{"id":98584,"date":"2026-09-01T07:00:11","date_gmt":"2026-08-31T23:00:11","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/98584.html"},"modified":"2026-09-01T07:00:11","modified_gmt":"2026-08-31T23:00:11","slug":"%e6%89%a9%e6%95%a3%e5%a4%a7%e8%af%ad%e8%a8%80%e6%a8%a1%e5%9e%8b%e6%96%b0%e6%a1%86%e6%9e%b6tracerl","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/98584.html","title":{"rendered":"\u6269\u6563\u5927\u8bed\u8a00\u6a21\u578b\u65b0\u6846\u67b6TraceRL"},"content":{"rendered":"<h2>\u6269\u6563\u5927\u8bed\u8a00\u6a21\u578b\u7684\u5f3a\u5316\u5b66\u4e60\u6846\u67b6\u9769\u65b0TraceRL&#xff1a;\u4ece\u7406\u8bba\u63a8\u5bfc\u5230\u7b97\u6cd5\u5b9e\u73b0<\/h2>\n<h3>\u76ee\u5f55<\/h3>\n<ul>\n<li>1. \u5f15\u8a00<\/li>\n<li>2. \u9884\u5907\u77e5\u8bc6\n<ul>\n<li>2.1 \u6269\u6563\u6982\u7387\u6a21\u578b\u7684\u5f62\u5f0f\u5316\u5b9a\u4e49<\/li>\n<li>2.2 \u63a9\u7801\u6269\u6563\u8fc7\u7a0b\u7684\u6570\u5b66\u63cf\u8ff0<\/li>\n<li>2.3 \u81ea\u56de\u5f52\u4e0e\u6269\u6563\u751f\u6210\u7684\u4fe1\u606f\u8bba\u5bf9\u6bd4<\/li>\n<\/ul>\n<\/li>\n<li>3. \u80cc\u666f\u4e0e\u52a8\u673a\n<ul>\n<li>3.1 \u6269\u6563\u8bed\u8a00\u6a21\u578b\u7684\u72ec\u7279\u4f18\u52bf<\/li>\n<li>3.2 \u4f20\u7edf\u5f3a\u5316\u5b66\u4e60\u65b9\u6cd5\u9762\u4e34\u7684\u6311\u6218<\/li>\n<\/ul>\n<\/li>\n<li>4. \u6838\u5fc3\u65b9\u6cd5&#xff1a;TraceRL \u6846\u67b6\n<ul>\n<li>4.1 \u6269\u6563\u8bed\u8a00\u6a21\u578b\u7684\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\u5f62\u5f0f\u5316<\/li>\n<li>4.2 \u8f68\u8ff9\u611f\u77e5\u7684\u5bc6\u96c6\u5956\u52b1\u5efa\u6a21<\/li>\n<li>4.3 \u6269\u6563\u57fa\u4ef7\u503c\u6a21\u578b\u7684\u7406\u8bba\u5206\u6790\u4e0e\u8bbe\u8ba1<\/li>\n<li>4.4 \u7b56\u7565\u4f18\u5316\u76ee\u6807\u7684\u6570\u5b66\u63a8\u5bfc<\/li>\n<li>4.5 \u67b6\u6784\u65e0\u5173\u6027\u7684\u7406\u8bba\u4fdd\u8bc1<\/li>\n<li>4.6 \u8bfe\u7a0b\u5b66\u4e60\u4e0e\u957f\u601d\u7ef4\u94fe\u63a8\u7406\u7684\u5f62\u5f0f\u5316\u5206\u6790<\/li>\n<\/ul>\n<\/li>\n<li>5. \u5b9e\u9a8c\u8bbe\u8ba1\u4e0e\u4e3b\u8981\u7ed3\u679c\n<ul>\n<li>5.1 \u8bc4\u4f30\u57fa\u51c6\u4e0e\u6570\u636e\u96c6<\/li>\n<li>5.2 \u5b9e\u73b0\u7ec6\u8282\u4e0e\u8d85\u53c2\u6570\u8bbe\u7f6e<\/li>\n<li>5.3 \u4e3b\u5b9e\u9a8c\u7ed3\u679c\u4e0e\u5206\u6790<\/li>\n<li>5.4 \u6d88\u878d\u5b9e\u9a8c\u4e0e\u654f\u611f\u6027\u5206\u6790<\/li>\n<\/ul>\n<\/li>\n<li>6. \u5c40\u9650\u6027\u4e0e\u672a\u6765\u7814\u7a76\u65b9\u5411<\/li>\n<li>7. \u4e00\u53e5\u8bdd\u603b\u7ed3<\/li>\n<li>8. \u8bba\u6587\u57fa\u672c\u4fe1\u606f<\/li>\n<\/ul>\n<hr \/>\n<h3>1. \u5f15\u8a00<\/h3>\n<p>\u6269\u6563\u6982\u7387\u6a21\u578b\u5728\u56fe\u50cf\u751f\u6210\u9886\u57df\u53d6\u5f97\u4e86\u663e\u8457\u6210\u529f&#xff0c;\u8fd1\u5e74\u6765\u7814\u7a76\u8005\u5f00\u59cb\u63a2\u7d22\u5176\u5728\u8bed\u8a00\u5efa\u6a21\u4e2d\u7684\u6f5c\u529b\u3002\u6269\u6563\u5927\u8bed\u8a00\u6a21\u578b\u91c7\u7528\u8fed\u4ee3\u53bb\u566a\u7684\u751f\u6210\u673a\u5236&#xff0c;\u4e0e\u4f20\u7edf\u7684\u81ea\u56de\u5f52\u6a21\u578b\u5f62\u6210\u672c\u8d28\u533a\u522b\u3002\u7136\u800c&#xff0c;\u5982\u4f55\u6709\u6548\u5730\u5bf9\u6269\u6563\u8bed\u8a00\u6a21\u578b\u8fdb\u884c\u540e\u8bad\u7ec3&#xff0c;\u7279\u522b\u662f\u5f15\u5165\u5f3a\u5316\u5b66\u4e60\u4ee5\u63d0\u5347\u63a8\u7406\u80fd\u529b&#xff0c;\u4ecd\u7136\u662f\u4e00\u4e2a\u5f00\u653e\u6027\u95ee\u9898\u3002<\/p>\n<p>Wang \u7b49\u4eba\u5728 ICLR 2026 \u53d1\u8868\u7684\u8bba\u6587\u300aRevolutionizing Reinforcement Learning Framework for Diffusion Large Language Models\u300b\u4e2d&#xff0c;\u63d0\u51fa\u4e86\u540d\u4e3a TraceRL \u7684\u65b0\u578b\u5f3a\u5316\u5b66\u4e60\u6846\u67b6\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260831230010-6a96077a6dcd9.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>2. \u9884\u5907\u77e5\u8bc6<\/h3>\n<h4>2.1 \u6269\u6563\u6982\u7387\u6a21\u578b\u7684\u5f62\u5f0f\u5316\u5b9a\u4e49<\/h4>\n<p>\u6269\u6563\u6982\u7387\u6a21\u578b&#xff08;Diffusion Probabilistic Model, DPM&#xff09;\u5b9a\u4e49\u4e86\u4e24\u4e2a\u968f\u673a\u8fc7\u7a0b&#xff1a;\u524d\u5411\u6269\u6563\u8fc7\u7a0b&#xff08;forward diffusion&#xff09;\u548c\u53cd\u5411\u53bb\u566a\u8fc7\u7a0b&#xff08;reverse denoising&#xff09;\u3002<\/p>\n<p>\u524d\u5411\u6269\u6563\u8fc7\u7a0b&#xff1a;\u8bbe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         0<\/p>\n<p>        )<\/p>\n<p>       q(\\\\mathbf{x}_0)<\/p>\n<p>    <\/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: 0.0359em\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u771f\u5b9e\u6570\u636e\u5206\u5e03&#xff0c;\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         0<\/p>\n<p>        \u2208<\/p>\n<p>         V<\/p>\n<p>         L<\/p>\n<p>       \\\\mathbf{x}_0 \\\\in \\\\mathcal{V}^L<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6891em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 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: 0.8413em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\" style=\"margin-right: 0.0822em\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><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\">L<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u957f\u5ea6\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        L<\/p>\n<p>       L<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/span> \u7684\u8bcd\u5143\u5e8f\u5217&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        V<\/p>\n<p>       \\\\mathcal{V}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathcal\" style=\"margin-right: 0.0822em\">V<\/span><\/span><\/span><\/span><\/span> \u4e3a\u8bcd\u8868\u3002\u524d\u5411\u8fc7\u7a0b\u5b9a\u4e49\u4e3a\u4e00\u4e2a\u9a6c\u5c14\u53ef\u592b\u94fe&#xff0c;\u9010\u6b65\u5411\u6570\u636e\u4e2d\u6dfb\u52a0\u566a\u58f0&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         q<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>           1<\/p>\n<p>           :<\/p>\n<p>           T<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>          0<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          \u220f<\/p>\n<p>           t<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          T<\/p>\n<p>         q<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         )<\/p>\n<p>         q(\\\\mathbf{x}_{1:T} | \\\\mathbf{x}_0) &#061; \\\\prod_{t&#061;1}^{T} q(\\\\mathbf{x}_t | \\\\mathbf{x}_{t-1}) <\/p>\n<p>     <\/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: 0.0359em\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/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 class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 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: 3.0954em;vertical-align: -1.2671em\"><\/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: -1.8829em;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\">t<\/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\">\u220f<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2671em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5bf9\u4e8e\u79bb\u6563\u8bcd\u5143\u7a7a\u95f4&#xff0c;\u63a9\u7801\u6269\u6563&#xff08;masked diffusion&#xff09;\u91c7\u7528\u5982\u4e0b\u8f6c\u79fb\u6838&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         q<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          \u220f<\/p>\n<p>           i<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          L<\/p>\n<p>         q<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>           (<\/p>\n<p>           i<\/p>\n<p>           )<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>           (<\/p>\n<p>           i<\/p>\n<p>           )<\/p>\n<p>         )<\/p>\n<p>         q(\\\\mathbf{x}_t | \\\\mathbf{x}_{t-1}) &#061; \\\\prod_{i&#061;1}^{L} q(x_t^{(i)} | x_{t-1}^{(i)}) <\/p>\n<p>     <\/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: 0.0359em\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"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: 3.106em;vertical-align: -1.2777em\"><\/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: -1.8723em;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\">\u220f<\/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 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/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 mathnormal\" style=\"margin-right: 0.0359em\">q<\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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 class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2458em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4337em;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\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3246em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d\u6bcf\u4e2a\u8bcd\u5143\u72ec\u7acb\u5730\u4ee5\u6982\u7387 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u03b2<\/p>\n<p>         t<\/p>\n<p>       \\\\beta_t<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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: -0.0528em;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> \u88ab\u66ff\u6362\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        [<\/p>\n<p>        MASK<\/p>\n<p>        ]<\/p>\n<p>       [\\\\text{MASK}]<\/p>\n<p>    <\/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 text\"><span class=\"mord\">MASK<\/span><\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span> \u6807\u8bb0&#xff0c;\u4ee5\u6982\u7387 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>        \u2212<\/p>\n<p>         \u03b2<\/p>\n<p>         t<\/p>\n<p>       1-\\\\beta_t<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/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: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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: -0.0528em;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> \u4fdd\u6301\u4e0d\u53d8\u3002\u8bb0 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        m<\/p>\n<p>       m<\/p>\n<p>    <\/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> \u4e3a\u63a9\u7801\u6807\u8bb0&#xff0c;\u5219\u5355\u6b65\u8f6c\u79fb\u53ef\u4ee5\u5199\u4f5c&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         q<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>           (<\/p>\n<p>           i<\/p>\n<p>           )<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>           (<\/p>\n<p>           i<\/p>\n<p>           )<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          {<\/p>\n<p>               1<\/p>\n<p>               \u2212<\/p>\n<p>                \u03b2<\/p>\n<p>                t<\/p>\n<p>               ,<\/p>\n<p>                x<\/p>\n<p>                t<\/p>\n<p>                 (<\/p>\n<p>                 i<\/p>\n<p>                 )<\/p>\n<p>               &#061;<\/p>\n<p>                x<\/p>\n<p>                 t<\/p>\n<p>                 \u2212<\/p>\n<p>                 1<\/p>\n<p>                 (<\/p>\n<p>                 i<\/p>\n<p>                 )<\/p>\n<p>               ,<\/p>\n<p>                x<\/p>\n<p>                 t<\/p>\n<p>                 \u2212<\/p>\n<p>                 1<\/p>\n<p>                 (<\/p>\n<p>                 i<\/p>\n<p>                 )<\/p>\n<p>               \u2260<\/p>\n<p>               m<\/p>\n<p>                \u03b2<\/p>\n<p>                t<\/p>\n<p>               ,<\/p>\n<p>                x<\/p>\n<p>                t<\/p>\n<p>                 (<\/p>\n<p>                 i<\/p>\n<p>                 )<\/p>\n<p>               &#061;<\/p>\n<p>               m<\/p>\n<p>               ,<\/p>\n<p>                x<\/p>\n<p>                 t<\/p>\n<p>                 \u2212<\/p>\n<p>                 1<\/p>\n<p>                 (<\/p>\n<p>                 i<\/p>\n<p>                 )<\/p>\n<p>               \u2260<\/p>\n<p>               m<\/p>\n<p>               1<\/p>\n<p>               ,<\/p>\n<p>                x<\/p>\n<p>                t<\/p>\n<p>                 (<\/p>\n<p>                 i<\/p>\n<p>                 )<\/p>\n<p>               &#061;<\/p>\n<p>               m<\/p>\n<p>               ,<\/p>\n<p>                