406\u89e3\u4e3a\u5bf9\u6a21\u578b\u7ed3\u6784&#xff08;\u53ca\u7531\u6b64\u4ea7\u751f\u7684\u635f\u5931\u51fd\u6570&#xff09;\u7684\u8c03\u6574&#xff0c;\u4f7f\u5176\u66f4\u5bb9\u6613\u901a\u8fc7\u7b80\u5355\u7684\u57fa\u4e8e\u68af\u5ea6\u7684\u65b9\u6cd5\u8fdb\u884c\u4f18\u5316 [16]\u3002\u56e0\u6b64&#xff0c;\u6211\u4eec\u4ece SGD \u51fa\u53d1\u6784\u5efa\u8054\u90a6\u4f18\u5316\u7b97\u6cd5\u662f\u5f88\u81ea\u7136\u7684\u3002<\/p>\n<p>SGD \u53ef\u4ee5\u7c97\u7cd9\u5730\u76f4\u63a5\u5e94\u7528\u4e8e\u8054\u90a6\u4f18\u5316\u95ee\u9898&#xff0c;\u5373\u5728\u6bcf\u4e00\u8f6e\u901a\u4fe1\u4e2d\u8fdb\u884c\u4e00\u6b21\u5355\u6279\u6b21\u7684\u68af\u5ea6\u8ba1\u7b97&#xff08;\u4f8b\u5982&#xff0c;\u5728\u4e00\u4e2a\u968f\u673a\u9009\u5b9a\u7684\u5ba2\u6237\u7aef\u4e0a&#xff09;\u3002\u8fd9\u79cd\u65b9\u6cd5\u5728\u8ba1\u7b97\u4e0a\u662f\u9ad8\u6548\u7684&#xff0c;\u4f46\u9700\u8981\u975e\u5e38\u5927\u91cf\u7684\u8bad\u7ec3\u8f6e\u6570\u624d\u80fd\u4ea7\u751f\u826f\u597d\u7684\u6a21\u578b&#xff08;\u4f8b\u5982&#xff0c;\u5373\u4f7f\u4f7f\u7528\u8bf8\u5982\u6279\u91cf\u5f52\u4e00\u5316\u7684\u5148\u8fdb\u65b9\u6cd5&#xff0c;Ioffe \u548c Szegedy [21] \u8fd8\u662f\u4f7f\u7528\u5927\u5c0f\u4e3a 60 \u7684\u5c0f\u6279\u91cf&#xff08;minibatch&#xff09;\u5728 MNIST \u4e0a\u8bad\u7ec3\u4e86 50000 \u6b65&#xff09;\u3002\u6211\u4eec\u5728 CIFAR-10 \u5b9e\u9a8c\u4e2d\u8003\u8651\u4e86\u8fd9\u4e00\u57fa\u7ebf\u65b9\u6cd5\u3002<\/p>\n<p>\u5728\u8054\u90a6\u8bbe\u7f6e\u4e2d&#xff0c;\u5f15\u5165\u66f4\u591a\u5ba2\u6237\u7aef\u5728\u6302\u949f\u65f6\u95f4\u4e0a\u7684\u6210\u672c\u5f88\u5c0f&#xff0c;\u56e0\u6b64\u5bf9\u4e8e\u6211\u4eec\u7684\u57fa\u7ebf&#xff0c;\u6211\u4eec\u91c7\u7528\u5927\u6279\u91cf\u540c\u6b65\u968f\u673a\u68af\u5ea6\u4e0b\u964d&#xff08;large-batch synchronous SGD&#xff09;&#xff1b;Chen \u7b49\u4eba [8] \u7684\u5b9e\u9a8c\u8868\u660e&#xff0c;\u8fd9\u79cd\u65b9\u6cd5\u5728\u6570\u636e\u4e2d\u5fc3\u8bbe\u7f6e\u4e2d\u662f\u76ee\u524d\u6700\u5148\u8fdb\u7684&#xff0c;\u5176\u6027\u80fd\u4f18\u4e8e\u5f02\u6b65\u65b9\u6cd5\u3002\u4e3a\u4e86\u5728\u8054\u90a6\u8bbe\u7f6e\u4e2d\u5e94\u7528\u8fd9\u79cd\u65b9\u6cd5&#xff0c;\u6211\u4eec\u5728\u6bcf\u4e00\u8f6e\u9009\u62e9\u4e00\u90e8\u5206\u6bd4\u4f8b\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span> \u7684\u5ba2\u6237\u7aef&#xff0c;\u5e76\u8ba1\u7b97\u8fd9\u4e9b\u5ba2\u6237\u7aef\u6240\u6301\u6709\u7684\u6240\u6709\u6570\u636e\u7684\u635f\u5931\u68af\u5ea6\u3002\u56e0\u6b64&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span> \u63a7\u5236\u5168\u5c40\u6279\u6b21\u5927\u5c0f&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;1C &#061; 1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u5bf9\u5e94\u4e8e\u5168\u6279\u6b21&#xff08;\u975e\u968f\u673a&#xff09;\u68af\u5ea6\u4e0b\u964d\u3002\u00b2 \u6211\u4eec\u5c06\u8fd9\u79cd\u57fa\u51c6\u7b97\u6cd5\u79f0\u4e3a FederatedSGD&#xff08;\u6216 FedSGD&#xff09;\u3002<\/p>\n<p>\u00b2 \u867d\u7136\u9009\u62e9\u6279\u6b21\u7684\u673a\u5236\u4e0e\u5747\u5300\u968f\u673a\u62bd\u53d6\u5355\u4e2a\u6837\u672c\u7684\u673a\u5236\u4e0d\u540c&#xff0c;\u4f46 FedSGD \u8ba1\u7b97\u7684\u6279\u6b21\u68af\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">gg<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><\/span><\/span><\/span><\/span> \u4ecd\u6ee1\u8db3 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E[g]&#061;\u2207f(w)\\\\mathbb{E}[g] &#061; \\\\nabla f(w)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathbb\">E<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2207<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;1C &#061; 1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u4e14\u5b66\u4e60\u7387\u6052\u5b9a\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7\\\\eta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span> \u7684\u60c5\u51b5\u4e0b&#xff0c;FedSGD \u7684\u5178\u578b\u5b9e\u73b0\u662f&#xff1a;\u6bcf\u4e2a\u5ba2\u6237\u7aef <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">kk<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span> \u8ba1\u7b97 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">gk&#061;\u2207Fk(wt)g_k &#061; \\\\nabla F_k(w_t)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2207<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff08;\u5373\u5728\u5f53\u524d\u6a21\u578b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">wtw_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e0b\u5176\u672c\u5730\u6570\u636e\u7684\u5e73\u5747\u68af\u5ea6&#xff09;&#xff0c;\u4e2d\u592e\u670d\u52a1\u5668\u805a\u5408\u8fd9\u4e9b\u68af\u5ea6\u5e76\u5e94\u7528\u66f4\u65b0 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">wt&#043;1\u2190wt\u2212\u03b7\u2211k&#061;1Knkngkw_{t&#043;1} \\\\leftarrow w_t &#8211; \\\\eta \\\\sum_{k&#061;1}^K \\\\frac{n_k}{n} g_k<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6389em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.3262em;vertical-align: -0.345em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9812em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7173em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4159em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u56e0\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2211k&#061;1Knkngk&#061;\u2207f(wt)\\\\sum_{k&#061;1}^K \\\\frac{n_k}{n} g_k &#061; \\\\nabla f(w_t)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.3262em;vertical-align: -0.345em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9812em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7173em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4159em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2207<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002\u4e00\u4e2a\u7b49\u6548\u7684\u66f4\u65b0\u5199\u6cd5\u662f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2200k,wt&#043;1k\u2190wt\u2212\u03b7gk\\\\forall k, w^k_{t&#043;1} \\\\leftarrow w_t &#8211; \\\\eta g_k<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1555em;vertical-align: -0.3064em\"><\/span><span class=\"mord\">\u2200<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -2.4519em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3064em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7136\u540e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">wt&#043;1\u2190\u2211k&#061;1Knknwt&#043;1kw_{t&#043;1} \\\\leftarrow \\\\sum_{k&#061;1}^K \\\\frac{n_k}{n} w^k_{t&#043;1}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6389em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.3262em;vertical-align: -0.345em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9812em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7173em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4159em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -2.4519em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3064em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u4e5f\u5c31\u662f\u8bf4&#xff0c;\u6bcf\u4e2a\u5ba2\u6237\u7aef\u5728\u5f53\u524d\u6a21\u578b\u4e0a\u4f7f\u7528\u5176\u672c\u5730\u6570\u636e\u5728\u672c\u5730\u6267\u884c\u4e00\u6b65\u68af\u5ea6\u4e0b\u964d&#xff0c;\u7136\u540e\u670d\u52a1\u5668\u5bf9\u751f\u6210\u7684\u6a21\u578b\u8fdb\u884c\u52a0\u6743\u5e73\u5747\u3002\u4e00\u65e6\u7b97\u6cd5\u5199\u6210\u8fd9\u79cd\u5f62\u5f0f&#xff0c;\u6211\u4eec\u5c31\u53ef\u4ee5\u901a\u8fc7\u5728\u5e73\u5747\u5316\u6b65\u9aa4\u4e4b\u524d\u8ba9\u5ba2\u6237\u7aef\u5bf9\u5c40\u90e8\u66f4\u65b0 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">wk\u2190wk\u2212\u03b7\u2207Fk(wk)w^k \\\\leftarrow w^k &#8211; \\\\eta \\\\nabla F_k(w^k)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9324em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0991em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mord\">\u2207<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u8fdb\u884c\u591a\u6b21\u8fed\u4ee3&#xff0c;\u4ece\u800c\u5728\u6bcf\u4e2a\u5ba2\u6237\u7aef\u4e0a\u589e\u52a0\u66f4\u591a\u8ba1\u7b97\u91cf\u3002\u6211\u4eec\u5c06\u8fd9\u79cd\u65b9\u6cd5\u79f0\u4e3a FederatedAveraging&#xff08;\u6216 FedAvg&#xff09;\u3002\u8ba1\u7b97\u91cf\u7531\u4e09\u4e2a\u5173\u952e\u53c2\u6570\u63a7\u5236&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6bcf\u8f6e\u8fdb\u884c\u8ba1\u7b97\u7684\u5ba2\u6237\u7aef\u7684\u6bd4\u4f8b&#xff1b;<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6bcf\u8f6e\u6bcf\u4e2a\u5ba2\u6237\u7aef\u904d\u5386\u5176\u672c\u5730\u6570\u636e\u96c6\u7684\u8bad\u7ec3\u8f6e\u6570&#xff08;epochs&#xff09;&#xff1b;<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">BB<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5ba2\u6237\u7aef\u66f4\u65b0\u6240\u4f7f\u7528\u7684\u672c\u5730\u5c0f\u6279\u91cf\u5927\u5c0f&#xff08;minibatch size&#xff09;\u3002<\/li>\n<\/ul>\n<p>\u6211\u4eec\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;\u221eB &#061; \\\\infty<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord\">\u221e<\/span><\/span><\/span><\/span><\/span> \u7528\u6765\u8868\u793a\u6574\u4e2a\u672c\u5730\u6570\u636e\u96c6\u88ab\u89c6\u4e3a\u5355\u4e2a\u5c0f\u6279\u91cf\u3002\u56e0\u6b64&#xff0c;\u5728\u8fd9\u4e2a\u7b97\u6cd5\u5bb6\u65cf\u7684\u4e00\u4e2a\u6781\u7aef\u60c5\u51b5\u4e2d&#xff0c;\u6211\u4eec\u53ef\u4ee5\u53d6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;\u221eB &#061; \\\\infty<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord\">\u221e<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E&#061;1E &#061; 1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8fd9\u6b63\u597d\u5bf9\u5e94\u4e8e FedSGD\u3002\u5bf9\u4e8e\u62e5\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">nkn_k<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e2a\u672c\u5730\u6837\u672c\u7684\u5ba2\u6237\u7aef&#xff0c;\u6bcf\u8f6e\u7684\u672c\u5730\u66f4\u65b0\u6b21\u6570\u7531 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uk&#061;EnkBu_k &#061; E \\\\frac{n_k}{B}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0623em;vertical-align: -0.345em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7173em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4159em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u7ed9\u51fa&#xff1b;\u5b8c\u6574\u7684\u4f2a\u4ee3\u7801\u8be6\u89c1\u7b97\u6cd5 1\u3002<\/p>\n<p>\u5bf9\u4e8e\u4e00\u822c\u7684\u975e\u51f8\u76ee\u6807&#xff0c;\u5728\u53c2\u6570\u7a7a\u95f4\u4e2d\u5bf9\u6a21\u578b\u8fdb\u884c\u5e73\u5747\u53ef\u80fd\u4f1a\u4ea7\u751f\u4efb\u610f\u7cdf\u7cd5\u7684\u6a21\u578b\u3002<\/p>\n<hr \/>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113323-69a42403604d9.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe 1 \u8bf4\u660e:<br \/>\n\u672c\u56fe\u5c55\u793a\u4e86\u7531\u4e24\u4e2a\u6a21\u578b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">w\u2032w&#039;<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7519em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u53c2\u6570\u5e73\u5747\u751f\u6210\u7684\u6a21\u578b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8w&#043;(1\u2212\u03b8)w\u2032\\\\theta w &#043; (1 &#8211; \\\\theta)w&#039;<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7778em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">\u03b8w<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0019em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5728\u5168\u91cf MNIST \u8bad\u7ec3\u96c6\u4e0a\u7684\u635f\u5931\u3002\u6a2a\u8f74 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8\\\\theta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><\/span><\/span><\/span><\/span> \u53d6\u503c\u8303\u56f4\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">[\u22120.2,1.2][-0.2, 1.2]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">0.2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">1.2<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5171\u670950\u4e2a\u5747\u5300\u5206\u5e03\u7684\u70b9\u3002\u6a21\u578b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">w\u2032w&#039;<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7519em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u5728\u4e0d\u540c\u7684\u5c0f\u578b\u6570\u636e\u96c6\u4e0a\u4f7f\u7528 SGD \u8bad\u7ec3\u5f97\u5230\u7684\u3002<br \/>\n\u5de6\u56fe\u4e2d&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">w\u2032w&#039;<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7519em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4f7f\u7528\u4e86\u4e0d\u540c\u7684\u968f\u673a\u79cd\u5b50\u521d\u59cb\u5316&#xff1b;\u53f3\u56fe\u4e2d&#xff0c;\u4f7f\u7528\u4e86\u76f8\u540c\u7684\u5171\u4eab\u79cd\u5b50\u521d\u59cb\u5316\u3002\u6ce8\u610f\u4e24\u56fe y \u8f74\u6bd4\u4f8b\u4e0d\u540c\u3002\u6c34\u5e73\u7ebf\u8868\u793a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u6216 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">w\u2032w&#039;<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7519em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8fbe\u5230\u7684\u6700\u4f73\u635f\u5931&#xff08;\u4e24\u8005\u975e\u5e38\u63a5\u8fd1&#xff0c;\u5bf9\u5e94\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8&#061;0\\\\theta&#061;0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8&#061;1\\\\theta&#061;1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u5904\u7684\u5782\u76f4\u7ebf&#xff09;\u3002\u901a\u8fc7\u5171\u4eab\u521d\u59cb\u5316&#xff0c;\u5e73\u5747\u8fd9\u4e24\u4e2a\u6a21\u578b\u5728\u603b\u8bad\u7ec3\u96c6\u4e0a\u663e\u8457\u964d\u4f4e\u4e86\u635f\u5931&#xff08;\u8fdc\u597d\u4e8e\u4efb\u4f55\u4e00\u4e2a\u5355\u4e00\u7236\u6a21\u578b\u7684\u635f\u5931&#xff09;\u3002<\/p>\n<p>\u9075\u5faa Goodfellow \u7b49\u4eba [17] \u7684\u7814\u7a76\u65b9\u6cd5&#xff0c;\u5f53\u6211\u4eec\u5c06\u4ece\u4e0d\u540c\u521d\u59cb\u6761\u4ef6\u8bad\u7ec3\u51fa\u7684\u4e24\u4e2a MNIST \u6570\u5b57\u8bc6\u522b\u6a21\u578b\u00b3\u8fdb\u884c\u5e73\u5747\u65f6&#xff0c;\u6211\u4eec\u786e\u5207\u5730\u770b\u5230\u4e86\u8fd9\u79cd\u7cdf\u7cd5\u7684\u884c\u4e3a&#xff08;\u56fe 1&#xff0c;\u5de6\u4fa7&#xff09;\u3002\u5728\u8fd9\u5f20\u56fe\u4e2d&#xff0c;\u7236\u6a21\u578b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">w\u2032w&#039;<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7519em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5206\u522b\u662f\u4ece MNIST \u8bad\u7ec3\u96c6\u4e2d\u62bd\u53d6\u7684\u3001\u4e92\u4e0d\u91cd\u53e0\u7684 600 \u4e2a\u6837\u672c\u7684 IID \u5b50\u96c6\u4e0a\u8fdb\u884c\u8bad\u7ec3\u7684\u3002\u8bad\u7ec3\u4f7f\u7528\u56fa\u5b9a\u5b66\u4e60\u7387 0.1 \u7684 SGD&#xff0c;\u6279\u5927\u5c0f\u4e3a 50&#xff0c;\u8fdb\u884c\u4e86 240 \u6b21\u66f4\u65b0&#xff08;\u76f8\u5f53\u4e8e\u5728\u5927\u5c0f\u4e3a 600 \u7684\u5c0f\u6570\u636e\u96c6\u4e0a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E&#061;20E &#061; 20<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">20<\/span><\/span><\/span><\/span><\/span> \u8f6e epoch&#xff09;\u3002\u8fd9\u5927\u7ea6\u662f\u6a21\u578b\u5f00\u59cb\u8fc7\u5ea6\u62df\u5408\u5176\u672c\u5730\u6570\u636e\u65f6\u7684\u8bad\u7ec3\u91cf\u3002<\/p>\n<p>\u8fd1\u671f\u7814\u7a76\u8868\u660e&#xff0c;\u5728\u5b9e\u8df5\u4e2d&#xff0c;\u5145\u5206\u53c2\u6570\u5316\u7684\u795e\u7ecf\u7f51\u7edc\u7684\u635f\u5931\u66f2\u9762\u51fa\u4e4e\u610f\u6599\u5730\u8868\u73b0\u826f\u597d&#xff0c;\u7279\u522b\u662f\u4e0d\u50cf\u4ee5\u524d\u8ba4\u4e3a\u7684\u90a3\u6837\u5bb9\u6613\u9677\u5165\u7cdf\u7cd5\u7684\u5c40\u90e8\u6700\u5c0f\u503c [11, 17, 9]\u3002\u4e8b\u5b9e\u4e0a&#xff0c;\u5f53\u6211\u4eec\u4ece\u540c\u4e00\u4e2a\u968f\u673a\u521d\u59cb\u5316\u5f00\u59cb\u8bad\u7ec3\u4e24\u4e2a\u6a21\u578b&#xff0c;\u7136\u540e\u518d\u6b21\u5728\u6570\u636e\u7684\u4e0d\u540c\u5b50\u96c6\u4e0a\u72ec\u7acb\u8bad\u7ec3\u5b83\u4eec&#xff08;\u5982\u4e0a\u6240\u8ff0&#xff09;\u65f6&#xff0c;\u6211\u4eec\u53d1\u73b0\u7b80\u5355\u7684\u53c2\u6570\u5e73\u5747\u6548\u679c\u597d\u5f97\u51fa\u5947&#xff08;\u56fe 1&#xff0c;\u53f3\u4fa7&#xff09;&#xff1a;\u8fd9\u4e24\u4e2a\u6a21\u578b\u7684\u5e73\u5747\u503c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">12w&#043;12w\u2032\\\\frac{1}{2}w &#043; \\\\frac{1}{2}w&#039;<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5728\u5b8c\u6574 MNIST \u8bad\u7ec3\u96c6\u4e0a\u5b9e\u73b0\u4e86\u660e\u663e\u4f4e\u4e8e\u4efb\u4f55\u4e00\u4e2a\u5c0f\u578b\u6570\u636e\u96c6\u4e0a\u72ec\u7acb\u8bad\u7ec3\u6240\u53d6\u5f97\u7684\u6700\u4f73\u635f\u5931\u3002\u867d\u7136\u56fe 1 \u4ece\u4e00\u4e2a\u968f\u673a\u521d\u59cb\u5316\u5f00\u59cb&#xff0c;\u4f46\u8bf7\u6ce8\u610f&#xff0c;\u5bf9\u4e8e\u6bcf\u4e00\u8f6e\u7684 FedAvg \u800c\u8a00&#xff0c;\u5b83\u90fd\u662f\u4ece\u4e00\u4e2a\u5171\u4eab\u7684\u8d77\u59cb\u6a21\u578b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">wtw_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5f00\u59cb\u7684&#xff0c;\u56e0\u6b64\u540c\u6837\u7684\u76f4\u89c9\u4e5f\u9002\u7528\u3002<\/p>\n<p>\u00b3 \u6211\u4eec\u4f7f\u7528\u7b2c3\u8282\u4e2d\u63cf\u8ff0\u7684\u201c2NN\u201d\u591a\u5c42\u611f\u77e5\u673a\u3002<\/p>\n<hr \/>\n<h4>[\u7b97\u6cd5 1: FederatedAveraging \u7b97\u6cd5]<\/h4>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113323-69a42403abe21.