x<\/p>\n<p>                 t<\/p>\n<p>                 \u2212<\/p>\n<p>                 1<\/p>\n<p>                 (<\/p>\n<p>                 i<\/p>\n<p>                 )<\/p>\n<p>               &#061;<\/p>\n<p>               m<\/p>\n<p>               0<\/p>\n<p>               ,<\/p>\n<p>              \u5176\u4ed6\u60c5\u51b5<\/p>\n<p>         q(x_t^{(i)} | x_{t-1}^{(i)}) &#061; \\\\begin{cases} 1 &#8211; \\\\beta_t, &amp; x_t^{(i)} &#061; x_{t-1}^{(i)}, \\\\quad x_{t-1}^{(i)} \\\\neq m \\\\\\\\ \\\\beta_t, &amp; x_t^{(i)} &#061; m, \\\\quad x_{t-1}^{(i)} \\\\neq m \\\\\\\\ 1, &amp; x_t^{(i)} &#061; m, \\\\quad x_{t-1}^{(i)} &#061; m \\\\\\\\ 0, &amp; \\\\text{\u5176\u4ed6\u60c5\u51b5} \\\\end{cases} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.3694em;vertical-align: -0.3246em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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 class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2458em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4337em;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\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3246em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/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: 5.8704em;vertical-align: -2.6852em\"><\/span><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.95em\"><span class=\"\" style=\"top: -1.6em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a9<\/span><\/span><\/span><span class=\"\" style=\"top: -1.592em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"\" style=\"height: 0.916em;width: 0.8889em\"><\/p>\n<p>              <\/span><\/span><span class=\"\" style=\"top: -3.15em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a8<\/span><\/span><\/span><span class=\"\" style=\"top: -4.292em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"\" style=\"height: 0.916em;width: 0.8889em\"><\/p>\n<p>              <\/span><\/span><span class=\"\" style=\"top: -5.2em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a7<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.45em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 3.1852em\"><span class=\"\" style=\"top: -5.1852em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><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 class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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: -0.0528em;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=\"mpunct\">,<\/span><\/span><\/span><span class=\"\" style=\"top: -3.7084em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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: -0.0528em;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=\"mpunct\">,<\/span><\/span><\/span><span class=\"\" style=\"top: -2.2316em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span class=\"\" style=\"top: -0.7916em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.6852em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 1em\"><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 3.1852em\"><span class=\"\" style=\"top: -5.1852em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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 class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2458em\"><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 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: 1.0448em\"><span class=\"\" style=\"top: -2.4337em;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\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3246em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4337em;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\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3246em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">\ue020<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace nobreak\"><\/span><span class=\"mrel\">&#061;<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord mathnormal\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.7084em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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 class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2458em\"><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 class=\"mord mathnormal\">m<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4337em;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\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3246em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">\ue020<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace nobreak\"><\/span><span class=\"mrel\">&#061;<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord mathnormal\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -2.2316em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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 class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2458em\"><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 class=\"mord mathnormal\">m<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4337em;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\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3246em\"><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 class=\"mord mathnormal\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -0.7916em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u5176\u4ed6\u60c5\u51b5<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.6852em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5373\u4e00\u65e6\u8bcd\u5143\u88ab\u63a9\u7801&#xff0c;\u5c06\u6c38\u4e45\u4fdd\u6301\u63a9\u7801\u72b6\u6001&#xff08;\u5438\u6536\u6001\u5047\u8bbe&#xff09;\u3002\u7ecf\u8fc7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        T<\/p>\n<p>       T<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span> \u6b65\u540e&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         T<\/p>\n<p>       \\\\mathbf{x}_T<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5944em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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 mathnormal mtight\" style=\"margin-right: 0.1389em\">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> \u4ee5\u9ad8\u6982\u7387\u6210\u4e3a\u5168\u63a9\u7801\u5e8f\u5217\u3002<\/p>\n<p>\u53cd\u5411\u53bb\u566a\u8fc7\u7a0b&#xff1a;\u53cd\u5411\u8fc7\u7a0b\u5b66\u4e60\u9006\u8f6c\u524d\u5411\u8fc7\u7a0b&#xff0c;\u4ece\u566a\u58f0\u5206\u5e03 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        p<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         T<\/p>\n<p>        )<\/p>\n<p>       p(\\\\mathbf{x}_T)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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 mathnormal mtight\" style=\"margin-right: 0.1389em\">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;\u901a\u5e38\u4e3a\u5168\u63a9\u7801\u5206\u5e03&#xff09;\u51fa\u53d1&#xff0c;\u9010\u6b65\u53bb\u566a\u751f\u6210\u6570\u636e&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          p<\/p>\n<p>          \u03b8<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>           0<\/p>\n<p>           :<\/p>\n<p>           T<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>         p<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          T<\/p>\n<p>         )<\/p>\n<p>          \u220f<\/p>\n<p>           t<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          T<\/p>\n<p>          p<\/p>\n<p>          \u03b8<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         )<\/p>\n<p>         p_\\\\theta(\\\\mathbf{x}_{0:T}) &#061; p(\\\\mathbf{x}_T) \\\\prod_{t&#061;1}^{T} p_\\\\theta(\\\\mathbf{x}_{t-1} | \\\\mathbf{x}_t) <\/p>\n<p>     <\/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\">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: 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: 0.0278em\">\u03b8<\/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 mathbf\">x<\/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\">0<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/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=\"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: 3.0954em;vertical-align: -1.2671em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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 mathnormal mtight\" style=\"margin-right: 0.1389em\">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 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: 1.8283em\"><span class=\"\" style=\"top: -1.8829em;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\">t<\/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\">\u220f<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2671em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">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: 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: 0.0278em\">\u03b8<\/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 mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         p<\/p>\n<p>         \u03b8<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>          t<\/p>\n<p>          \u2212<\/p>\n<p>          1<\/p>\n<p>        \u2223<\/p>\n<p>         x<\/p>\n<p>         t<\/p>\n<p>        )<\/p>\n<p>       p_\\\\theta(\\\\mathbf{x}_{t-1} | \\\\mathbf{x}_t)<\/p>\n<p>    <\/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\">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: 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: 0.0278em\">\u03b8<\/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 mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u662f\u7531\u53c2\u6570\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u03b8<\/p>\n<p>       \\\\theta<\/p>\n<p>    <\/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> \u7684\u795e\u7ecf\u7f51\u7edc\u53c2\u6570\u5316\u7684\u53bb\u566a\u6838\u3002\u8bad\u7ec3\u76ee\u6807\u4e3a\u53d8\u5206\u4e0b\u754c&#xff08;ELBO&#xff09;&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         log<\/p>\n<p>         \u2061<\/p>\n<p>          p<\/p>\n<p>          \u03b8<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          0<\/p>\n<p>         )<\/p>\n<p>         \u2265<\/p>\n<p>          L<\/p>\n<p>          ELBO<\/p>\n<p>         &#061;<\/p>\n<p>          E<\/p>\n<p>           q<\/p>\n<p>           (<\/p>\n<p>            x<\/p>\n<p>             1<\/p>\n<p>             :<\/p>\n<p>             T<\/p>\n<p>           \u2223<\/p>\n<p>            x<\/p>\n<p>            0<\/p>\n<p>           )<\/p>\n<p>          [<\/p>\n<p>          log<\/p>\n<p>          \u2061<\/p>\n<p>             p<\/p>\n<p>             \u03b8<\/p>\n<p>            (<\/p>\n<p>             x<\/p>\n<p>              0<\/p>\n<p>              :<\/p>\n<p>              T<\/p>\n<p>            )<\/p>\n<p>            q<\/p>\n<p>            (<\/p>\n<p>             x<\/p>\n<p>              1<\/p>\n<p>              :<\/p>\n<p>              T<\/p>\n<p>            \u2223<\/p>\n<p>             x<\/p>\n<p>             0<\/p>\n<p>            )<\/p>\n<p>          ]<\/p>\n<p>         \\\\log p_\\\\theta(\\\\mathbf{x}_0) \\\\geq \\\\mathcal{L}_{\\\\text{ELBO}} &#061; \\\\mathbb{E}_{q(\\\\mathbf{x}_{1:T}|\\\\mathbf{x}_0)} \\\\left[ \\\\log \\\\frac{p_\\\\theta(\\\\mathbf{x}_{0:T})}{q(\\\\mathbf{x}_{1:T}|\\\\mathbf{x}_0)} \\\\right] <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">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: 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: 0.0278em\">\u03b8<\/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 mathbf\">x<\/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: 0em;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 class=\"mclose\">)<\/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: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\">L<\/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 text mtight\"><span class=\"mord mtight\">ELBO<\/span><\/span><\/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: 2.4em;vertical-align: -0.95em\"><\/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: 0.3448em\"><span class=\"\" style=\"top: -2.5198em;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: 0.0359em\">q<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">x<\/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: -2.3567em;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 mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1433em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2223<\/span><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><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 mtight\">0<\/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 class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3552em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/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: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/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 class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 class=\"mclose\">)<\/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\">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: 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: 0.0278em\">\u03b8<\/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 mathbf\">x<\/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\">0<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/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 class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5c55\u5f00\u540e\u5f97\u5230&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          L<\/p>\n<p>          ELBO<\/p>\n<p>         &#061;<\/p>\n<p>             E<\/p>\n<p>              q<\/p>\n<p>              (<\/p>\n<p>               x<\/p>\n<p>               1<\/p>\n<p>              \u2223<\/p>\n<p>               x<\/p>\n<p>               0<\/p>\n<p>              )<\/p>\n<p>            [<\/p>\n<p>            log<\/p>\n<p>            \u2061<\/p>\n<p>             p<\/p>\n<p>             \u03b8<\/p>\n<p>            (<\/p>\n<p>             x<\/p>\n<p>             0<\/p>\n<p>            \u2223<\/p>\n<p>             x<\/p>\n<p>             1<\/p>\n<p>            )<\/p>\n<p>            ]<\/p>\n<p>           \u23df<\/p>\n<p>          \u91cd\u6784\u9879<\/p>\n<p>         \u2212<\/p>\n<p>          \u2211<\/p>\n<p>           t<\/p>\n<p>           &#061;<\/p>\n<p>           2<\/p>\n<p>          T<\/p>\n<p>             D<\/p>\n<p>             KL<\/p>\n<p>            (<\/p>\n<p>            q<\/p>\n<p>            (<\/p>\n<p>             x<\/p>\n<p>              t<\/p>\n<p>              \u2212<\/p>\n<p>              1<\/p>\n<p>            \u2223<\/p>\n<p>             x<\/p>\n<p>             t<\/p>\n<p>            ,<\/p>\n<p>             x<\/p>\n<p>             0<\/p>\n<p>            )<\/p>\n<p>            \u2225<\/p>\n<p>             p<\/p>\n<p>             \u03b8<\/p>\n<p>            (<\/p>\n<p>             x<\/p>\n<p>              t<\/p>\n<p>              \u2212<\/p>\n<p>              1<\/p>\n<p>            \u2223<\/p>\n<p>             x<\/p>\n<p>             t<\/p>\n<p>            )<\/p>\n<p>            )<\/p>\n<p>           \u23df<\/p>\n<p>          \u53bb\u566a\u5339\u914d\u9879<\/p>\n<p>         \u2212<\/p>\n<p>             D<\/p>\n<p>             KL<\/p>\n<p>            (<\/p>\n<p>            q<\/p>\n<p>            (<\/p>\n<p>             x<\/p>\n<p>             T<\/p>\n<p>            \u2223<\/p>\n<p>             x<\/p>\n<p>             0<\/p>\n<p>            )<\/p>\n<p>            \u2225<\/p>\n<p>            p<\/p>\n<p>            (<\/p>\n<p>             x<\/p>\n<p>             T<\/p>\n<p>            )<\/p>\n<p>            )<\/p>\n<p>           \u23df<\/p>\n<p>          \u5148\u9a8c\u5339\u914d\u9879<\/p>\n<p>         \\\\mathcal{L}_{\\\\text{ELBO}} &#061; \\\\underbrace{\\\\mathbb{E}_{q(\\\\mathbf{x}_1|\\\\mathbf{x}_0)}[\\\\log p_\\\\theta(\\\\mathbf{x}_0 | \\\\mathbf{x}_1)]}_{\\\\text{\u91cd\u6784\u9879}} &#8211; \\\\sum_{t&#061;2}^{T} \\\\underbrace{D_{\\\\text{KL}}(q(\\\\mathbf{x}_{t-1}|\\\\mathbf{x}_t, \\\\mathbf{x}_0) \\\\| p_\\\\theta(\\\\mathbf{x}_{t-1}|\\\\mathbf{x}_t))}_{\\\\text{\u53bb\u566a\u5339\u914d\u9879}} &#8211; \\\\underbrace{D_{\\\\text{KL}}(q(\\\\mathbf{x}_T|\\\\mathbf{x}_0) \\\\| p(\\\\mathbf{x}_T))}_{\\\\text{\u5148\u9a8c\u5339\u914d\u9879}} <\/p>\n<p>     <\/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\">L<\/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 text mtight\"><span class=\"mord mtight\">ELBO<\/span><\/span><\/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: 2.4315em;vertical-align: -1.6815em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.75em\"><span class=\"\" style=\"top: -1.3185em\"><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 cjk_fallback mtight\">\u91cd\u6784\u9879<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.75em\"><span class=\"svg-align\" style=\"top: -1.9968em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"stretchy\" style=\"height: 0.548em;min-width: 1.6em\"><span class=\"brace-left\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-center\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-right\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><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: 0.3448em\"><span class=\"\" style=\"top: -2.5198em;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: 0.0359em\">q<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><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 mtight\">1<\/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 class=\"mord mtight\">\u2223<\/span><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><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 mtight\">0<\/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 class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3552em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">[<\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">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: 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: 0.0278em\">\u03b8<\/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 mathbf\">x<\/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: 0em;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 class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/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 class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0032em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.6815em\"><span class=\"\"><\/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: 3.4047em;vertical-align: -1.5763em\"><\/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: -1.8829em;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\">t<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">2<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2671em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.75em\"><span class=\"\" style=\"top: -1.4237em\"><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 cjk_fallback mtight\">\u53bb\u566a\u5339\u914d\u9879<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.75em\"><span class=\"svg-align\" style=\"top: -2.102em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"stretchy\" style=\"height: 0.548em;min-width: 1.6em\"><span class=\"brace-left\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-center\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-right\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/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: -0.0278em;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 text mtight\"><span class=\"mord mtight\">KL<\/span><\/span><\/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: 0.0359em\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 class=\"mclose\">)<\/span><span class=\"mord\">\u2225<\/span><span class=\"mord\"><span class=\"mord mathnormal\">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: 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: 0.0278em\">\u03b8<\/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 mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mclose\">))<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.898em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.5763em\"><span class=\"\"><\/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: 2.3263em;vertical-align: -1.5763em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.75em\"><span class=\"\" style=\"top: -1.4237em\"><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 cjk_fallback mtight\">\u5148\u9a8c\u5339\u914d\u9879<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.75em\"><span class=\"svg-align\" style=\"top: -2.102em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"stretchy\" style=\"height: 0.548em;min-width: 1.6em\"><span class=\"brace-left\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-center\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-right\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/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: -0.0278em;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 text mtight\"><span class=\"mord mtight\">KL<\/span><\/span><\/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: 0.0359em\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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 mathnormal mtight\" style=\"margin-right: 0.1389em\">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=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 class=\"mclose\">)<\/span><span class=\"mord\">\u2225<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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 mathnormal mtight\" style=\"margin-right: 0.1389em\">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 class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.898em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.5763em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4>2.2 \u63a9\u7801\u6269\u6563\u8fc7\u7a0b\u7684\u6570\u5b66\u63cf\u8ff0<\/h4>\n<p>\u5728\u63a9\u7801\u6269\u6563\u6a21\u578b\u4e2d&#xff0c;\u540e\u9a8c\u5206\u5e03 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        q<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>          t<\/p>\n<p>          \u2212<\/p>\n<p>          1<\/p>\n<p>        \u2223<\/p>\n<p>         x<\/p>\n<p>         t<\/p>\n<p>        ,<\/p>\n<p>         x<\/p>\n<p>         0<\/p>\n<p>        )<\/p>\n<p>       q(\\\\mathbf{x}_{t-1} | \\\\mathbf{x}_t, \\\\mathbf{x}_0)<\/p>\n<p>    <\/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: 0.0359em\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5177\u6709\u5c01\u95ed\u5f62\u5f0f\u3002\u8bbe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          \u03b1<\/p>\n<p>          \u02c9<\/p>\n<p>         t<\/p>\n<p>        &#061;<\/p>\n<p>         \u220f<\/p>\n<p>          s<\/p>\n<p>          &#061;<\/p>\n<p>          1<\/p>\n<p>         t<\/p>\n<p>        (<\/p>\n<p>        1<\/p>\n<p>        \u2212<\/p>\n<p>         \u03b2<\/p>\n<p>         s<\/p>\n<p>        )<\/p>\n<p>       \\\\bar{\\\\alpha}_t &#061; \\\\prod_{s&#061;1}^t (1-\\\\beta_s)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7178em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5678em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/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: -0.0037em;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\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2332em;vertical-align: -0.2997em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u220f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9335em\"><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\">s<\/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\">t<\/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=\"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: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0528em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">s<\/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> \u4e3a\u7d2f\u79ef\u4fdd\u7559\u6982\u7387&#xff0c;\u5219 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        t<\/p>\n<p>       