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u7b97\u6cd5 1 \u8bd1\u6587:<br \/>\nFederatedAveraging. \u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">KK<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><\/span> \u4e2a\u5ba2\u6237\u7aef\u7531 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">kk<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span> \u7d22\u5f15&#xff1b;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">BB<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><\/span> \u662f\u672c\u5730\u5c0f\u6279\u91cf\u5927\u5c0f&#xff1b;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u662f\u672c\u5730 epoch \u6570&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7\\\\eta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span> \u662f\u5b66\u4e60\u7387\u3002<\/p>\n<p>\u670d\u52a1\u5668\u6267\u884c:<br \/>\n\u521d\u59cb\u5316 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">w0w_0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n\u5bf9\u4e8e (for) \u6bcf\u4e2a\u8f6e\u6b21 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">t&#061;1,2,\u2026t &#061; 1, 2, \\\\ldots<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em\"><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8389em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u2026<\/span><\/span><\/span><\/span><\/span> \u6267\u884c (do):<br \/>\n<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">m\u2190max\u2061(C\u22c5K,1)m \\\\leftarrow \\\\max(C \\\\cdot K, 1)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mop\">max<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><br \/>\n<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">St\u2190S_t \\\\leftarrow<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0576em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><\/span><\/span><\/span><\/span> (\u968f\u673a\u9009\u62e9\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">mm<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">m<\/span><\/span><\/span><\/span><\/span> \u4e2a\u5ba2\u6237\u7aef\u7684\u96c6\u5408)<br \/>\n\u5bf9\u4e8e (for) \u6bcf\u4e2a\u5ba2\u6237\u7aef <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">k\u2208Stk \\\\in S_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7335em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0576em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5e76\u884c\u6267\u884c (in parallel do):<br \/>\n<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">wt&#043;1k\u2190ClientUpdate(k,wt)w_{t&#043;1}^k \\\\leftarrow \\\\text{ClientUpdate}(k, w_t)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1555em;vertical-align: -0.3064em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -2.4519em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3064em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord text\"><span class=\"mord\">ClientUpdate<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><br \/>\n<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">mt\u2190\u2211k\u2208Stnkm_t \\\\leftarrow \\\\sum_{k \\\\in S_t} n_k<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1498em;vertical-align: -0.3998em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1864em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mrel mtight\">\u2208<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2963em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0576em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3998em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">wt&#043;1\u2190\u2211k\u2208Stnkmtwt&#043;1kw_{t&#043;1} \\\\leftarrow \\\\sum_{k \\\\in S_t} \\\\frac{n_k}{m_t} w_{t&#043;1}^k<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6389em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2942em;vertical-align: -0.4451em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1864em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mrel mtight\">\u2208<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2963em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0576em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3998em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7173em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">m<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2963em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4159em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4451em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -2.4519em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3064em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>  \/\/ \u52d8\u8bef4: \u8bba\u6587\u65e9\u671f\u7248\u672c\u5728\u8fd9\u91cc\u9519\u8bef\u5730\u6807\u660e\u4e86\u5bf9\u6240\u6709 K \u4e2a\u5ba2\u6237\u7aef\u8fdb\u884c\u6c42\u548c\u3002<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ClientUpdate(k,w)\\\\text{ClientUpdate}(k, w)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord text\"><span class=\"mord\">ClientUpdate<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>: \/\/ \u5728\u5ba2\u6237\u7aef <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">kk<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span> \u4e0a\u8fd0\u884c<br \/>\n<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B\u2190\\\\mathcal{B} \\\\leftarrow<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathcal\" style=\"margin-right: 0.0304em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><\/span><\/span><\/span><\/span> (\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Pk\\\\mathcal{P}_k<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\" style=\"margin-right: 0.0822em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0822em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5206\u5272\u6210\u5927\u5c0f\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">BB<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><\/span> \u7684\u6279\u6b21)<br \/>\n\u5bf9\u4e8e (for) \u6bcf\u4e2a\u672c\u5730 epoch <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ii<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span><\/span> \u4ece 1 \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u6267\u884c (do):<br \/>\n\u5bf9\u4e8e (for) \u6279\u6b21 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">b\u2208Bb \\\\in \\\\mathcal{B}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7335em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathcal\" style=\"margin-right: 0.0304em\">B<\/span><\/span><\/span><\/span><\/span> \u6267\u884c (do):<br \/>\n<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">w\u2190w\u2212\u03b7\u2207\u2113(w;b)w \\\\leftarrow w &#8211; \\\\eta \\\\nabla \\\\ell(w; b)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mord\">\u2207<\/span><span class=\"mord\">\u2113<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mpunct\">;<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><br \/>\n\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u8fd4\u56de\u7ed9\u670d\u52a1\u5668<\/p>\n<hr \/>\n<h4>3 \u5b9e\u9a8c\u7ed3\u679c (Experimental Results)<\/h4>\n<p>\u6211\u4eec\u7684\u52a8\u673a\u6765\u81ea\u4e8e\u56fe\u50cf\u5206\u7c7b\u548c\u8bed\u8a00\u5efa\u6a21\u4efb\u52a1&#xff0c;\u4f18\u79c0\u7684\u6a21\u578b\u53ef\u4ee5\u6781\u5927\u5730\u63d0\u9ad8\u79fb\u52a8\u8bbe\u5907\u7684\u53ef\u7528\u6027\u3002\u5bf9\u4e8e\u8fd9\u4e9b\u4efb\u52a1\u4e2d\u7684\u6bcf\u4e00\u4e2a&#xff0c;\u6211\u4eec\u9996\u5148\u6311\u9009\u4e86\u4e00\u4e2a\u89c4\u6a21\u9002\u4e2d\u7684\u4ee3\u7406\u6570\u636e\u96c6&#xff0c;\u4ee5\u4fbf\u6211\u4eec\u53ef\u4ee5\u5f7b\u5e95\u7814\u7a76 FedAvg \u7b97\u6cd5\u7684\u8d85\u53c2\u6570\u3002\u867d\u7136\u6bcf\u4e00\u6b21\u5355\u72ec\u7684\u8bad\u7ec3\u8fd0\u884c\u76f8\u5bf9\u8f83\u5c0f&#xff0c;\u4f46\u6211\u4eec\u4e3a\u8fd9\u4e9b\u5b9e\u9a8c\u8bad\u7ec3\u4e86 2000 \u591a\u4e2a\u72ec\u7acb\u6a21\u578b\u3002\u7136\u540e\u6211\u4eec\u5c55\u793a\u4e86\u57fa\u51c6 CIFAR-10 \u56fe\u50cf\u5206\u7c7b\u4efb\u52a1\u7684\u7ed3\u679c\u3002\u6700\u540e&#xff0c;\u4e3a\u4e86\u8bc1\u660e FedAvg \u5728\u81ea\u7136\u5206\u5e03\u4e8e\u5ba2\u6237\u7aef\u7684\u73b0\u5b9e\u95ee\u9898\u4e0a\u7684\u6709\u6548\u6027&#xff0c;\u6211\u4eec\u5728\u4e00\u4e2a\u5927\u89c4\u6a21\u8bed\u8a00\u5efa\u6a21\u4efb\u52a1\u4e0a\u8fdb\u884c\u4e86\u8bc4\u4f30\u3002<\/p>\n<p>\u6211\u4eec\u7684\u521d\u6b65\u7814\u7a76\u5305\u62ec\u4e24\u4e2a\u6570\u636e\u96c6\u4e0a\u7684\u4e09\u4e2a\u6a21\u578b\u7cfb\u5217\u3002\u524d\u4e24\u4e2a\u7528\u4e8e MNIST \u6570\u5b57\u8bc6\u522b\u4efb\u52a1 [26]&#xff1a;1) \u4e00\u4e2a\u7b80\u5355\u7684\u591a\u5c42\u611f\u77e5\u673a&#xff08;\u5177\u6709 2 \u4e2a\u9690\u542b\u5c42&#xff0c;\u6bcf\u5c42 200 \u4e2a\u5355\u5143&#xff0c;\u4f7f\u7528 ReLu \u6fc0\u6d3b\u51fd\u6570&#xff0c;\u603b\u8ba1 199,210 \u4e2a\u53c2\u6570&#xff09;&#xff0c;\u6211\u4eec\u5c06\u5176\u79f0\u4e3a MNIST 2NN\u30022) \u4e00\u4e2a CNN&#xff0c;\u5177\u6709\u4e24\u4e2a 5&#215;5 \u5377\u79ef\u5c42&#xff08;\u7b2c\u4e00\u5c42 32 \u4e2a\u901a\u9053&#xff0c;\u7b2c\u4e8c\u5c42 64 \u4e2a&#xff0c;\u6bcf\u5c42\u540e\u63a5 2&#215;2 \u6700\u5927\u6c60\u5316&#xff09;&#xff0c;\u4e00\u4e2a\u5177\u6709 512 \u4e2a\u5355\u5143\u548c ReLu \u6fc0\u6d3b\u7684\u5168\u8fde\u63a5\u5c42&#xff0c;\u4ee5\u53ca\u6700\u7ec8\u7684 softmax \u8f93\u51fa\u5c42&#xff08;\u603b\u8ba1 1,663,370 \u4e2a\u53c2\u6570&#xff09;\u3002\u4e3a\u4e86\u7814\u7a76\u8054\u90a6\u4f18\u5316&#xff0c;\u6211\u4eec\u8fd8\u9700\u8981\u6307\u660e\u6570\u636e\u662f\u5982\u4f55\u5206\u5e03\u5728\u5ba2\u6237\u7aef\u4e0a\u7684\u3002\u6211\u4eec\u7814\u7a76\u4e86\u4e24\u79cd\u5c06 MNIST \u6570\u636e\u5212\u5206\u7ed9\u5ba2\u6237\u7aef\u7684\u65b9\u6cd5&#xff1a;IID (\u72ec\u7acb\u540c\u5206\u5e03)&#xff1a;\u6570\u636e\u88ab\u6d17\u724c\u540e\u5206\u4e3a 100 \u4e2a\u5ba2\u6237\u7aef&#xff0c;\u6bcf\u4e2a\u83b7\u5f97 600 \u4e2a\u6837\u672c&#xff1b;\u4ee5\u53ca