t<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span> \u65f6\u523b\u8bcd\u5143\u672a\u88ab\u63a9\u7801\u7684\u6982\u7387\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          \u03b1<\/p>\n<p>          \u02c9<\/p>\n<p>         t<\/p>\n<p>       \\\\bar{\\\\alpha}_t<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7178em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5678em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/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: -0.0037em;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>\u3002\u7ed9\u5b9a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         t<\/p>\n<p>       \\\\mathbf{x}_t<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5944em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         0<\/p>\n<p>       \\\\mathbf{x}_0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5944em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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>&#xff0c;\u540e\u9a8c\u6982\u7387\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         q<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>           (<\/p>\n<p>           i<\/p>\n<p>           )<\/p>\n<p>         &#061;<\/p>\n<p>         w<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>           (<\/p>\n<p>           i<\/p>\n<p>           )<\/p>\n<p>         ,<\/p>\n<p>          x<\/p>\n<p>          0<\/p>\n<p>           (<\/p>\n<p>           i<\/p>\n<p>           )<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          {<\/p>\n<p>                  \u03b1<\/p>\n<p>                  \u02c9<\/p>\n<p>                  t<\/p>\n<p>                  \u2212<\/p>\n<p>                  1<\/p>\n<p>                  \u03b1<\/p>\n<p>                  \u02c9<\/p>\n<p>                 t<\/p>\n<p>               \u22c5<\/p>\n<p>               I<\/p>\n<p>               [<\/p>\n<p>               w<\/p>\n<p>               &#061;<\/p>\n<p>                x<\/p>\n<p>                0<\/p>\n<p>                 (<\/p>\n<p>                 i<\/p>\n<p>                 )<\/p>\n<p>               ]<\/p>\n<p>               ,<\/p>\n<p>                x<\/p>\n<p>                t<\/p>\n<p>                 (<\/p>\n<p>                 i<\/p>\n<p>                 )<\/p>\n<p>               &#061;<\/p>\n<p>               m<\/p>\n<p>               ,<\/p>\n<p>                x<\/p>\n<p>                0<\/p>\n<p>                 (<\/p>\n<p>                 i<\/p>\n<p>                 )<\/p>\n<p>               \u2260<\/p>\n<p>               m<\/p>\n<p>               I<\/p>\n<p>               [<\/p>\n<p>               w<\/p>\n<p>               &#061;<\/p>\n<p>                x<\/p>\n<p>                t<\/p>\n<p>                 (<\/p>\n<p>                 i<\/p>\n<p>                 )<\/p>\n<p>               ]<\/p>\n<p>               ,<\/p>\n<p>                x<\/p>\n<p>                t<\/p>\n<p>                 (<\/p>\n<p>                 i<\/p>\n<p>                 )<\/p>\n<p>               \u2260<\/p>\n<p>               m<\/p>\n<p>         q(x_{t-1}^{(i)} &#061; w | x_t^{(i)}, x_0^{(i)}) &#061; \\\\begin{cases} \\\\frac{\\\\bar{\\\\alpha}_{t-1}}{\\\\bar{\\\\alpha}_t} \\\\cdot \\\\mathbb{I}[w &#061; x_0^{(i)}], &amp; x_t^{(i)} &#061; m, \\\\quad x_0^{(i)} \\\\neq m \\\\\\\\ \\\\mathbb{I}[w &#061; x_t^{(i)}], &amp; x_t^{(i)} \\\\neq m \\\\end{cases} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.3694em;vertical-align: -0.3246em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4337em;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\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3246em\"><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: 1.3111em;vertical-align: -0.2663em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord\">\u2223<\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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 class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2458em\"><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\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0448em\"><span class=\"\" style=\"top: -2.4337em;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\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2663em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/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: 3em;vertical-align: -1.25em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.7334em\"><span class=\"\" style=\"top: -3.7334em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><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: 0.8492em\"><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 accent mtight\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5678em\"><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0037em\">\u03b1<\/span><\/span><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord mtight\">\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/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: -0.0037em;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: -3.4518em\"><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 accent mtight\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5678em\"><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0037em\">\u03b1<\/span><\/span><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord mtight\">\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0037em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/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: 0.2025em\"><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=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathbb\">I<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/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 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: 1.0448em\"><span class=\"\" style=\"top: -2.4337em;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\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2663em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span class=\"\" style=\"top: -2.2435em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">I<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/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 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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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 class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2458em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2333em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 1em\"><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.7334em\"><span class=\"\" style=\"top: -3.7334em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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 class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2458em\"><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 class=\"mord mathnormal\">m<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4337em;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\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2663em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">\ue020<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace nobreak\"><\/span><span class=\"mrel\">&#061;<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord mathnormal\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -2.2435em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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 class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2458em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">\ue020<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace nobreak\"><\/span><span class=\"mrel\">&#061;<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord mathnormal\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2333em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        w<\/p>\n<p>        \u2208<\/p>\n<p>        V<\/p>\n<p>       w \\\\in \\\\mathcal{V}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5782em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/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: 0.0822em\">V<\/span><\/span><\/span><\/span><\/span>\u3002\u8be5\u5c01\u95ed\u5f62\u5f0f\u4f7f\u5f97\u6211\u4eec\u53ef\u4ee5\u7cbe\u786e\u8ba1\u7b97 KL \u6563\u5ea6\u9879&#xff0c;\u4ece\u800c\u7b80\u5316\u8bad\u7ec3\u8fc7\u7a0b\u3002<\/p>\n<h4>2.3 \u81ea\u56de\u5f52\u4e0e\u6269\u6563\u751f\u6210\u7684\u4fe1\u606f\u8bba\u5bf9\u6bd4<\/h4>\n<p>\u4ece\u4fe1\u606f\u8bba\u89c6\u89d2&#xff0c;\u4e24\u79cd\u751f\u6210\u8303\u5f0f\u5b58\u5728\u672c\u8d28\u5dee\u5f02\u3002\u8bbe\u5e8f\u5217 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       \\\\mathbf{x}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4444em\"><\/span><span class=\"mord mathbf\">x<\/span><\/span><\/span><\/span><\/span> \u7684\u71b5\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        H<\/p>\n<p>        (<\/p>\n<p>        x<\/p>\n<p>        )<\/p>\n<p>       H(\\\\mathbf{x})<\/p>\n<p>    <\/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: 0.0813em\">H<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002\u81ea\u56de\u5f52\u751f\u6210\u5c06\u8054\u5408\u5206\u5e03\u5206\u89e3\u4e3a\u6761\u4ef6\u6982\u7387\u7684\u4e58\u79ef&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         H<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          \u2211<\/p>\n<p>           i<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          L<\/p>\n<p>         H<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          i<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>           &lt;<\/p>\n<p>           i<\/p>\n<p>         )<\/p>\n<p>         H(\\\\mathbf{x}) &#061; \\\\sum_{i&#061;1}^{L} H(x_i | \\\\mathbf{x}_{&lt;i}) <\/p>\n<p>     <\/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: 0.0813em\">H<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/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: 3.106em;vertical-align: -1.2777em\"><\/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: -1.8723em;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 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/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 mathnormal\" style=\"margin-right: 0.0813em\">H<\/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=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">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 mtight\"><span class=\"mrel mtight\">&lt;<\/span><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1774em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u751f\u6210\u8fc7\u7a0b\u6309\u7167\u56fa\u5b9a\u7684\u56e0\u679c\u987a\u5e8f\u9010\u4f4d\u786e\u5b9a\u4fe1\u606f\u3002\u6269\u6563\u751f\u6210\u5219\u91c7\u7528\u8fed\u4ee3\u7cbe\u5316\u7b56\u7565&#xff1a;\u6bcf\u4e2a\u751f\u6210\u6b65 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        t<\/p>\n<p>       t<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span> \u63ed\u793a\u90e8\u5206\u4fe1\u606f\u3002\u5b9a\u4e49\u4e92\u4fe1\u606f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        I<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         0<\/p>\n<p>        ;<\/p>\n<p>         x<\/p>\n<p>         t<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>        H<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         0<\/p>\n<p>        )<\/p>\n<p>        \u2212<\/p>\n<p>        H<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         0<\/p>\n<p>        \u2223<\/p>\n<p>         x<\/p>\n<p>         t<\/p>\n<p>        )<\/p>\n<p>       I(\\\\mathbf{x}_0; \\\\mathbf{x}_t) &#061; H(\\\\mathbf{x}_0) &#8211; H(\\\\mathbf{x}_0 | \\\\mathbf{x}_t)<\/p>\n<p>    <\/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: 0.0785em\">I<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 class=\"mpunct\">;<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"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: 0.0813em\">H<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 class=\"mclose\">)<\/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: 