Non-IID (\u975e\u72ec\u7acb\u540c\u5206\u5e03)&#xff1a;\u6211\u4eec\u9996\u5148\u6309\u6570\u5b57\u6807\u7b7e\u5bf9\u6570\u636e\u8fdb\u884c\u6392\u5e8f&#xff0c;\u5c06\u5176\u5206\u6210 200 \u4e2a\u5206\u7247&#xff0c;\u6bcf\u4e2a\u5206\u7247\u5927\u5c0f\u4e3a 300&#xff0c;\u7136\u540e\u4e3a 100 \u4e2a\u5ba2\u6237\u7aef\u5404\u5206\u914d 2 \u4e2a\u5206\u7247\u3002\u8fd9\u662f\u4e00\u79cd\u75c5\u6001\u7684&#xff08;pathological&#xff09;\u975e\u72ec\u7acb\u540c\u5206\u5e03\u6570\u636e\u5212\u5206&#xff0c;\u56e0\u4e3a\u5927\u591a\u6570\u5ba2\u6237\u7aef\u53ea\u6709\u4e24\u4e2a\u6570\u5b57\u7684\u6837\u672c&#xff0c;\u8fd9\u8ba9\u6211\u4eec\u5f97\u4ee5\u63a2\u7d22\u6211\u4eec\u7684\u7b97\u6cd5\u5728\u9ad8\u5ea6 non-IID \u6570\u636e\u4e0a\u7684\u5d29\u6e83\u7a0b\u5ea6\u3002\u4e0d\u8fc7&#xff0c;\u8fd9\u4e24\u79cd\u5212\u5206\u662f\u5e73\u8861\u7684\u3002\u2075<\/p>\n<p>\u5bf9\u4e8e\u8bed\u8a00\u5efa\u6a21&#xff0c;\u6211\u4eec\u4ece\u300a\u838e\u58eb\u6bd4\u4e9a\u5168\u96c6\u300b[32] \u4e2d\u6784\u5efa\u4e86\u4e00\u4e2a\u6570\u636e\u96c6\u3002\u6211\u4eec\u4e3a\u620f\u5267\u4e2d\u81f3\u5c11\u6709\u4e24\u53e5\u53f0\u8bcd\u7684\u6bcf\u4e00\u4e2a\u89d2\u8272\u6784\u5efa\u4e00\u4e2a\u5ba2\u6237\u7aef\u6570\u636e\u96c6\u3002\u8fd9\u4ea7\u751f\u4e86\u4e00\u4e2a\u5305\u542b 1146 \u4e2a\u5ba2\u6237\u7aef\u7684\u6570\u636e\u96c6\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u5ba2\u6237\u7aef&#xff0c;\u6211\u4eec\u5c06\u6570\u636e\u5206\u4e3a\u4e00\u7ec4\u8bad\u7ec3\u884c&#xff08;\u8be5\u89d2\u8272\u524d 80% \u7684\u53f0\u8bcd&#xff09;\u548c\u6d4b\u8bd5\u884c&#xff08;\u540e 20%&#xff0c;\u5411\u4e0a\u53d6\u6574\u81f3\u5c11\u4fdd\u7559\u4e00\u884c&#xff09;\u3002\u5f97\u5230\u7684\u6570\u636e\u96c6\u5728\u8bad\u7ec3\u96c6\u4e2d\u6709 3,564,579 \u4e2a\u5b57\u7b26&#xff0c;\u5728\u6d4b\u8bd5\u96c6\u4e2d\u6709 870,014 \u4e2a\u5b57\u7b26\u2076\u3002\u8fd9\u4e9b\u6570\u636e\u6781\u4e0d\u5e73\u8861&#xff0c;\u8bb8\u591a\u89d2\u8272\u53ea\u6709\u51e0\u53e5\u53f0\u8bcd&#xff0c;\u800c\u5c11\u6570\u89d2\u8272\u6709\u5927\u91cf\u53f0\u8bcd\u3002\u6b64\u5916&#xff0c;\u8bf7\u6ce8\u610f&#xff0c;\u6d4b\u8bd5\u96c6\u5e76\u4e0d\u662f\u53e5\u5b50\u7684\u968f\u673a\u62bd\u53d6&#xff0c;\u800c\u662f\u6309\u7167\u6bcf\u90e8\u620f\u5267\u7684\u65f6\u95f4\u987a\u5e8f\u8fdb\u884c\u65f6\u95f4\u5206\u79bb\u7684\u3002\u4f7f\u7528\u76f8\u540c\u7684\u8bad\u7ec3\/\u6d4b\u8bd5\u62c6\u5206&#xff0c;\u6211\u4eec\u4e5f\u5f62\u6210\u4e86\u8be5\u6570\u636e\u96c6\u7684\u4e00\u4e2a\u5e73\u8861\u4e14 IID \u7684\u7248\u672c&#xff0c;\u540c\u6837\u5305\u542b 1146 \u4e2a\u5ba2\u6237\u7aef\u3002<\/p>\n<p>\u5728\u8fd9\u4efd\u6570\u636e\u4e0a&#xff0c;\u6211\u4eec\u8bad\u7ec3\u4e86\u4e00\u4e2a\u5806\u53e0\u5f0f\u5b57\u7b26\u7ea7 LSTM \u8bed\u8a00\u6a21\u578b&#xff0c;\u5b83\u5728\u8bfb\u53d6\u4e00\u884c\u4e2d\u7684\u6bcf\u4e2a\u5b57\u7b26\u540e&#xff0c;\u9884\u6d4b\u4e0b\u4e00\u4e2a\u5b57\u7b26 [22]\u3002\u8be5\u6a21\u578b\u5c06\u4e00\u7cfb\u5217\u5b57\u7b26\u4f5c\u4e3a\u8f93\u5165&#xff0c;\u5e76\u5c06\u6bcf\u4e2a\u5b57\u7b26\u5d4c\u5165\u5230\u4e00\u4e2a\u5b66\u4e60\u5230\u7684 8 \u7ef4\u7a7a\u95f4\u4e2d\u3002\u7136\u540e\u8fd9\u4e9b\u5d4c\u5165\u5b57\u7b26\u901a\u8fc7 2 \u4e2a LSTM \u5c42\u8fdb\u884c\u5904\u7406&#xff0c;\u6bcf\u5c42 256 \u4e2a\u8282\u70b9\u3002\u6700\u540e&#xff0c;\u7b2c\u4e8c\u4e2a LSTM \u5c42\u7684\u8f93\u51fa\u53d1\u9001\u5230\u4e00\u4e2a softmax \u8f93\u51fa\u5c42&#xff0c;\u6bcf\u4e2a\u5b57\u7b26\u5bf9\u5e94\u4e00\u4e2a\u8282\u70b9\u3002\u5b8c\u6574\u6a21\u578b\u6709 866,578 \u4e2a\u53c2\u6570&#xff0c;\u6211\u4eec\u4f7f\u7528\u4e86 80 \u4e2a\u5b57\u7b26\u7684\u5c55\u5f00\u957f\u5ea6&#xff08;unroll length&#xff09;\u8fdb\u884c\u8bad\u7ec3\u3002<\/p>\n<p>SGD \u5bf9\u5b66\u4e60\u7387\u53c2\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7\\\\eta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span> \u7684\u8c03\u4f18\u5f88\u654f\u611f\u3002\u6b64\u5904\u62a5\u544a\u7684\u7ed3\u679c\u57fa\u4e8e\u5bf9\u8db3\u591f\u5bbd\u7684\u5b66\u4e60\u7387\u7f51\u683c\u8fdb\u884c\u8bad\u7ec3\u5f97\u51fa&#xff08;\u901a\u5e38\u6211\u4eec\u5728\u5206\u8fa8\u7387\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">101\/310^{1\/3}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.888em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.888em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1\/3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6216 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">101\/610^{1\/6}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.888em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.888em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1\/6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u4e58\u6cd5\u7f51\u683c\u4e0a\u9009\u53d6 11-13 \u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7\\\\eta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span> \u503c&#xff09;\u3002\u6211\u4eec\u68c0\u67e5\u4ee5\u786e\u4fdd\u6700\u4f73\u5b66\u4e60\u7387\u5904\u4e8e\u6211\u4eec\u7f51\u683c\u7684\u4e2d\u95f4\u90e8\u5206&#xff0c;\u5e76\u4e14\u6700\u4f73\u5b66\u4e60\u7387\u4e4b\u95f4\u6ca1\u6709\u663e\u8457\u5dee\u5f02\u3002\u9664\u975e\u53e6\u6709\u8bf4\u660e&#xff0c;\u6211\u4eec\u7ed8\u5236\u7684\u662f\u5404\u4e2a x \u8f74\u503c\u5bf9\u5e94\u5355\u72ec\u9009\u51fa\u7684\u6700\u4f73\u6027\u80fd\u901f\u7387\u7684\u6307\u6807\u56fe\u3002\u6211\u4eec\u53d1\u73b0\u6700\u4f73\u5b66\u4e60\u7387\u5e76\u6ca1\u6709\u968f\u5176\u4ed6\u53c2\u6570\u7684\u6539\u53d8\u800c\u53d1\u751f\u592a\u5927\u7684\u53d8\u5316\u3002<\/p>\n<p>\u2075 \u6211\u4eec\u5728\u8fd9\u4e9b\u6570\u636e\u96c6\u7684\u4e0d\u5e73\u8861\u7248\u672c\u4e0a\u8fdb\u884c\u4e86\u989d\u5916\u7684\u5b9e\u9a8c&#xff0c;\u53d1\u73b0\u5b83\u4eec\u5b9e\u9645\u4e0a\u5bf9 FedAvg \u6765\u8bf4\u7a0d\u5fae\u66f4\u5bb9\u6613\u4e00\u4e9b\u3002<br \/>\n\u2076 \u6211\u4eec\u59cb\u7ec8\u4f7f\u7528\u5b57\u7b26 (character) \u6765\u6307\u4ee3\u4e00\u4e2a\u5355\u5b57\u8282\u5b57\u7b26\u4e32&#xff0c;\u5e76\u4f7f\u7528\u89d2\u8272 (role) \u6765\u6307\u4ee3\u620f\u5267\u4e2d\u7684\u89d2\u8272\u3002<\/p>\n<h4>\u589e\u52a0\u5e76\u884c\u5ea6 (Increasing parallelism)<\/h4>\n<p>\u6211\u4eec\u9996\u5148\u5bf9\u5ba2\u6237\u7aef\u6bd4\u4f8b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span> \u8fdb\u884c\u5b9e\u9a8c&#xff0c;\u8be5\u53c2\u6570\u63a7\u5236\u591a\u5ba2\u6237\u7aef\u7684\u5e76\u884c\u5ea6\u3002\u8868 1 \u663e\u793a\u4e86\u6539\u53d8 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span> \u5bf9\u4e24\u79cd MNIST \u6a21\u578b\u7684\u5f71\u54cd\u3002\u6211\u4eec\u62a5\u544a\u4e86\u8fbe\u5230\u76ee\u6807\u6d4b\u8bd5\u96c6\u51c6\u786e\u7387\u6240\u9700\u7684\u901a\u4fe1\u8f6e\u6570\u3002\u4e3a\u4e86\u8ba1\u7b97\u8fd9\u4e2a\u503c&#xff0c;\u6211\u4eec\u4e3a\u6bcf\u4e2a\u53c2\u6570\u8bbe\u7f6e\u7ec4\u5408\u6784\u5efa\u4e86\u4e00\u6761\u5b66\u4e60\u66f2\u7ebf&#xff0c;\u5982\u4e0a\u6587\u6240\u8ff0\u4f18\u5316 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7\\\\eta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7136\u540e\u901a\u8fc7\u5728\u4e4b\u524d\u6240\u6709\u8f6e\u6b21\u4e2d\u53d6\u5f97\u6700\u4f73\u6d4b\u8bd5\u96c6\u51c6\u786e\u7387&#xff0c;\u4f7f\u5f97\u6bcf\u6761\u66f2\u7ebf\u5355\u8c03\u9012\u589e\u3002\u968f\u540e&#xff0c;\u6211\u4eec\u4f7f\u7528\u6784\u6210\u66f2\u7ebf\u7684\u79bb\u6563\u70b9\u4e4b\u95f4\u7684\u7ebf\u6027\u63d2\u503c\u6765\u8ba1\u7b97\u66f2\u7ebf\u8d8a\u8fc7\u76ee\u6807\u51c6\u786e\u7387\u7684\u8f6e\u6570\u3002\u901a\u8fc7\u53c2\u8003\u56fe 2&#xff08;\u56fe\u4e2d\u7070\u7ebf\u663e\u793a\u76ee\u6807&#xff09;\u53ef\u4ee5\u6700\u597d\u5730\u7406\u89e3\u8fd9\u4e00\u70b9\u3002<\/p>\n<hr \/>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113323-69a42403c43b0.png\" alt=\"\u88681\" \/><\/p>\n<p>\u8868 1 \u8bf4\u660e:<br \/>\n\u672c\u8868\u5c55\u793a\u4e86\u5ba2\u6237\u7aef\u6bd4\u4f8b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span> \u5bf9 MNIST 2NN (\u8bbe\u5b9a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E&#061;1E &#061; 1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>) \u548c CNN (\u8bbe\u5b9a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E&#061;5E &#061; 5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>) \u6a21\u578b\u7684\u5f71\u54cd\u3002\u6ce8\u610f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;0.0C &#061; 0.0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.0<\/span><\/span><\/span><\/span><\/span> \u5bf9\u5e94\u4e8e\u6bcf\u8f6e\u4ec5\u4e00\u4e2a\u5ba2\u6237\u7aef&#xff1b;\u7531\u4e8e\u6211\u4eec\u5bf9 MNIST \u6570\u636e\u4f7f\u7528 100 \u4e2a\u5ba2\u6237\u7aef&#xff0c;\u8fd9\u4e9b\u884c\u5206\u522b\u5bf9\u5e94\u4e8e 1\u300110\u300120\u300150 \u548c 100 \u4e2a\u5ba2\u6237\u7aef\u53c2\u4e0e\u3002\u6bcf\u4e2a\u8868\u683c\u6761\u76ee\u7ed9\u51fa\u4e86\u8fbe\u5230\u76ee\u6807\u6d4b\u8bd5\u96c6\u51c6\u786e\u7387&#xff08;2NN \u4e3a 97%&#xff0c;CNN \u4e3a 99%&#xff09;\u6240\u9700\u7684\u901a\u4fe1\u8f6e\u6570&#xff0c;\u4ee5\u53ca\u76f8\u5bf9\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;0C &#061; 0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u57fa\u7ebf\u7684\u52a0\u901f\u6bd4\u3002\u5176\u4e2d\u4e94\u6b21\u4f7f\u7528\u5927\u6279\u91cf\u7684\u8fd0\u884c\u672a\u5728\u5141\u8bb8\u7684\u65f6\u95f4\u5185\u8fbe\u5230\u76ee\u6807\u51c6\u786e\u7387\u3002<\/p>\n<p>\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;\u221eB &#061; \\\\infty<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord\">\u221e<\/span><\/span><\/span><\/span><\/span>&#xff08;\u5bf9\u4e8e MNIST \u800c\u8a00&#xff0c;\u6bcf\u8f6e\u5c06\u6240\u6709 600 \u4e2a\u5ba2\u6237\u7aef\u6837\u672c\u4f5c\u4e3a\u4e00\u4e2a\u5355\u6279\u6b21\u5904\u7406&#xff09;\u7684\u60c5\u51b5\u4e0b&#xff0c;\u589e\u52a0\u5ba2\u6237\u7aef\u6bd4\u4f8b\u7684\u4f18\u52bf\u975e\u5e38\u5c0f\u3002\u7136\u800c&#xff0c;\u4f7f\u7528\u8f83\u5c0f\u7684\u6279\u6b21\u5927\u5c0f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;10B &#061; 10<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span> \u65f6&#xff0c;\u4f7f\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C\u22650.1C \\\\ge 0.1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8193em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.1<\/span><\/span><\/span><\/span><\/span> \u4f1a\u6709\u663e\u8457\u7684\u6539\u8fdb&#xff0c;\u5c24\u5176\u662f\u5728\u975e IID \u7684\u60c5\u51b5\u4e0b\u3002\u57fa\u4e8e\u8fd9\u4e9b\u7ed3\u679c&#xff0c;\u5728\u6211\u4eec\u5927\u591a\u6570\u5269\u4f59\u5b9e\u9a8c\u4e2d&#xff0c;\u6211\u4eec\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span> \u56fa\u5b9a\u4e3a 0.1&#xff0c;\u8fd9\u5728\u8ba1\u7b97\u6548\u7387\u548c\u6536\u655b\u901f\u5ea6\u4e4b\u95f4\u53d6\u5f97\u4e86\u826f\u597d\u7684\u5e73\u8861\u3002\u6bd4\u8f83\u8868 1 \u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;\u221eB &#061; \\\\infty<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord\">\u221e<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;10B &#061; 10<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span> \u4e24\u5217\u8fbe\u5230\u76ee\u6807\u6240\u9700\u8f6e\u6570&#xff0c;\u53ef\u4ee5\u770b\u5230\u620f\u5267\u6027\u7684\u52a0\u901f&#xff0c;\u6211\u4eec\u5728\u4e0b\u6587\u4e2d\u5c06\u5bf9\u6b64\u8fdb\u884c\u7814\u7a76\u3002<\/p>\n<h4>\u589e\u52a0\u6bcf\u4e2a\u5ba2\u6237\u7aef\u7684\u8ba1\u7b97\u91cf (Increasing computation per client)<\/h4>\n<p>\u5728\u672c\u8282\u4e2d&#xff0c;\u6211\u4eec\u56fa\u5b9a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;0.1C &#061; 0.1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.1<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5e76\u5728\u6bcf\u4e00\u8f6e\u589e\u52a0\u6bcf\u4e2a\u5ba2\u6237\u7aef\u7684\u8ba1\u7b97\u91cf\u2014\u2014\u8fd9\u53ef\u4ee5\u901a\u8fc7\u51cf\u5c0f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">BB<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><\/span>\u3001\u589e\u52a0 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u6216\u4e24\u8005\u517c\u65bd\u6765\u5b9e\u73b0\u3002\u56fe 2 \u8868\u660e&#xff0c;\u6bcf\u8f6e\u589e\u52a0\u5c40\u90e8 SGD \u7684\u66f4\u65b0\u6b21\u6570\u53ef\u4ee5\u6781\u5927\u5730\u964d\u4f4e\u901a\u4fe1\u6210\u672c&#xff0c;\u8868 2 \u5219\u91cf\u5316\u4e86\u8fd9\u4e9b\u52a0\u901f\u3002\u6bcf\u8f6e\u6bcf\u4e2a\u5ba2\u6237\u7aef\u7684\u9884\u671f\u66f4\u65b0\u6b21\u6570\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">u&#061;(E[nk]\/B)E&#061;nE\/(KB)u &#061; (\\\\mathbb{E}[n_k]\/B)E &#061; nE\/(KB)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbb\">E<\/span><span class=\"mopen\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><span class=\"mord\">\/<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mord\">\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5176\u4e2d\u671f\u671b\u662f\u5bf9\u968f\u673a\u62bd\u53d6\u5ba2\u6237\u7aef <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">kk<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span> \u6c42\u7684\u3002\u6211\u4eec\u5728\u8868 2 \u7684\u6bcf\u4e2a\u90e8\u5206\u6839\u636e\u8be5\u7edf\u8ba1\u91cf\u5bf9\u884c\u8fdb\u884c\u4e86\u6392\u5e8f\u3002\u6211\u4eec\u770b\u5230\u901a\u8fc7\u8c03\u6574 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">BB<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><\/span> \u6765\u589e\u52a0 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u90fd\u662f\u6709\u6548\u7684\u3002\u53ea\u8981 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">BB<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><\/span> \u8db3\u591f\u5927\u4ee5\u5145\u5206\u5229\u7528\u5ba2\u6237\u7aef\u786c\u4ef6\u4e0a\u7684\u53ef\u7528\u5e76\u884c\u6027&#xff0c;\u964d\u4f4e\u5b83\u5b9e\u9645\u4e0a\u4e0d\u4f1a\u5e26\u6765\u8ba1\u7b97\u65f6\u95f4\u4e0a\u7684\u6210\u672c&#xff0c;\u56e0\u6b64\u5728\u5b9e\u8df5\u4e2d\u5b83\u5e94\u8be5\u662f\u9996\u5148\u88ab\u8c03\u4f18\u7684\u53c2\u6570\u3002<\/p>\n<hr \/>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113323-69a42403e7e3e.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u8868 2 \u8bf4\u660e:<br \/>\n\u672c\u8868\u5c55\u793a\u4e86\u8fbe\u5230\u76ee\u6807\u51c6\u786e\u7387\u6240\u9700\u7684\u901a\u4fe1\u8f6e\u6570&#xff1a;FedAvg \u5bf9\u6bd4 FedSGD&#xff08;\u7b2c\u4e00\u884c&#xff0c;\u8bbe\u5b9a\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E&#061;1E &#061; 1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;\u221eB &#061; \\\\infty<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord\">\u221e<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u5217\u7ed9\u51fa\u4e86 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">u&#061;En\/(KB)u &#061; En\/(KB)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord\">\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5373\u6bcf\u8f6e\u9884\u671f\u7684\u66f4\u65b0\u6b21\u6570\u3002\u4e0a\u534a\u90e8\u5206\u662f MNIST CNN&#xff0c;\u76ee\u6807\u51c6\u786e\u7387\u4e3a 99%&#xff1b;\u4e0b\u534a\u90e8\u5206\u662f Shakespeare LSTM&#xff0c;\u76ee\u6807\u51c6\u786e\u7387\u4e3a 54%\u3002\u5747\u5217\u51fa\u4e86 IID \u548c Non-IID \u4e0b\u7684\u7ed3\u679c\u53ca\u52a0\u901f\u500d\u6570\u3002<\/p>\n<p>\u5bf9\u4e8e MNIST \u6570\u636e\u7684 IID \u5212\u5206&#xff0c;\u5728\u6bcf\u4e2a\u5ba2\u6237\u7aef\u4e0a\u4f7f\u7528\u66f4\u591a\u7684\u8ba1\u7b97\u91cf\u4f7f\u8fbe\u5230\u76ee\u6807\u51c6\u786e\u7387\u6240\u9700\u7684\u8f6e\u6570\u5927\u5e45\u51cf\u5c11&#xff1a;CNN \u51cf\u5c11\u4e86 35 \u500d&#xff0c;2NN \u51cf\u5c11\u4e86 46 \u500d&#xff08;\u8be6\u89c1\u9644\u5f55 A \u4e2d\u7684\u8868 4 \u4ee5\u83b7\u53d6 2NN \u7684\u7ec6\u8282&#xff09;\u3002\u75c5\u6001\u5212\u5206\u7684 Non-IID \u6570\u636e\u7684\u52a0\u901f\u6548\u679c\u7a0d\u5f31&#xff0c;\u4f46\u4f9d\u7136\u663e\u8457&#xff08;2.8 &#8211; 3.7 \u500d&#xff09;\u3002\u5f53\u6211\u4eec\u5929\u771f\u5730\u5bf9\u5728\u5b8c\u5168\u4e0d\u540c\u7684\u4e00\u5bf9\u6570\u5b57\u4e0a\u8bad\u7ec3\u51fa\u7684\u6a21\u578b\u53c2\u6570\u8fdb\u884c\u5e73\u5747\u65f6&#xff0c;\u53d1\u73b0\u8fd9\u79cd\u5e73\u5747\u7adf\u7136\u80fd\u63d0\u4f9b\u4efb\u4f55\u4f18\u52bf&#xff08;\u800c\u6ca1\u6709\u5bfc\u81f4\u5b9e\u9645\u53d1\u6563&#xff09;&#xff0c;\u8fd9\u662f\u4ee4\u4eba\u5370\u8c61\u6df1\u523b\u7684\u3002\u56e0\u6b64&#xff0c;\u6211\u4eec\u5c06\u6b64\u89c6\u4e3a\u8fd9\u79cd\u65b9\u6cd5\u9c81\u68d2\u6027\u7684\u6709\u529b\u8bc1\u636e\u3002<\/p>\n<p>Shakespeare \u6570\u636e\u96c6&#xff08;\u6309\u5267\u4e2d\u89d2\u8272\u5212\u5206&#xff09;\u4e0d\u5e73\u8861\u548c\u975e\u72ec\u7acb\u540c\u5206\u5e03\u7684\u7279\u6027&#xff0c;\u66f4\u80fd\u4ee3\u8868\u6211\u4eec\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u9884\u671f\u4f1a\u9047\u5230\u7684\u6570\u636e\u5206\u5e03\u79cd\u7c7b\u3002\u4ee4\u4eba\u9f13\u821e\u7684\u662f&#xff0c;\u5bf9\u4e8e\u8fd9\u4e2a\u95ee\u9898&#xff0c;\u5728 non-IID \u4e14\u4e0d\u5e73\u8861\u7684\u6570\u636e\u4e0a\u5b66\u4e60\u5b9e\u9645\u4e0a\u8981\u5bb9\u6613\u5f97\u591a&#xff08;\u8fbe\u5230\u4e86 95 \u500d\u7684\u52a0\u901f&#xff0c;\u800c\u5e73\u8861\u7684 IID \u6570\u636e\u53ea\u6709 13 \u500d\u52a0\u901f&#xff09;&#xff1b;\u6211\u4eec\u63a8\u6d4b\u8fd9\u5728\u5f88\u5927\u7a0b\u5ea6\u4e0a\u662f\u56e0\u4e3a\u6709\u4e9b\u89d2\u8272\u62e5\u6709\u76f8\u5bf9\u5e9e\u5927\u7684\u672c\u5730\u6570\u636e\u96c6&#xff0c;\u8fd9\u4f7f\u5f97\u589e\u52a0\u5c40\u90e8\u8bad\u7ec3\u53d8\u5f97\u5c24\u4e3a\u6709\u4ef7\u503c\u3002<\/p>\n<p>\u5bf9\u4e8e\u6240\u6709\u4e09\u4e2a\u6a21\u578b\u7c7b\u522b&#xff0c;FedAvg \u6700\u7ec8\u6536\u655b\u5230\u7684\u6d4b\u8bd5\u96c6\u51c6\u786e\u7387\u90fd\u9ad8\u4e8e\u57fa\u7ebf FedSGD \u6a21\u578b\u3002\u5373\u4f7f\u6211\u4eec\u5c06\u6d4b\u8bd5\u7ebf\u6761\u5ef6\u957f\u8d85\u51fa\u6240\u7ed8\u8303\u56f4&#xff0c;\u8fd9\u4e00\u8d8b\u52bf\u4f9d\u7136\u6301\u7eed\u3002\u4f8b\u5982&#xff0c;\u5bf9\u4e8e CNN \u6a21\u578b&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;\u221e,E&#061;1B &#061; \\\\infty, E &#061; 1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">\u221e<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u7684 FedSGD \u6a21\u578b\u6700\u7ec8\u5728 