0.0813em\">H<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002\u5f53 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        t<\/p>\n<p>       t<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span> \u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        T<\/p>\n<p>       T<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span> \u9012\u51cf\u81f3 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        0<\/p>\n<p>       0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u65f6&#xff0c;\u4e92\u4fe1\u606f\u9010\u6e10\u589e\u52a0&#xff0c;\u8868\u660e\u566a\u58f0\u9010\u6b65\u88ab\u79fb\u9664\u3002\u8fd9\u79cd\u5dee\u5f02\u51b3\u5b9a\u4e86\u5f3a\u5316\u5b66\u4e60\u65b9\u6cd5\u7684\u8bbe\u8ba1\u5fc5\u987b\u8003\u8651\u4e0d\u540c\u7684\u4fe1\u606f\u7ed3\u6784\u3002<\/p>\n<h3>3. \u80cc\u666f\u4e0e\u52a8\u673a<\/h3>\n<h4>3.1 \u6269\u6563\u8bed\u8a00\u6a21\u578b\u7684\u72ec\u7279\u4f18\u52bf<\/h4>\n<p>\u6269\u6563\u8bed\u8a00\u6a21\u578b\u76f8\u8f83\u4e8e\u81ea\u56de\u5f52\u6a21\u578b\u5177\u6709\u4ee5\u4e0b\u6f5c\u5728\u4f18\u52bf&#xff1a;<\/p>\n<li>\u53cc\u5411\u4e0a\u4e0b\u6587\u5efa\u6a21&#xff1a;\u5728\u6bcf\u6b65\u53bb\u566a\u8fc7\u7a0b\u4e2d&#xff0c;\u6a21\u578b\u53ef\u4ee5\u540c\u65f6\u5229\u7528\u5f53\u524d\u4f4d\u7f6e\u5de6\u53f3\u4e24\u4fa7\u7684\u4e0a\u4e0b\u6587\u4fe1\u606f\u8fdb\u884c\u9884\u6d4b\u3002<\/li>\n<li>\u53ef\u63a7\u751f\u6210\u80fd\u529b&#xff1a;\u901a\u8fc7\u5728\u53bb\u566a\u8fc7\u7a0b\u4e2d\u6ce8\u5165\u7ea6\u675f\u6761\u4ef6&#xff0c;\u53ef\u4ee5\u7075\u6d3b\u5730\u5f15\u5bfc\u751f\u6210\u65b9\u5411\u3002<\/li>\n<li>\u5e76\u884c\u751f\u6210\u6f5c\u529b&#xff1a;\u7406\u8bba\u4e0a\u53ef\u4ee5\u5728\u6bd4\u5e8f\u5217\u957f\u5ea6\u66f4\u5c11\u7684\u6b65\u6570\u5185\u5b8c\u6210\u751f\u6210\u3002<\/li>\n<h4>3.2 \u4f20\u7edf\u5f3a\u5316\u5b66\u4e60\u65b9\u6cd5\u9762\u4e34\u7684\u6311\u6218<\/h4>\n<p>\u4f20\u7edf\u5f3a\u5316\u5b66\u4e60\u7b97\u6cd5&#xff0c;\u5982\u8fd1\u7aef\u7b56\u7565\u4f18\u5316&#xff08;PPO&#xff09;&#xff0c;\u5728\u5e94\u7528\u4e8e\u81ea\u56de\u5f52\u8bed\u8a00\u6a21\u578b\u65f6&#xff0c;\u9ad8\u5ea6\u4f9d\u8d56\u751f\u6210\u8fc7\u7a0b\u6982\u7387\u7684\u94fe\u5f0f\u5206\u89e3&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          p<\/p>\n<p>          AR<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          \u220f<\/p>\n<p>           t<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          L<\/p>\n<p>         p<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>           &lt;<\/p>\n<p>           t<\/p>\n<p>         )<\/p>\n<p>         p_{\\\\text{AR}}(\\\\mathbf{x}) &#061; \\\\prod_{t&#061;1}^{L} p(x_t | \\\\mathbf{x}_{&lt;t}) <\/p>\n<p>     <\/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\">p<\/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 text mtight\"><span class=\"mord mtight\">AR<\/span><\/span><\/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 mathbf\">x<\/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: 3.0954em;vertical-align: -1.2671em\"><\/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: -1.8829em;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\">t<\/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\">\u220f<\/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 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2671em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">p<\/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: 0.2806em\"><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=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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 mtight\"><span class=\"mrel mtight\">&lt;<\/span><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1774em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5728\u6b64\u6846\u67b6\u4e0b&#xff0c;\u7b56\u7565\u68af\u5ea6\u5177\u6709\u7b80\u6d01\u5f62\u5f0f&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          \u2207<\/p>\n<p>          \u03b8<\/p>\n<p>         J<\/p>\n<p>         (<\/p>\n<p>         \u03b8<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          E<\/p>\n<p>           \u03c4<\/p>\n<p>           \u223c<\/p>\n<p>            p<\/p>\n<p>            \u03b8<\/p>\n<p>          [<\/p>\n<p>           \u2211<\/p>\n<p>            t<\/p>\n<p>            &#061;<\/p>\n<p>            1<\/p>\n<p>           L<\/p>\n<p>           \u2207<\/p>\n<p>           \u03b8<\/p>\n<p>          log<\/p>\n<p>          \u2061<\/p>\n<p>           p<\/p>\n<p>           \u03b8<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           t<\/p>\n<p>          \u2223<\/p>\n<p>           x<\/p>\n<p>            &lt;<\/p>\n<p>            t<\/p>\n<p>          )<\/p>\n<p>          \u22c5<\/p>\n<p>          R<\/p>\n<p>          (<\/p>\n<p>          \u03c4<\/p>\n<p>          )<\/p>\n<p>          ]<\/p>\n<p>         \\\\nabla_\\\\theta J(\\\\theta) &#061; \\\\mathbb{E}_{\\\\tau \\\\sim p_\\\\theta} \\\\left[ \\\\sum_{t&#061;1}^{L} \\\\nabla_\\\\theta \\\\log p_\\\\theta(x_t | \\\\mathbf{x}_{&lt;t}) \\\\cdot R(\\\\tau) \\\\right] <\/p>\n<p>     <\/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\">\u2207<\/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: 0.0278em\">\u03b8<\/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 mathnormal\" style=\"margin-right: 0.0962em\">J<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/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: 3.0954em;vertical-align: -1.2671em\"><\/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: 0.1514em\"><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 mathnormal mtight\" style=\"margin-right: 0.1132em\">\u03c4<\/span><span class=\"mrel mtight\">\u223c<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">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: 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: 0.0278em\">\u03b8<\/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: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">[<\/span><\/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: -1.8829em;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\">t<\/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 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2671em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2207<\/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: 0.0278em\">\u03b8<\/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: 0.1667em\"><\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">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: 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: 0.0278em\">\u03b8<\/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\">x<\/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=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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 mtight\"><span class=\"mrel mtight\">&lt;<\/span><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1774em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/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 class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1132em\">\u03c4<\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u7136\u800c&#xff0c;\u6269\u6563\u8bed\u8a00\u6a21\u578b\u7684\u751f\u6210\u6982\u7387\u65e0\u6cd5\u5206\u89e3\u4e3a\u56e0\u679c\u94fe\u5f0f\u7ed3\u6784\u3002\u5176\u9006\u5411\u53bb\u566a\u8f68\u8ff9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         T<\/p>\n<p>        \u2192<\/p>\n<p>         x<\/p>\n<p>          T<\/p>\n<p>          \u2212<\/p>\n<p>          1<\/p>\n<p>        \u2192<\/p>\n<p>        \u22ef<\/p>\n<p>        \u2192<\/p>\n<p>         x<\/p>\n<p>         0<\/p>\n<p>       \\\\mathbf{x}_T \\\\rightarrow \\\\mathbf{x}_{T-1} \\\\rightarrow \\\\cdots \\\\rightarrow \\\\mathbf{x}_0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5944em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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 mathnormal mtight\" style=\"margin-right: 0.1389em\">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\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6528em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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 mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mbin mtight\">\u2212<\/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\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.3669em\"><\/span><span class=\"minner\">\u22ef<\/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: 0.5944em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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> \u4e2d&#xff0c;\u6bcf\u4e2a\u65f6\u95f4\u6b65\u5bf9\u6240\u6709\u4f4d\u7f6e\u8fdb\u884c\u8054\u5408\u66f4\u65b0&#xff0c;\u4f4d\u7f6e\u95f4\u7684\u4f9d\u8d56\u6027\u5448\u5168\u5c40\u8026\u5408\u72b6\u6001\u3002\u56e0\u6b64&#xff0c;\u76f4\u63a5\u5c06\u4f20\u7edf\u5f3a\u5316\u5b66\u4e60\u65b9\u6cd5\u5e94\u7528\u4e8e\u6269\u6563\u8bed\u8a00\u6a21\u578b\u5b58\u5728\u6839\u672c\u6027\u7684\u4e0d\u5339\u914d\u95ee\u9898\u3002<\/p>\n<h3>4. \u6838\u5fc3\u65b9\u6cd5&#xff1a;TraceRL \u6846\u67b6<\/h3>\n<p>TraceRL \u6846\u67b6\u5c06\u6574\u4e2a\u53bb\u566a\u8fc7\u7a0b\u89c6\u4e3a\u4e00\u6761\u5b8c\u6574\u7684\u63a8\u7406\u8f68\u8ff9&#xff0c;\u5e76\u5728\u6b64\u57fa\u7840\u4e0a\u5f15\u5165\u8f68\u8ff9\u611f\u77e5\u7684\u5f3a\u5316\u5b66\u4e60\u673a\u5236\u3002<\/p>\n<h4>4.1 \u6269\u6563\u8bed\u8a00\u6a21\u578b\u7684\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\u5f62\u5f0f\u5316<\/h4>\n<p>\u5c06\u9006\u5411\u53bb\u566a\u8fc7\u7a0b\u5efa\u6a21\u4e3a\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b&#xff08;MDP&#xff09;\u3002\u5b9a\u4e49\u5143\u7ec4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        S<\/p>\n<p>        ,<\/p>\n<p>        A<\/p>\n<p>        ,<\/p>\n<p>        P<\/p>\n<p>        ,<\/p>\n<p>        R<\/p>\n<p>        ,<\/p>\n<p>        \u03b3<\/p>\n<p>        )<\/p>\n<p>       (\\\\mathcal{S}, \\\\mathcal{A}, P, R, \\\\gamma)<\/p>\n<p>    <\/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 mathcal\" style=\"margin-right: 0.075em\">S<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathcal\">A<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0556em\">\u03b3<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff1a;<\/p>\n<ul>\n<li>\n<p>\u72b6\u6001\u7a7a\u95f4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           S<\/p>\n<p>          \\\\mathcal{S}<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathcal\" style=\"margin-right: 0.075em\">S<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u6240\u6709\u90e8\u5206\u63a9\u7801\u5e8f\u5217\u7684\u96c6\u5408&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          S<\/p>\n<p>          &#061;<\/p>\n<p>          (<\/p>\n<p>          V<\/p>\n<p>          \u222a<\/p>\n<p>          {<\/p>\n<p>          m<\/p>\n<p>          }<\/p>\n<p>           )<\/p>\n<p>           L<\/p>\n<p>         \\\\mathcal{S} &#061; (\\\\mathcal{V} \\\\cup \\\\{m\\\\})^L<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathcal\" style=\"margin-right: 0.075em\">S<\/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 mathcal\" style=\"margin-right: 0.0822em\">V<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u222a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0913em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mclose\">}<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><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\">L<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u72b6\u6001 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           s<\/p>\n<p>           t<\/p>\n<p>          &#061;<\/p>\n<p>           x<\/p>\n<p>           t<\/p>\n<p>         s_t &#061; \\\\mathbf{x}_t<\/p>\n<p>      <\/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\">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: 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\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5944em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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><\/span><\/span><\/span> \u8868\u793a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          