1200 \u8f6e\u540e\u8fbe\u5230 99.22% \u7684\u51c6\u786e\u7387&#xff08;\u5e76\u4e14\u76f4\u5230 6000 \u8f6e\u90fd\u6ca1\u6709\u8fdb\u4e00\u6b65\u63d0\u9ad8&#xff09;&#xff0c;\u800c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;10,E&#061;20B &#061; 10, E &#061; 20<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">10<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">20<\/span><\/span><\/span><\/span><\/span> \u7684 FedAvg \u6a21\u578b\u5728\u4ec5 300 \u8f6e\u540e\u5c31\u8fbe\u5230\u4e86 99.44% \u7684\u51c6\u786e\u7387\u3002\u6211\u4eec\u63a8\u6d4b&#xff0c;\u9664\u4e86\u964d\u4f4e\u901a\u4fe1\u6210\u672c\u5916&#xff0c;\u6a21\u578b\u5e73\u5747\u8fd8\u80fd\u4ea7\u751f\u7c7b\u4f3c\u4e8e dropout [36] \u6240\u5e26\u6765\u7684\u6b63\u5219\u5316\u6548\u76ca\u3002<\/p>\n<p>\u6211\u4eec\u4e3b\u8981\u5173\u6ce8\u6cdb\u5316\u6027\u80fd&#xff0c;\u4f46 FedAvg \u5728\u4f18\u5316\u8bad\u7ec3\u635f\u5931\u65b9\u9762\u4e5f\u5f88\u6709\u6548&#xff0c;\u751a\u81f3\u5728\u6d4b\u8bd5\u96c6\u51c6\u786e\u7387\u8fbe\u5230\u5e73\u53f0\u671f\u4e4b\u540e\u4f9d\u7136\u5982\u6b64\u3002\u6211\u4eec\u89c2\u5bdf\u5230\u6240\u6709\u4e09\u4e2a\u6a21\u578b\u7c7b\u90fd\u6709\u7c7b\u4f3c\u7684\u884c\u4e3a&#xff0c;\u5e76\u5728\u9644\u5f55 A \u7684\u56fe 6 \u4e2d\u5c55\u793a\u4e86 MNIST CNN \u7684\u56fe\u8868\u3002<\/p>\n<hr \/>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113324-69a424040d295.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe 2 \u8bf4\u660e:<br \/>\n\u5bf9\u4e8e MNIST CNN&#xff08;\u5148\u662f IID&#xff0c;\u7136\u540e\u662f\u75c5\u6001 non-IID&#xff09;\u548c Shakespeare LSTM&#xff08;\u5148\u662f IID&#xff0c;\u7136\u540e\u662f\u6309 Play&amp;Role \u5212\u5206&#xff09;&#xff0c;\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;0.1C &#061; 0.1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.1<\/span><\/span><\/span><\/span><\/span> \u4e14\u4f18\u5316 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7\\\\eta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span> \u7684\u60c5\u51b5\u4e0b&#xff0c;\u6d4b\u8bd5\u96c6\u51c6\u786e\u7387\u4e0e\u901a\u4fe1\u8f6e\u6570\u7684\u5173\u7cfb\u3002\u7070\u7ebf\u663e\u793a\u8868 2 \u4e2d\u4f7f\u7528\u7684\u76ee\u6807\u51c6\u786e\u7387\u30022NN \u6a21\u578b\u7684\u56fe\u8868\u4f5c\u4e3a\u9644\u5f55 A \u4e2d\u7684\u56fe 7 \u7ed9\u51fa\u3002<\/p>\n<hr \/>\n<h4>\u6211\u4eec\u4f1a\u5728\u5ba2\u6237\u7aef\u6570\u636e\u96c6\u4e0a\u8fc7\u5ea6\u4f18\u5316\u5417&#xff1f; (Can we over-optimize on the client datasets?)<\/h4>\n<p>\u5f53\u524d\u7684\u5168\u5c40\u6a21\u578b\u53c2\u6570\u4ec5\u4ec5\u901a\u8fc7\u521d\u59cb\u5316\u7684\u65b9\u5f0f\u5f71\u54cd\u6bcf\u4e2a ClientUpdate \u5185\u90e8\u7684\u4f18\u5316\u3002\u56e0\u6b64&#xff0c;\u968f\u7740 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E\u2192\u221eE \\\\rightarrow \\\\infty<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord\">\u221e<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u81f3\u5c11\u5bf9\u4e8e\u51f8\u95ee\u9898&#xff0c;\u6700\u7ec8\u521d\u59cb\u6761\u4ef6\u5e94\u8be5\u662f\u65e0\u5173\u7d27\u8981\u7684&#xff0c;\u65e0\u8bba\u5982\u4f55\u521d\u59cb\u5316\u90fd\u4f1a\u8fbe\u5230\u5168\u5c40\u6700\u5c0f\u503c\u3002\u5373\u4f7f\u5bf9\u4e8e\u975e\u51f8\u95ee\u9898&#xff0c;\u6211\u4eec\u4e5f\u53ef\u4ee5\u731c\u60f3&#xff0c;\u53ea\u8981\u521d\u59cb\u5316\u4f4d\u4e8e\u540c\u4e00\u4e2a\u5438\u5f15\u76c6\u5185&#xff0c;\u7b97\u6cd5\u5c31\u4f1a\u6536\u655b\u5230\u76f8\u540c\u7684\u5c40\u90e8\u6700\u5c0f\u503c\u3002\u4e5f\u5c31\u662f\u8bf4&#xff0c;\u6211\u4eec\u9884\u8ba1\u867d\u7136\u4e00\u8f6e\u5e73\u5747\u53ef\u80fd\u4f1a\u4ea7\u751f\u4e00\u4e2a\u5408\u7406\u7684\u6a21\u578b&#xff0c;\u4f46\u989d\u5916\u7684\u901a\u4fe1&#xff08;\u548c\u5e73\u5747&#xff09;\u8f6e\u6b21\u53ef\u80fd\u4e0d\u4f1a\u5e26\u6765\u8fdb\u4e00\u6b65\u7684\u6539\u8fdb\u3002<\/p>\n<p>\u56fe 3 \u5c55\u793a\u4e86\u5728 Shakespeare LSTM \u95ee\u9898\u4e2d&#xff0c;\u521d\u59cb\u8bad\u7ec3\u9636\u6bb5\u4f7f\u7528\u6781\u5927 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u503c\u7684\u5f71\u54cd\u3002\u4e8b\u5b9e\u4e0a&#xff0c;\u5bf9\u4e8e\u975e\u5e38\u5927\u91cf\u7684\u672c\u5730 epoch&#xff0c;FedAvg \u53ef\u80fd\u4f1a\u9677\u5165\u505c\u6ede\u6216\u53d1\u6563\u3002\u2077 \u8fd9\u4e00\u7ed3\u679c\u8868\u660e&#xff0c;\u5bf9\u4e8e\u67d0\u4e9b\u6a21\u578b&#xff0c;\u5c24\u5176\u662f\u5728\u6536\u655b\u7684\u540e\u671f\u9636\u6bb5&#xff0c;\u51cf\u5c11\u6bcf\u8f6e\u672c\u5730\u8ba1\u7b97\u7684\u6570\u91cf&#xff08;\u901a\u8fc7\u8f6c\u800c\u4f7f\u7528\u66f4\u5c0f\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u6216\u66f4\u5927\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">BB<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><\/span>&#xff09;\u53ef\u80fd\u4f1a\u6709\u5e2e\u52a9&#xff0c;\u5176\u65b9\u5f0f\u4e0e\u8870\u51cf\u5b66\u4e60\u7387\u7c7b\u4f3c\u3002\u9644\u5f55 A \u4e2d\u7684\u56fe 8 \u7ed9\u51fa\u4e86\u9488\u5bf9 MNIST CNN \u7684\u7c7b\u6bd4\u5b9e\u9a8c\u3002\u6709\u8da3\u7684\u662f&#xff0c;\u5bf9\u4e8e\u8fd9\u4e2a\u6a21\u578b&#xff0c;\u5728\u8f83\u5927\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u503c\u4e0b&#xff0c;\u6211\u4eec\u6ca1\u6709\u770b\u5230\u6536\u655b\u901f\u5ea6\u6709\u663e\u8457\u4e0b\u964d\u3002\u7136\u800c&#xff0c;\u5728\u4e0b\u6587\u63cf\u8ff0\u7684\u5927\u89c4\u6a21\u8bed\u8a00\u5efa\u6a21\u4efb\u52a1\u4e2d&#xff0c;\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E&#061;5E &#061; 5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u76f8\u6bd4&#xff0c;\u6211\u4eec\u786e\u5b9e\u89c2\u5bdf\u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E&#061;1E &#061; 1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u65f6\u8868\u73b0\u7565\u597d&#xff08;\u53c2\u89c1\u9644\u5f55 A \u4e2d\u7684\u56fe 10&#xff09;\u3002<\/p>\n<p>\u2077 \u8bf7\u6ce8\u610f&#xff0c;\u7531\u4e8e\u8fd9\u79cd\u884c\u4e3a&#xff0c;\u5e76\u4e14\u7531\u4e8e\u5728\u8f83\u5927 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u503c\u4e0b\u5e76\u672a\u5bf9\u6240\u6709\u5b66\u4e60\u7387\u8fd0\u884c\u5b8c\u6574\u7684\u8f6e\u6b21&#xff0c;\u6211\u4eec\u5728\u56fe 3 \u4e2d\u62a5\u544a\u7684\u662f\u56fa\u5b9a\u5b66\u4e60\u7387\u4e0b\u7684\u7ed3\u679c&#xff08;\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f&#xff0c;\u8be5\u5b66\u4e60\u7387\u5728\u6574\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u53c2\u6570\u8303\u56f4\u5185\u8fd1\u4e4e\u6700\u4f73&#xff09;&#xff0c;\u5e76\u4e14\u672a\u5f3a\u5236\u8fd9\u4e9b\u7ebf\u6761\u5448\u73b0\u5355\u8c03\u6027\u3002<\/p>\n<hr \/>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113324-69a424042d4b5.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe 3 \u8bf4\u660e:<br \/>\n\u8bbe\u5b9a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;10B &#061; 10<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span> \u4e14 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;0.1C &#061; 0.1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.1<\/span><\/span><\/span><\/span><\/span>&#xff0c;Shakespeare LSTM \u5728\u56fa\u5b9a\u5b66\u4e60\u7387 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7&#061;1.47\\\\eta &#061; 1.47<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1.47<\/span><\/span><\/span><\/span><\/span> \u7684\u60c5\u51b5\u4e0b&#xff0c;\u5728\u5404\u5e73\u5747\u6b65\u9aa4\u4e4b\u95f4\u8bad\u7ec3\u4f17\u591a\u672c\u5730 epoch&#xff08;\u5927 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u503c&#xff09;\u6240\u4ea7\u751f\u7684\u5f71\u54cd\u3002<\/p>\n<hr \/>\n<h4>CIFAR \u5b9e\u9a8c (CIFAR experiments)<\/h4>\n<p>\u6211\u4eec\u8fd8\u5728 CIFAR-10 \u6570\u636e\u96c6 [24] \u4e0a\u8fdb\u884c\u4e86\u5b9e\u9a8c&#xff0c;\u4ee5\u8fdb\u4e00\u6b65\u9a8c\u8bc1 FedAvg\u3002\u8be5\u6570\u636e\u96c6\u7531 10 \u4e2a\u7c7b\u522b\u7684 32&#215;32 RGB \u5f69\u8272\u56fe\u50cf\u7ec4\u6210\u3002\u5171\u6709 50,000 \u4e2a\u8bad\u7ec3\u6837\u672c\u548c 10,000 \u4e2a\u6d4b\u8bd5\u6837\u672c\u3002\u6211\u4eec\u5c06\u5b83\u4eec\u5212\u5206\u5230 100 \u4e2a\u5ba2\u6237\u7aef\u4e2d&#xff0c;\u6bcf\u4e2a\u5ba2\u6237\u7aef\u5305\u542b 500 \u4e2a\u8bad\u7ec3\u6837\u672c\u548c 100 \u4e2a\u6d4b\u8bd5\u6837\u672c&#xff1b;\u7531\u4e8e\u8be5\u6570\u636e\u6ca1\u6709\u81ea\u7136\u7684\u7528\u6237\u5206\u5e03\u5c5e\u6027&#xff0c;\u6211\u4eec\u8003\u8651\u7684\u662f\u5e73\u8861\u4e14 IID \u7684\u573a\u666f\u3002\u6a21\u578b\u67b6\u6784\u53d6\u81ea TensorFlow \u6559\u7a0b [38]&#xff0c;\u7531\u4e24\u4e2a\u5377\u79ef\u5c42\u3001\u4e24\u4e2a\u5168\u8fde\u63a5\u5c42\u548c\u4e00\u4e2a\u8f93\u51fa logits \u7684\u7ebf\u6027\u53d8\u6362\u5c42\u7ec4\u6210&#xff0c;\u603b\u8ba1\u7ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">10610^6<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e2a\u53c2\u6570\u3002\u8bf7\u6ce8\u610f&#xff0c;\u76ee\u524d\u7684\u5148\u8fdb\u65b9\u6cd5\u5728 CIFAR \u4e0a\u5df2\u8fbe\u5230 96.5% \u7684\u6d4b\u8bd5\u51c6\u786e\u7387 [19]&#xff1b;\u5c3d\u7ba1\u5982\u6b64&#xff0c;\u6211\u4eec\u4f7f\u7528\u7684\u6807\u51c6\u6a21\u578b\u8db3\u4ee5\u6ee1\u8db3\u6211\u4eec\u7684\u9700\u6c42&#xff0c;\u56e0\u4e3a\u6211\u4eec\u7684\u76ee\u6807\u662f\u8bc4\u4f30\u6211\u4eec\u7684\u4f18\u5316\u65b9\u6cd5&#xff0c;\u800c\u4e0d\u662f\u5728\u6b64\u4efb\u52a1\u4e0a\u8fbe\u5230\u5c3d\u53ef\u80fd\u9ad8\u7684\u51c6\u786e\u7387\u3002\u56fe\u50cf\u9884\u5904\u7406\u4f5c\u4e3a\u8bad\u7ec3\u8f93\u5165\u7ba1\u9053\u7684\u4e00\u90e8\u5206\u8fdb\u884c&#xff0c;\u5305\u62ec\u5c06\u56fe\u50cf\u88c1\u526a\u4e3a 24&#215;24&#xff0c;\u968f\u673a\u5de6\u53f3\u7ffb\u8f6c&#xff0c;\u4ee5\u53ca\u8c03\u6574\u5bf9\u6bd4\u5ea6\u3001\u4eae\u5ea6\u548c\u8fdb\u884c\u767d\u5316\u5904\u7406\u3002<\/p>\n<p>\u5bf9\u4e8e\u8fd9\u4e9b\u5b9e\u9a8c&#xff0c;\u6211\u4eec\u8003\u8651\u4e86\u4e00\u4e2a\u989d\u5916\u7684\u57fa\u7ebf\u65b9\u6cd5&#xff1a;\u5728\u5b8c\u6574\u8bad\u7ec3\u96c6&#xff08;\u65e0\u7528\u6237\u5212\u5206&#xff09;\u4e0a\u4f7f\u7528\u5927\u5c0f\u4e3a 100 \u7684\u5c0f\u6279\u91cf\u8fdb\u884c\u6807\u51c6 SGD \u8bad\u7ec3\u3002\u8be5\u65b9\u6cd5\u5728 197,500 \u6b21\u5c0f\u6279\u91cf\u66f4\u65b0&#xff08;\u5728\u8054\u90a6\u573a\u666f\u4e2d&#xff0c;\u6bcf\u6b21\u5c0f\u6279\u91cf\u66f4\u65b0\u90fd\u9700\u8981\u4e00\u8f6e\u901a\u4fe1&#xff09;\u540e\u8fbe\u5230\u4e86 86% \u7684\u6d4b\u8bd5\u51c6\u786e\u7387\u3002\u800c FedAvg \u5728\u4ec5\u4ec5 2,000 \u8f6e\u901a\u4fe1\u540e&#xff0c;\u5c31\u5b9e\u73b0\u4e86\u7c7b\u4f3c\u7684 85% \u7684\u6d4b\u8bd5\u51c6\u786e\u7387\u3002\u5bf9\u4e8e\u6240\u6709\u7b97\u6cd5&#xff0c;\u9664\u4e86\u521d\u59cb\u5b66\u4e60\u7387\u4e4b\u5916&#xff0c;\u6211\u4eec\u8fd8\u8c03\u4f18\u4e86\u5b66\u4e60\u7387\u8870\u51cf\u53c2\u6570\u3002\u8868 3 \u7ed9\u51fa\u4e86\u57fa\u7ebf SGD\u3001FedSGD \u548c FedAvg \u8fbe\u5230\u4e09\u4e2a\u4e0d\u540c\u76ee\u6807\u51c6\u786e\u7387\u6240\u9700\u7684\u901a\u4fe1\u8f6e\u6570&#xff0c;\u56fe 4 \u5219\u5c55\u793a\u4e86 FedAvg \u4e0e FedSGD \u7684\u5b66\u4e60\u7387\u66f2\u7ebf\u5bf9\u6bd4\u3002<\/p>\n<p>\u901a\u8fc7\u5728 SGD \u548c FedAvg \u4e24\u8005\u4e0a\u90fd\u8fd0\u884c\u5c0f\u6279\u91cf\u5927\u5c0f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;50B &#061; 50<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">50<\/span><\/span><\/span><\/span><\/span> \u7684\u5b9e\u9a8c&#xff0c;\u6211\u4eec\u8fd8\u53ef\u4ee5\u8003\u5bdf\u51c6\u786e\u7387\u4f5c\u4e3a\u8fd9\u6837\u7684\u5c0f\u6279\u91cf\u68af\u5ea6\u8ba1\u7b97\u6b21\u6570\u7684\u51fd\u6570\u7684\u8868\u73b0\u3002\u6211\u4eec\u9884\u8ba1\u6807\u51c6 SGD \u5728\u8fd9\u91cc\u4f1a\u505a\u5f97\u66f4\u597d&#xff0c;\u56e0\u4e3a\u5728\u6bcf\u6b21\u5c0f\u6279\u91cf\u8ba1\u7b97\u540e\u90fd\u4f1a\u4f9d\u6b21\u8fc8\u51fa\u66f4\u65b0\u7684\u6b65\u5b50\u3002\u7136\u800c&#xff0c;\u6b63\u5982\u9644\u5f55\u4e2d\u7684\u56fe 9 \u6240\u5c55\u793a\u7684\u90a3\u6837&#xff0c;\u5bf9\u4e8e\u4e2d\u7b49\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u503c&#xff0c;FedAvg \u5728\u6bcf\u6b21\u5c0f\u6279\u91cf\u8ba1\u7b97\u4e2d\u53d6\u5f97\u7684\u8fdb\u5c55\u4e0e\u4e4b\u4e0d\u76f8\u4e0a\u4e0b\u3002\u6b64\u5916&#xff0c;\u6211\u4eec\u770b\u5230\u6807\u51c6 SGD \u548c\u4ec5\u6709\u4e00\u540d\u5ba2\u6237\u7aef&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;0C &#061; 0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>&#xff09;\u7684 FedAvg \u5728\u51c6\u786e\u7387\u4e0a\u90fd\u8868\u73b0\u51fa\u663e\u8457\u7684\u9707\u8361&#xff0c;\u800c\u5728\u66f4\u591a\u5ba2\u6237\u7aef\u4e0a\u8fdb\u884c\u5e73\u5747\u5219\u5e73\u6ed1\u4e86\u8fd9\u4e9b\u6ce2\u52a8\u3002<\/p>\n<hr \/>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113324-69a42404413ea.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe 4 \u8bf4\u660e:<br \/>\nCIFAR-10 \u5b9e\u9a8c\u7684\u6d4b\u8bd5\u51c6\u786e\u7387\u4e0e\u901a\u4fe1\u8f6e\u6570\u5bf9\u6bd4\u3002FedSGD \u4f7f\u7528\u6bcf\u8f6e 0.9934 \u7684\u5b66\u4e60\u7387\u8870\u51cf&#xff1b;FedAvg \u4f7f\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;50B &#061; 50<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">50<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6bcf\u8f6e 0.99 \u7684\u5b66\u4e60\u7387\u8870\u51cf&#xff0c;\u5e76\u4e14 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E&#061;5E &#061; 5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113324-69a424045260e.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u8868 3 \u8bf4\u660e:<br \/>\n\u5728 CIFAR10 \u4e0a\u8fbe\u5230\u76ee\u6807\u6d4b\u8bd5\u96c6\u51c6\u786e\u7387\u6240\u9700\u7684\u901a\u4fe1\u8f6e\u6570\u53ca\u76f8\u8f83\u4e8e\u57fa\u7ebf SGD \u7684\u52a0\u901f\u6bd4\u3002SGD \u8bbe\u5b9a\u5c0f\u6279\u91cf\u5927\u5c0f\u4e3a 100\u3002FedSGD \u548c FedAvg \u90fd\u4f7f\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;0.1C &#061; 0.1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.1<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5176\u4e2d FedAvg \u4f7f\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E&#061;5E &#061; 5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;50B &#061; 50<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">50<\/span><\/span><\/span><\/span><\/span>\u3002\u8868\u683c\u7ed9\u51fa\u4e86 80%\u300182% \u548c 85% \u4e09\u4e2a\u51c6\u786e\u7387\u9608\u503c\u4e0b\u7684\u5bf9\u6bd4\u6570\u636e\u3002<\/p>\n<hr \/>\n<h4>\u5927\u89c4\u6a21 LSTM \u5b9e\u9a8c (Large-scale LSTM experiments)<\/h4>\n<p>\u6211\u4eec\u5728\u4e00\u4e2a\u5927\u89c4\u6a21\u7684\u4e0b\u4e00\u4e2a\u8bcd\u9884\u6d4b\u4efb\u52a1\u4e0a\u8fdb\u884c\u4e86\u5b9e\u9a8c&#xff0c;\u4ee5\u8bc1\u660e\u6211\u4eec\u7684\u65b9\u6cd5\u5728\u771f\u5b9e\u4e16\u754c\u95ee\u9898\u4e0a\u7684\u6709\u6548\u6027\u3002\u6211\u4eec\u7684\u8bad\u7ec3\u6570\u636e\u96c6\u5305\u62ec\u6765\u81ea\u4e00\u4e2a\u5927\u578b\u793e\u4ea4\u7f51\u7edc\u7684 1000 \u4e07\u6761\u516c\u5f00\u5e16\u5b50\u3002\u6211\u4eec\u6309\u4f5c\u8005\u5bf9\u5e16\u5b50\u8fdb\u884c\u5206\u7ec4&#xff0c;\u603b\u8ba1\u8d85\u8fc7 500,000 \u4e2a\u5ba2\u6237\u7aef\u3002\u8fd9\u4e2a\u6570\u636e\u96c6\u975e\u5e38\u771f\u5b9e\u5730\u6a21\u62df\u4e86\u7528\u6237\u79fb\u52a8\u8bbe\u5907\u4e0a\u53ef\u80fd\u5b58\u5728\u7684\u6587\u672c\u8f93\u5165\u7c7b\u578b\u6570\u636e\u3002\u6211\u4eec\u9650\u5236\u6bcf\u4e2a\u5ba2\u6237\u7aef\u7684\u6570\u636e\u96c6\u6700\u591a\u4e0d\u8d85\u8fc7 5000 \u4e2a\u5355\u8bcd&#xff0c;\u5e76\u5728\u4e00\u4e2a\u5305\u542b 10 \u4e07\u6761\u4e0d\u540c&#xff08;\u975e\u8bad\u7ec3&#xff09;\u4f5c\u8005\u5e16\u5b50\u7684\u6d4b\u8bd5\u96c6\u4e0a\u62a5\u544a\u51c6\u786e\u7387&#xff08;\u51c6\u786e\u7387\u88ab\u5b9a\u4e49\u4e3a\u5728 10000 \u79cd\u53ef\u80fd\u6027\u7684\u8bcd\u6c47\u8868\u4e2d&#xff0c;\u9884\u6d4b\u6982\u7387\u6700\u9ad8\u7684\u6b63\u662f\u6b63\u786e\u4e0b\u4e00\u4e2a\u8bcd\u7684\u6570\u636e\u6bd4\u4f8b&#xff09;\u3002\u6211\u4eec\u7684\u6a21\u578b\u662f\u4e00\u4e2a\u5728 10000 \u8bcd\u6c47\u91cf\u4e0a\u7684 256 \u8282\u70b9 LSTM\u3002\u6bcf\u4e2a\u5355\u8bcd\u7684\u8f93\u5165\u548c\u8f93\u51fa\u5d4c\u5165\u7ef4\u5ea6\u5747\u4e3a 192&#xff0c;\u5e76\u4e0e\u6a21\u578b\u534f\u540c\u8bad\u7ec3&#xff1b;\u603b\u8ba1\u6709 4,950,544 \u4e2a\u53c2\u6570\u3002\u6211\u4eec\u4f7f\u7528 10 \u4e2a\u5355\u8bcd\u7684\u5c55\u5f00\u957f\u5ea6\u3002<\/p>\n<p>\u8fd9\u4e9b\u5b9e\u9a8c\u9700\u8981\u5927\u91cf\u7684\u8ba1\u7b97\u8d44\u6e90&#xff0c;\u56e0\u6b64\u6211\u4eec\u6ca1\u6709\u90a3\u4e48\u5f7b\u5e95\u5730\u63a2\u7d22\u8d85\u53c2\u6570&#xff1a;\u6240\u6709\u7684\u8fd0\u884c\u6bcf\u8f6e\u5747\u62bd\u53d6 200 \u4e2a\u5ba2\u6237\u7aef\u8fdb\u884c\u8bad\u7ec3&#xff1b;FedAvg \u4f7f\u7528\u4e86 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;8B &#061; 8<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">8<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E&#061;1E &#061; 1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u3002\u6211\u4eec\u63a2\u7d22\u4e86\u9488\u5bf9 FedAvg \u548c\u57fa\u7ebf FedSGD \u7684\u4e00\u7cfb\u5217\u5b66\u4e60\u7387\u3002\u56fe 5 \u663e\u793a\u4e86\u6700\u4f73\u5b66\u4e60\u7387\u7684\u5355\u8c03\u5b66\u4e60\u66f2\u7ebf\u3002\u5f53 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7&#061;18.0\\\\eta &#061; 18.0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">18.0<\/span><\/span><\/span><\/span><\/span> \u65f6&#xff0c;FedSGD \u9700\u8981 820 \u8f6e\u624d\u80fd\u8fbe\u5230 10.5% \u7684\u51c6\u786e\u7387&#xff0c;\u800c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7&#061;9.0\\\\eta &#061; 9.0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">9.0<\/span><\/span><\/span><\/span><\/span> \u65f6&#xff0c;FedAvg \u4ec5\u5728 35 \u8f6e\u901a\u4fe1\u540e\u5c31\u8fbe\u5230\u4e86 10.5% \u7684\u51c6\u786e\u7387&#xff08;\u6240\u9700\u901a\u4fe1\u8f6e\u6570\u6bd4 FedSGD \u5c11 23 \u500d&#xff09;\u3002\u6211\u4eec\u89c2\u5bdf\u5230 FedAvg \u6d4b\u8bd5\u51c6\u786e\u7387\u7684\u65b9\u5dee\u8f83\u4f4e&#xff0c;\u8be6\u60c5\u89c1\u9644\u5f55 A \u7684\u56fe 10\u3002\u8be5\u56fe\u8fd8\u5305\u62ec\u4e86 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E&#061;5E &#061; 5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u65f6\u7684\u7ed3\u679c&#xff0c;\u5b83\u8868\u73b0\u5f97\u6bd4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E&#061;1E &#061; 1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u7a0d\u5dee\u4e00\u70b9\u3002<\/p>\n<hr \/>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113324-69a424045bbf4.