t<\/p>\n<p>         t<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span> \u65f6\u523b\u7684\u5e8f\u5217\u72b6\u6001\u3002<\/p>\n<\/li>\n<li>\n<p>\u52a8\u4f5c\u7a7a\u95f4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           A<\/p>\n<p>          \\\\mathcal{A}<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathcal\">A<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u53bb\u566a\u52a8\u4f5c&#xff0c;\u5bf9\u5e94\u4e8e\u4ece\u5f53\u524d\u72b6\u6001\u9884\u6d4b\u5e76\u586b\u5145\u63a9\u7801\u4f4d\u7f6e\u3002\u8bb0 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          M<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           t<\/p>\n<p>          )<\/p>\n<p>          &#061;<\/p>\n<p>          {<\/p>\n<p>          i<\/p>\n<p>          :<\/p>\n<p>           x<\/p>\n<p>           t<\/p>\n<p>            (<\/p>\n<p>            i<\/p>\n<p>            )<\/p>\n<p>          &#061;<\/p>\n<p>          m<\/p>\n<p>          }<\/p>\n<p>         \\\\mathcal{M}(\\\\mathbf{x}_t) &#061; \\\\{i: x_t^{(i)} &#061; m\\\\}<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathcal\">M<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"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=\"mopen\">{<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">:<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2906em;vertical-align: -0.2458em\"><\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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 class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2458em\"><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 mathnormal\">m<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span> \u4e3a\u63a9\u7801\u4f4d\u7f6e\u96c6\u5408\u3002\u52a8\u4f5c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           a<\/p>\n<p>           t<\/p>\n<p>         a_t<\/p>\n<p>      <\/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\">a<\/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><\/span><\/span><\/span> \u5b9a\u4e49\u4e3a\u4e00\u4e2a\u6620\u5c04 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           a<\/p>\n<p>           t<\/p>\n<p>          :<\/p>\n<p>          M<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           t<\/p>\n<p>          )<\/p>\n<p>          \u2192<\/p>\n<p>          V<\/p>\n<p>         a_t: \\\\mathcal{M}(\\\\mathbf{x}_t) \\\\rightarrow \\\\mathcal{V}<\/p>\n<p>      <\/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\">a<\/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\">:<\/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 mathcal\">M<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mclose\">)<\/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: 0.6833em\"><\/span><span class=\"mord mathcal\" style=\"margin-right: 0.0822em\">V<\/span><\/span><\/span><\/span><\/span>\u3002\u5728\u5b9e\u9645\u5b9e\u73b0\u4e2d&#xff0c;\u52a8\u4f5c\u7531\u7b56\u7565\u7f51\u7edc\u8f93\u51fa\u7684\u6982\u7387\u5206\u5e03\u91c7\u6837\u5f97\u5230\u3002<\/p>\n<\/li>\n<li>\n<p>\u8f6c\u79fb\u51fd\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           P<\/p>\n<p>          P<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u786e\u5b9a\u6027\u8f6c\u79fb\u3002\u7ed9\u5b9a\u72b6\u6001 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           x<\/p>\n<p>           t<\/p>\n<p>         \\\\mathbf{x}_t<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5944em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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><\/span><\/span><\/span> \u548c\u52a8\u4f5c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           a<\/p>\n<p>           t<\/p>\n<p>         a_t<\/p>\n<p>      <\/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\">a<\/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><\/span><\/span><\/span>&#xff0c;\u65b0\u72b6\u6001 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           x<\/p>\n<p>            t<\/p>\n<p>            \u2212<\/p>\n<p>            1<\/p>\n<p>         \\\\mathbf{x}_{t-1}<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6528em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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><\/span><\/span><\/span> \u7531\u4e0b\u5f0f\u786e\u5b9a&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            x<\/p>\n<p>             t<\/p>\n<p>             \u2212<\/p>\n<p>             1<\/p>\n<p>             (<\/p>\n<p>             i<\/p>\n<p>             )<\/p>\n<p>           &#061;<\/p>\n<p>            {<\/p>\n<p>                  a<\/p>\n<p>                  t<\/p>\n<p>                 (<\/p>\n<p>                 i<\/p>\n<p>                 )<\/p>\n<p>                 ,<\/p>\n<p>                 i<\/p>\n<p>                 \u2208<\/p>\n<p>                 M<\/p>\n<p>                 (<\/p>\n<p>                  x<\/p>\n<p>                  t<\/p>\n<p>                 )<\/p>\n<p>                  x<\/p>\n<p>                  t<\/p>\n<p>                   (<\/p>\n<p>                   i<\/p>\n<p>                   )<\/p>\n<p>                 ,<\/p>\n<p>                 i<\/p>\n<p>                 \u2209<\/p>\n<p>                 M<\/p>\n<p>                 (<\/p>\n<p>                  x<\/p>\n<p>                  t<\/p>\n<p>                 )<\/p>\n<p>           x_{t-1}^{(i)} &#061; \\\\begin{cases} a_t(i), &amp; i \\\\in \\\\mathcal{M}(\\\\mathbf{x}_t) \\\\\\\\ x_t^{(i)}, &amp; i \\\\notin \\\\mathcal{M}(\\\\mathbf{x}_t) \\\\end{cases} <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.3694em;vertical-align: -0.3246em\"><\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4337em;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\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3246em\"><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: 3em;vertical-align: -1.25em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.7084em\"><span class=\"\" style=\"top: -3.7452em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/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=\"mopen\">(<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span class=\"\" style=\"top: -2.2684em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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 class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2458em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2084em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 1em\"><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.7084em\"><span class=\"\" style=\"top: -3.7452em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">i<\/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 class=\"mord mathcal\">M<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -2.2684em\"><span class=\"pstrut\" style=\"height: 3.0448em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">i<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\"><span class=\"mord\"><span class=\"mrel\">\u2208<\/span><\/span><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"llap\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mord\">\/<\/span><span class=\"mspace\" style=\"margin-right: 0.0556em\"><\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord mathcal\">M<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2084em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>\u5956\u52b1\u51fd\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           R<\/p>\n<p>          R<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u5b9a\u4e49\u5728\u72b6\u6001\u8f6c\u79fb\u4e0a\u3002\u901a\u5e38\u4ec5\u5728\u6700\u7ec8\u72b6\u6001\u63d0\u4f9b\u5956\u52b1&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           R<\/p>\n<p>           (<\/p>\n<p>            x<\/p>\n<p>            t<\/p>\n<p>           ,<\/p>\n<p>            x<\/p>\n<p>             t<\/p>\n<p>             \u2212<\/p>\n<p>             1<\/p>\n<p>           )<\/p>\n<p>           &#061;<\/p>\n<p>            {<\/p>\n<p>                 r<\/p>\n<p>                 (<\/p>\n<p>                  x<\/p>\n<p>                  0<\/p>\n<p>                 )<\/p>\n<p>                 ,<\/p>\n<p>                 t<\/p>\n<p>                 &#061;<\/p>\n<p>                 0<\/p>\n<p>                 0<\/p>\n<p>                 ,<\/p>\n<p>                 t<\/p>\n<p>                 &gt;<\/p>\n<p>                 0<\/p>\n<p>           R(\\\\mathbf{x}_t, \\\\mathbf{x}_{t-1}) &#061; \\\\begin{cases} r(\\\\mathbf{x}_0), &amp; t &#061; 0 \\\\\\\\ 0, &amp; t &gt; 0 \\\\end{cases} <\/p>\n<p>       <\/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: 0.0077em\">R<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"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: 3em;vertical-align: -1.25em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.69em\"><span class=\"\" style=\"top: -3.69em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span class=\"\" style=\"top: -2.25em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.19em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 1em\"><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.69em\"><span class=\"\" style=\"top: -3.69em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><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 class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -2.25em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.19em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          r<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           0<\/p>\n<p>          )<\/p>\n<p>         r(\\\\mathbf{x}_0)<\/p>\n<p>      <\/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: 0.0278em\">r<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u662f\u4efb\u52a1\u76f8\u5173\u7684\u5956\u52b1\u4fe1\u53f7\u3002<\/p>\n<\/li>\n<li>\n<p>\u6298\u6263\u56e0\u5b50 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           \u03b3<\/p>\n<p>           \u2208<\/p>\n<p>           [<\/p>\n<p>           0<\/p>\n<p>           ,<\/p>\n<p>           1<\/p>\n<p>           )<\/p>\n<p>          \\\\gamma \\\\in [0,1)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7335em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0556em\">\u03b3<\/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: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">0<\/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>&#xff1a;\u63a7\u5236\u672a\u6765\u5956\u52b1\u7684\u6743\u91cd\u3002<\/p>\n<\/li>\n<\/ul>\n<h4>4.2 \u8f68\u8ff9\u611f\u77e5\u7684\u5bc6\u96c6\u5956\u52b1\u5efa\u6a21<\/h4>\n<p>\u7a00\u758f\u5956\u52b1&#xff08;\u4ec5\u5728\u6700\u7ec8\u6b65\u63d0\u4f9b&#xff09;\u5bfc\u81f4\u4fe1\u7528\u5206\u914d\u95ee\u9898\u3002\u4e3a\u7f13\u89e3\u6b64\u95ee\u9898&#xff0c;TraceRL \u5f15\u5165\u8f68\u8ff9\u7ea7\u522b\u7684\u5956\u52b1\u5efa\u6a21\u3002\u8bbe\u5b8c\u6574\u7684\u9006\u5411\u8f68\u8ff9\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u03c4<\/p>\n<p>        &#061;<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         T<\/p>\n<p>        ,<\/p>\n<p>         x<\/p>\n<p>          T<\/p>\n<p>          \u2212<\/p>\n<p>          1<\/p>\n<p>        ,<\/p>\n<p>        \u2026<\/p>\n<p>        ,<\/p>\n<p>         x<\/p>\n<p>         0<\/p>\n<p>        )<\/p>\n<p>       \\\\tau &#061; (\\\\mathbf{x}_T, \\\\mathbf{x}_{T-1}, \\\\dots, \\\\mathbf{x}_0)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1132em\">\u03c4<\/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\"><span class=\"mord mathbf\">x<\/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 mathnormal mtight\" style=\"margin-right: 0.1389em\">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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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 mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mbin mtight\">\u2212<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002\u5b9a\u4e49\u4e2d\u95f4\u72b6\u6001\u7684\u8d28\u91cf\u8bc4\u4f30\u51fd\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u03d5<\/p>\n<p>        :<\/p>\n<p>        S<\/p>\n<p>        \u2192<\/p>\n<p>        R<\/p>\n<p>       \\\\phi: \\\\mathcal{S} \\\\rightarrow \\\\mathbb{R}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">:<\/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: 0.075em\">S<\/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: 0.6889em\"><\/span><span class=\"mord mathbb\">R<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8f68\u8ff9\u5956\u52b1\u53ef\u5199\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          R<\/p>\n<p>          total<\/p>\n<p>         (<\/p>\n<p>         \u03c4<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>         r<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          0<\/p>\n<p>         )<\/p>\n<p>         &#043;<\/p>\n<p>         \u03bb<\/p>\n<p>          \u2211<\/p>\n<p>           t<\/p>\n<p>           &#061;<\/p>\n<p>           0<\/p>\n<p>           T<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>          \u03b3<\/p>\n<p>          t<\/p>\n<p>         \u22c5<\/p>\n<p>         \u03d5<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         )<\/p>\n<p>         R_{\\\\text{total}}(\\\\tau) &#061; r(\\\\mathbf{x}_0) &#043; \\\\lambda \\\\sum_{t&#061;0}^{T-1} \\\\gamma^t \\\\cdot \\\\phi(\\\\mathbf{x}_t) <\/p>\n<p>     <\/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: 0.0077em\">R<\/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: -0.0077em;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 text mtight\"><span class=\"mord mtight\">total<\/span><\/span><\/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: 0.1132em\">\u03c4<\/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: 0.0278em\">r<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 class=\"mclose\">)<\/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: 3.0954em;vertical-align: -1.2671em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/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: 1.8283em\"><span class=\"\" style=\"top: -1.8829em;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\">t<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">0<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mbin mtight\">\u2212<\/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: 1.2671em\"><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: 0.0556em\">\u03b3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8436em\"><span class=\"\" style=\"top: -3.113em;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><\/span><\/span><\/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\">\u03d5<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u03bb<\/p>\n<p>        \u2265<\/p>\n<p>        0<\/p>\n<p>       \\\\lambda \\\\geq 0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8304em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/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<\/span><\/span><\/span><\/span><\/span> \u4e3a\u5e73\u8861\u7cfb\u6570\u3002\u76f8\u5e94\u5730&#xff0c;\u6bcf\u4e00\u6b65\u7684\u5373\u65f6\u5956\u52b1\u53ef\u5b9a\u4e49\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          R<\/p>\n<p>          t<\/p>\n<p>         &#061;<\/p>\n<p>         R<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         ,<\/p>\n<p>          x<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          {<\/p>\n<p>               r<\/p>\n<p>               (<\/p>\n<p>                x<\/p>\n<p>                0<\/p>\n<p>               )<\/p>\n<p>               &#043;<\/p>\n<p>               \u03bb<\/p>\n<p>               \u03d5<\/p>\n<p>               (<\/p>\n<p>                x<\/p>\n<p>                0<\/p>\n<p>               )<\/p>\n<p>               ,<\/p>\n<p>               t<\/p>\n<p>               &#061;<\/p>\n<p>               0<\/p>\n<p>               \u03bb<\/p>\n<p>               \u03d5<\/p>\n<p>               (<\/p>\n<p>                x<\/p>\n<p>                t<\/p>\n<p>               )<\/p>\n<p>               ,<\/p>\n<p>               t<\/p>\n<p>               &gt;<\/p>\n<p>               0<\/p>\n<p>         R_t &#061; R(\\\\mathbf{x}_t, \\\\mathbf{x}_{t-1}) &#061; \\\\begin{cases} r(\\\\mathbf{x}_0) &#043; \\\\lambda \\\\phi(\\\\mathbf{x}_0), &amp; t &#061; 0 \\\\\\\\ \\\\lambda \\\\phi(\\\\mathbf{x}_t), &amp; t &gt; 0 \\\\end{cases} <\/p>\n<p>     <\/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: 0.0077em\">R<\/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: -0.0077em;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\">&#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: 0.0077em\">R<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"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: 3em;vertical-align: -1.25em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.69em\"><span class=\"\" style=\"top: -3.69em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 class=\"mclose\">)<\/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 class=\"mord mathnormal\">\u03bb<\/span><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 0em;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 class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span class=\"\" style=\"top: -2.25em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.19em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 1em\"><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.69em\"><span class=\"\" style=\"top: -3.69em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><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 class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -2.25em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.19em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u901a\u8fc7\u4e2d\u95f4\u72b6\u6001\u5956\u52b1\u7684\u5f15\u5165&#xff0c;\u6a21\u578b\u5728\u6bcf\u4e00\u4e2a\u53bb\u566a\u6b65\u9aa4\u5747\u53ef\u83b7\u5f97\u53cd\u9988\u4fe1\u53f7&#xff0c;\u4ece\u800c\u5f62\u6210\u5bc6\u96c6\u7684\u5956\u52b1\u5206\u5e03\u3002<\/p>\n<h4>4.3 \u6269\u6563\u57fa\u4ef7\u503c\u6a21\u578b\u7684\u7406\u8bba\u5206\u6790\u4e0e\u8bbe\u8ba1<\/h4>\n<p>\u4e3a\u4e86\u5b9e\u73b0\u4ef7\u503c\u4f30\u8ba1&#xff0c;\u7814\u7a76\u56e2\u961f\u63d0\u51fa\u4e86\u6269\u6563\u57fa\u4ef7\u503c\u6a21\u578b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         V<\/p>\n<p>         \u03c8<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         t<\/p>\n<p>        )<\/p>\n<p>       V_\\\\psi(\\\\mathbf{x}_t)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/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: -0.2222em;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: 0.0359em\">\u03c8<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002\u8be5\u6a21\u578b\u4ee5\u5f53\u524d\u7684\u53bb\u566a\u72b6\u6001\u4e3a\u8f93\u5165&#xff0c;\u8f93\u51fa\u671f\u671b\u7d2f\u79ef\u5956\u52b1&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          V<\/p>\n<p>          \u03c8<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          E<\/p>\n<p>            p<\/p>\n<p>            \u03b8<\/p>\n<p>           (<\/p>\n<p>            x<\/p>\n<p>             t<\/p>\n<p>             \u2212<\/p>\n<p>             1<\/p>\n<p>           ,<\/p>\n<p>           \u2026<\/p>\n<p>           ,<\/p>\n<p>            x<\/p>\n<p>            0<\/p>\n<p>           \u2223<\/p>\n<p>            x<\/p>\n<p>            t<\/p>\n<p>           )<\/p>\n<p>          [<\/p>\n<p>           \u2211<\/p>\n<p>            k<\/p>\n<p>            &#061;<\/p>\n<p>            0<\/p>\n<p>           t<\/p>\n<p>           \u03b3<\/p>\n<p>           k<\/p>\n<p>          R<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           k<\/p>\n<p>          ,<\/p>\n<p>           x<\/p>\n<p>            k<\/p>\n<p>            \u2212<\/p>\n<p>            1<\/p>\n<p>          )<\/p>\n<p>          ]<\/p>\n<p>         V_\\\\psi(\\\\mathbf{x}_t) &#061; \\\\mathbb{E}_{p_\\\\theta(\\\\mathbf{x}_{t-1}, \\\\dots, \\\\mathbf{x}_0 | \\\\mathbf{x}_t)} \\\\left[ \\\\sum_{k&#061;0}^{t} \\\\gamma^k R(\\\\mathbf{x}_k, \\\\mathbf{x}_{k-1}) \\\\right] <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/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: -0.2222em;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: 0.0359em\">\u03c8<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"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: 3.0827em;vertical-align: -1.3021em\"><\/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: 0.3448em\"><span class=\"\" style=\"top: -2.5198em;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 mathnormal mtight\">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: 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: 0.0278em\">\u03b8<\/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 class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><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 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/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: 0.2025em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct mtight\">,<\/span><span class=\"minner mtight\">\u2026<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><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 mtight\">0<\/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 class=\"mord mtight\">\u2223<\/span><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">x<\/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 class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3552em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">[<\/span><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.7806em\"><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\">0<\/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 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/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=\"mord mathnormal\" style=\"margin-right: 0.0556em\">\u03b3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;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=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/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=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u4ef7\u503c\u7f51\u7edc\u91c7\u7528\u4e0e\u7b56\u7565\u7f51\u7edc\u5171\u4eab\u5e95\u5c42\u8868\u793a\u7684\u67b6\u6784\u3002\u65f6\u5e8f\u5dee\u5206&#xff08;TD&#xff09;\u8bef\u5dee\u5b9a\u4e49\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          \u03b4<\/p>\n<p>          t<\/p>\n<p>         &#061;<\/p>\n<p>         R<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         ,<\/p>\n<p>          x<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         )<\/p>\n<p>         &#043;<\/p>\n<p>         \u03b3<\/p>\n<p>          V<\/p>\n<p>          \u03c8<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         )<\/p>\n<p>         \u2212<\/p>\n<p>          V<\/p>\n<p>          \u03c8<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         )<\/p>\n<p>         \\\\delta_t &#061; R(\\\\mathbf{x}_t, \\\\mathbf{x}_{t-1}) &#043; \\\\gamma V_\\\\psi(\\\\mathbf{x}_{t-1}) &#8211; V_\\\\psi(\\\\mathbf{x}_t) <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0379em\">\u03b4<\/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: -0.0379em;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\">&#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: 0.0077em\">R<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"mclose\">)<\/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: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0556em\">\u03b3<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/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: -0.2222em;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: 0.0359em\">\u03c8<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"mclose\">)<\/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: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/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: -0.2222em;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: 0.0359em\">\u03c8<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u4ef7\u503c\u7f51\u7edc\u7684\u635f\u5931\u51fd\u6570\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          