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe 5 \u8bf4\u660e:<br \/>\n\u5728\u975e\u72ec\u7acb\u540c\u5206\u5e03\u6570\u636e\u4e0a\u7684\u5927\u89c4\u6a21\u8bed\u8a00\u6a21\u578b\u8bcd\u7ea7 LSTM \u7684\u5355\u8c03\u5b66\u4e60\u66f2\u7ebf\u6bd4\u8f83\u3002\u663e\u793a\u4e86\u4e0d\u540c\u5b66\u4e60\u7387\u4e0b\u7684 FedSGD \u4e0e FedAvg (E&#061;1) \u7684\u5bf9\u6bd4\u3002<\/p>\n<hr \/>\n<h4>4 \u7ed3\u8bba\u548c\u672a\u6765\u5de5\u4f5c (Conclusions and Future Work)<\/h4>\n<p>\u6211\u4eec\u7684\u5b9e\u9a8c\u8868\u660e&#xff0c;\u8054\u90a6\u5b66\u4e60\u53ef\u4ee5\u505a\u5230\u5177\u6709\u5b9e\u7528\u6027&#xff0c;\u56e0\u4e3a FedAvg \u901a\u8fc7\u5229\u7528\u76f8\u5bf9\u8f83\u5c11\u7684\u901a\u4fe1\u8f6e\u6b21\u5c31\u80fd\u8bad\u7ec3\u51fa\u9ad8\u8d28\u91cf\u7684\u6a21\u578b&#xff0c;\u8fd9\u4e00\u70b9\u5728\u591a\u79cd\u6a21\u578b\u67b6\u6784\u7684\u5b9e\u9a8c\u4e2d\u5f97\u5230\u4e86\u8bc1\u660e&#xff1a;\u5305\u62ec\u4e00\u4e2a\u591a\u5c42\u611f\u77e5\u673a\u3001\u4e24\u4e2a\u4e0d\u540c\u7684\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u3001\u4e00\u4e2a\u4e24\u5c42\u5b57\u7b26\u7ea7 LSTM&#xff0c;\u4ee5\u53ca\u4e00\u4e2a\u5927\u89c4\u6a21\u8bcd\u7ea7 LSTM\u3002<\/p>\n<p>\u867d\u7136\u8054\u90a6\u5b66\u4e60\u63d0\u4f9b\u4e86\u8bf8\u591a\u5b9e\u9645\u7684\u9690\u79c1\u4fdd\u969c&#xff0c;\u4f46\u662f\u901a\u8fc7\u5dee\u5206\u9690\u79c1 [14, 13, 1]\u3001\u5b89\u5168\u591a\u65b9\u8ba1\u7b97 [18] \u6216\u4e24\u8005\u7684\u7ed3\u5408\u63d0\u4f9b\u66f4\u5f3a\u6709\u529b\u7684\u6570\u636e\u4fdd\u969c&#xff0c;\u4f9d\u7136\u662f\u672a\u6765\u4e00\u4e2a\u5f15\u4eba\u5165\u80dc\u7684\u7814\u7a76\u65b9\u5411\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f&#xff0c;\u8fd9\u4e24\u7c7b\u6280\u672f\u90fd\u6700\u81ea\u7136\u5730\u9002\u7528\u4e8e\u50cf FedAvg \u8fd9\u6837\u7684\u540c\u6b65\u7b97\u6cd5\u3002\u2078<\/p>\n<p>\u2078 \u5728\u8fd9\u9879\u5de5\u4f5c\u4e4b\u540e&#xff0c;Bonawitz \u7b49\u4eba [6] \u5f15\u5165\u4e86\u4e00\u79cd\u7528\u4e8e\u8054\u90a6\u5b66\u4e60\u7684\u9ad8\u6548\u5b89\u5168\u805a\u5408\u534f\u8bae&#xff0c;Kone\u010dn\u00fd \u7b49\u4eba [23] \u63d0\u51fa\u4e86\u8fdb\u4e00\u6b65\u964d\u4f4e\u901a\u4fe1\u6210\u672c\u7684\u7b97\u6cd5\u3002<\/p>\n<hr \/>\n<h4>\u53c2\u8003\u6587\u732e (References)<\/h4>\n<p>\u89c1\u8bba\u6587<\/p>\n<hr \/>\n<h4>\u9644\u5f55 A: \u8865\u5145\u56fe\u8868 (A Supplemental Figures and Tables)<\/h4>\n<hr \/>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113324-69a424046d211.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe 6 \u8bf4\u660e:<br \/>\nMNIST CNN \u7684\u8bad\u7ec3\u96c6\u6536\u655b\u60c5\u51b5\u3002\u6ce8\u610f y \u8f74\u91c7\u7528\u5bf9\u6570\u523b\u5ea6&#xff0c;x \u8f74\u6db5\u76d6\u7684\u8bad\u7ec3\u65f6\u95f4\u6bd4\u56fe 2 \u66f4\u957f\u3002\u8fd9\u4e9b\u56fe\u8868\u56fa\u5b9a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;0.1C &#061; 0.1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.1<\/span><\/span><\/span><\/span><\/span>\u3002\u56fe\u793a\u5206\u5de6\u53f3&#xff0c;\u5de6\u4e3a IID&#xff0c;\u53f3\u4e3a Non-IID\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113324-69a424049c9c4.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe 7 \u8bf4\u660e:<br \/>\nMNIST 2NN \u6a21\u578b\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;0.1C &#061; 0.1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.1<\/span><\/span><\/span><\/span><\/span> \u4e14\u4f18\u5316 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7\\\\eta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span> \u65f6\u7684\u6d4b\u8bd5\u96c6\u51c6\u786e\u7387\u4e0e\u901a\u4fe1\u8f6e\u6570\u3002\u5de6\u5217\u662f IID \u6570\u636e\u96c6&#xff0c;\u53f3\u5217\u662f\u75c5\u6001\u7684\u6bcf\u4e2a\u5ba2\u6237\u7aef 2 \u4e2a\u6570\u5b57\u7684 Non-IID \u6570\u636e\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113324-69a42404adaf5.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe 8 \u8bf4\u660e:<br \/>\n\u56fa\u5b9a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;10B &#061; 10<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;0.1C &#061; 0.1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.1<\/span><\/span><\/span><\/span><\/span> \u65f6&#xff0c;\u5728\u5404\u4e2a\u5e73\u5747\u6b65\u9aa4\u4e4b\u95f4\u8fdb\u884c\u591a\u6b21\u672c\u5730\u8f6e\u6570\u8bad\u7ec3&#xff08;\u5927 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u503c&#xff09;\u6240\u4ea7\u751f\u7684\u5f71\u54cd\u3002\u6b64\u56fe\u5c55\u793a MNIST CNN \u7684\u8bad\u7ec3\u635f\u5931\u3002\u6ce8\u610f&#xff0c;\u7531\u4e8e\u6211\u4eec\u75c5\u6001\u7684\u975e\u72ec\u7acb\u540c\u5206\u5e03&#xff08;non-IID&#xff09; MNIST \u6570\u636e\u96c6\u7684\u5b66\u4e60\u96be\u5ea6&#xff0c;\u4f7f\u7528\u4e86\u4e0d\u540c\u7684\u5b66\u4e60\u7387\u548c y \u8f74\u523b\u5ea6\u3002\u56fe\u793a\u5206\u5de6\u53f3&#xff0c;\u5de6\u4e3a IID (\u5bf9\u5e94 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7&#061;0.215\\\\eta &#061; 0.215<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.215<\/span><\/span><\/span><\/span><\/span>)&#xff0c;\u53f3\u4e3a Non-IID (\u5bf9\u5e94 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b7&#061;0.1\\\\eta &#061; 0.1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.1<\/span><\/span><\/span><\/span><\/span>)\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113324-69a42404bd190.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u8868 4 \u8bf4\u660e:<br \/>\n\u5bf9\u4e8e MNIST 2NN \u6a21\u578b&#xff0c;\u8fbe\u5230 97% \u76ee\u6807\u51c6\u786e\u7387\u65f6 FedAvg \u76f8\u8f83\u4e8e FedSGD&#xff08;\u7b2c\u4e00\u884c&#xff09;\u5728\u901a\u4fe1\u8f6e\u6570\u4e0a\u7684\u52a0\u901f\u6bd4\u8868\u683c\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113324-69a42404cd84f.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe 9 \u8bf4\u660e:<br \/>\n\u6d4b\u8bd5\u51c6\u786e\u7387\u4e0e\u5c0f\u6279\u91cf\u68af\u5ea6\u8ba1\u7b97\u6b21\u6570&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">B&#061;50B &#061; 50<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">50<\/span><\/span><\/span><\/span><\/span>&#xff09;\u4e4b\u95f4\u7684\u5173\u7cfb\u56fe\u3002\u57fa\u7ebf\u662f\u6807\u51c6\u7684\u987a\u5e8f SGD (\u7eff\u8272\u7ec6\u7ebf)&#xff0c;\u4e0e\u91c7\u7528\u4e0d\u540c\u5ba2\u6237\u7aef\u6bd4\u4f8b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span>&#xff08;\u56de\u5fc6\u4e00\u4e0b&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;0C &#061; 0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u610f\u5473\u7740\u6bcf\u8f6e\u53ea\u6709\u4e00\u4e2a\u5ba2\u6237\u7aef&#xff09;\u548c\u4e0d\u540c\u672c\u5730 epoch \u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">EE<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><\/span> \u7684 FedAvg \u8fdb\u884c\u5bf9\u6bd4\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260301113324-69a42404dd3dc.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe 10 \u8bf4\u660e:<br \/>\n\u5927\u89c4\u6a21\u8bed\u8a00\u6a21\u578b\u8bcd\u7ea7 LSTM \u7684\u5b66\u4e60\u66f2\u7ebf&#xff0c;\u6bcf 20 \u8f6e\u8bc4\u4f30\u4e00\u6b21\u3002\u5728\u8f83\u5c11\u7684\u672c\u5730 epoch \u4e0b&#xff08;1 \u4f18\u4e8e 5&#xff09;&#xff0c;FedAvg \u5b9e\u9645\u4e0a\u8868\u73b0\u66f4\u597d&#xff0c;\u800c\u4e14\u4e0e FedSGD \u76f8\u6bd4&#xff0c;\u5728\u8de8\u8f6e\u6b21\u8bc4\u4f30\u65f6\u6d4b\u8bd5\u51c6\u786e\u7387\u7684\u65b9\u5dee\u4e5f\u66f4\u5c0f\u3002<\/p>\n<hr \/>\n<p>\u8bba\u6587\u4e0b\u8f7d\u5730\u5740&#xff1a;https:\/\/arxiv.org\/abs\/1602.05629<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u57fa\u4e8e\u53bb\u4e2d\u5fc3\u5316\u6570\u636e\u7684\u6df1\u5ea6\u7f51\u7edc\u901a\u4fe1\u9ad8\u6548\u5b66\u4e60<br \/>\n(Communication-Efficient Learning of Deep Networks from Decentralized Data)<br \/>\n\u6458\u8981 (Abstract)<br \/>\n\u73b0\u4ee3\u79fb\u52a8\u8bbe\u5907\u80fd\u591f\u8bbf\u95ee\u5927\u91cf\u9002\u5408\u7528\u4e8e\u8bad\u7ec3\u6a21\u578b\u7684\u6570\u636e&#xff0c;\u8fd9\u4e9b\u6a21\u578b\u53cd\u8fc7\u6765\u53c8\u80fd\u6781\u5927\u5730\u6539\u5584\u8bbe\u5907\u4e0a\u7684\u7528\u6237\u4f53\u9a8c\u3002\u4f8b\u5982&#xff0c;\u8bed\u8a00\u6a21\u578b\u53ef\u4ee5\u6539\u5584\u8bed\u97f3\u8bc6\u522b\u548c\u6587\u672c\u8f93\u5165&#xff0c;\u56fe\u50cf\u6a21\u578b\u53ef\u4ee5\u81ea\u52a8\u6311\u9009\u4f18\u8d28\u7167\u7247\u3002\u7136\u800c&#xff0c;\u8fd9\u4e9b\u4e30\u5bcc\u7684\u6570\u636e\u5f80\u5f80\u5177\u6709\u9690\u79c1\u654f\u611f\u6027<\/p>\n","protected":false},"author":2,"featured_media":79317,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[8838,8837,8836,3183],"topic":[],"class_list":["post-79332","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-fedavg","tag-fl","tag-8836","tag-3183"],"yoast_head":"<!-- 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