L<\/p>\n<p>          V<\/p>\n<p>         (<\/p>\n<p>         \u03c8<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          E<\/p>\n<p>           (<\/p>\n<p>            x<\/p>\n<p>            t<\/p>\n<p>           ,<\/p>\n<p>            x<\/p>\n<p>             t<\/p>\n<p>             \u2212<\/p>\n<p>             1<\/p>\n<p>           )<\/p>\n<p>           \u223c<\/p>\n<p>           D<\/p>\n<p>          [<\/p>\n<p>           \u03b4<\/p>\n<p>           t<\/p>\n<p>           2<\/p>\n<p>          ]<\/p>\n<p>         \\\\mathcal{L}_V(\\\\psi) &#061; \\\\mathbb{E}_{(\\\\mathbf{x}_t, \\\\mathbf{x}_{t-1}) \\\\sim \\\\mathcal{D}} \\\\left[ \\\\delta_t^2 \\\\right] <\/p>\n<p>     <\/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 mathcal\">L<\/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 mathnormal mtight\" style=\"margin-right: 0.2222em\">V<\/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: 0.0359em\">\u03c8<\/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: 1.2193em;vertical-align: -0.3552em\"><\/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: 0.3448em\"><span class=\"\" style=\"top: -2.5198em;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=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">x<\/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 class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><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 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/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: 0.2025em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><span class=\"mrel mtight\">\u223c<\/span><span class=\"mord mathcal mtight\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3552em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">[<\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0379em\">\u03b4<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -2.453em;margin-left: -0.0379em;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 class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       \\\\mathcal{D}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathcal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7ecf\u9a8c\u56de\u653e\u7f13\u51b2\u533a\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260831230010-6a96077a7fc67.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>4.4 \u7b56\u7565\u4f18\u5316\u76ee\u6807\u7684\u6570\u5b66\u63a8\u5bfc<\/h4>\n<p>TraceRL \u91c7\u7528\u57fa\u4e8e\u7b56\u7565\u68af\u5ea6\u7684\u4f18\u5316\u65b9\u6cd5&#xff0c;\u76ee\u6807\u51fd\u6570\u4e3a\u5e26 KL \u7ea6\u675f\u7684\u671f\u671b\u5956\u52b1\u6700\u5927\u5316&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          L<\/p>\n<p>          RL<\/p>\n<p>         (<\/p>\n<p>         \u03b8<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          E<\/p>\n<p>           \u03c4<\/p>\n<p>           \u223c<\/p>\n<p>            p<\/p>\n<p>            \u03b8<\/p>\n<p>          [<\/p>\n<p>           \u2211<\/p>\n<p>            t<\/p>\n<p>            &#061;<\/p>\n<p>            0<\/p>\n<p>            T<\/p>\n<p>            \u2212<\/p>\n<p>            1<\/p>\n<p>           \u03b3<\/p>\n<p>           t<\/p>\n<p>           A<\/p>\n<p>           \u03c8<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           t<\/p>\n<p>          ,<\/p>\n<p>           x<\/p>\n<p>            t<\/p>\n<p>            \u2212<\/p>\n<p>            1<\/p>\n<p>          )<\/p>\n<p>          ]<\/p>\n<p>         \u2212<\/p>\n<p>         \u03b2<\/p>\n<p>         \u22c5<\/p>\n<p>          D<\/p>\n<p>          KL<\/p>\n<p>         (<\/p>\n<p>          p<\/p>\n<p>          \u03b8<\/p>\n<p>         \u2225<\/p>\n<p>          p<\/p>\n<p>          ref<\/p>\n<p>         )<\/p>\n<p>         \\\\mathcal{L}_{\\\\text{RL}}(\\\\theta) &#061; \\\\mathbb{E}_{\\\\tau \\\\sim p_\\\\theta} \\\\left[ \\\\sum_{t&#061;0}^{T-1} \\\\gamma^t A_\\\\psi(\\\\mathbf{x}_t, \\\\mathbf{x}_{t-1}) \\\\right] &#8211; \\\\beta \\\\cdot D_{\\\\text{KL}}(p_\\\\theta \\\\| p_{\\\\text{ref}}) <\/p>\n<p>     <\/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 mathcal\">L<\/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 text mtight\"><span class=\"mord mtight\">RL<\/span><\/span><\/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: 0.0278em\">\u03b8<\/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: 3.0954em;vertical-align: -1.2671em\"><\/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: 0.1514em\"><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 mathnormal mtight\" style=\"margin-right: 0.1132em\">\u03c4<\/span><span class=\"mrel mtight\">\u223c<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">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: 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: 0.0278em\">\u03b8<\/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: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">[<\/span><\/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: -1.8829em;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\">t<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">0<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mbin mtight\">\u2212<\/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: 1.2671em\"><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: 0.0556em\">\u03b3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8436em\"><span class=\"\" style=\"top: -3.113em;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><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/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: 0.0359em\">\u03c8<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">]<\/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: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/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: -0.0278em;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 text mtight\"><span class=\"mord mtight\">KL<\/span><\/span><\/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\">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: 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: 0.0278em\">\u03b8<\/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\">\u2225<\/span><span class=\"mord\"><span class=\"mord mathnormal\">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: 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 text mtight\"><span class=\"mord mtight\">ref<\/span><\/span><\/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><\/span><\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          A<\/p>\n<p>          \u03c8<\/p>\n<p>        A_\\\\psi<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/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: 0.0359em\">\u03c8<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u4f18\u52bf\u51fd\u6570&#xff0c;\u53ef\u901a\u8fc7\u5e7f\u4e49\u4f18\u52bf\u4f30\u8ba1&#xff08;GAE&#xff09;\u8ba1\u7b97\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          p<\/p>\n<p>          ref<\/p>\n<p>        p_{\\\\text{ref}}<\/p>\n<p>     <\/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\">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: 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 text mtight\"><span class=\"mord mtight\">ref<\/span><\/span><\/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> \u4e3a\u53c2\u8003\u7b56\u7565&#xff08;\u901a\u5e38\u662f\u76d1\u7763\u5b66\u4e60\u5f97\u5230\u7684\u521d\u59cb\u7b56\u7565&#xff09;\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         \u03b2<\/p>\n<p>         &gt;<\/p>\n<p>         0<\/p>\n<p>        \\\\beta &gt; 0<\/p>\n<p>     <\/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: 0.0528em\">\u03b2<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/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> \u4e3a KL \u60e9\u7f5a\u7cfb\u6570\u3002<\/li>\n<\/ul>\n<p>\u7b56\u7565\u68af\u5ea6\u53ef\u8fd1\u4f3c\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          \u2207<\/p>\n<p>          \u03b8<\/p>\n<p>          L<\/p>\n<p>          RL<\/p>\n<p>         \u2248<\/p>\n<p>         E<\/p>\n<p>          [<\/p>\n<p>           \u2211<\/p>\n<p>            t<\/p>\n<p>            &#061;<\/p>\n<p>            0<\/p>\n<p>            T<\/p>\n<p>            \u2212<\/p>\n<p>            1<\/p>\n<p>           \u2207<\/p>\n<p>           \u03b8<\/p>\n<p>          log<\/p>\n<p>          \u2061<\/p>\n<p>           p<\/p>\n<p>           \u03b8<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>            t<\/p>\n<p>            \u2212<\/p>\n<p>            1<\/p>\n<p>          \u2223<\/p>\n<p>           x<\/p>\n<p>           t<\/p>\n<p>          )<\/p>\n<p>          \u22c5<\/p>\n<p>           A<\/p>\n<p>           \u03c8<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           t<\/p>\n<p>          ,<\/p>\n<p>           x<\/p>\n<p>            t<\/p>\n<p>            \u2212<\/p>\n<p>            1<\/p>\n<p>          )<\/p>\n<p>          ]<\/p>\n<p>         \u2212<\/p>\n<p>         \u03b2<\/p>\n<p>          \u2207<\/p>\n<p>          \u03b8<\/p>\n<p>          D<\/p>\n<p>          KL<\/p>\n<p>         (<\/p>\n<p>          p<\/p>\n<p>          \u03b8<\/p>\n<p>         \u2225<\/p>\n<p>          p<\/p>\n<p>          ref<\/p>\n<p>         )<\/p>\n<p>         \\\\nabla_\\\\theta \\\\mathcal{L}_{\\\\text{RL}} \\\\approx \\\\mathbb{E} \\\\left[ \\\\sum_{t&#061;0}^{T-1} \\\\nabla_\\\\theta \\\\log p_\\\\theta(\\\\mathbf{x}_{t-1} | \\\\mathbf{x}_t) \\\\cdot A_\\\\psi(\\\\mathbf{x}_t, \\\\mathbf{x}_{t-1}) \\\\right] &#8211; \\\\beta \\\\nabla_\\\\theta D_{\\\\text{KL}}(p_\\\\theta \\\\| p_{\\\\text{ref}}) <\/p>\n<p>     <\/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\">\u2207<\/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: 0.0278em\">\u03b8<\/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\"><span class=\"mord mathcal\">L<\/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 text mtight\"><span class=\"mord mtight\">RL<\/span><\/span><\/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\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.0954em;vertical-align: -1.2671em\"><\/span><span class=\"mord mathbb\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">[<\/span><\/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: -1.8829em;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\">t<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">0<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mbin mtight\">\u2212<\/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: 1.2671em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2207<\/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: 0.0278em\">\u03b8<\/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: 0.1667em\"><\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">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: 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: 0.0278em\">\u03b8<\/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 mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mclose\">)<\/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 class=\"mord\"><span class=\"mord mathnormal\">A<\/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: 0.0359em\">\u03c8<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">]<\/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: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"mord\"><span class=\"mord\">\u2207<\/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: 0.0278em\">\u03b8<\/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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/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: -0.0278em;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 text mtight\"><span class=\"mord mtight\">KL<\/span><\/span><\/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\">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: 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: 0.0278em\">\u03b8<\/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\">\u2225<\/span><span class=\"mord\"><span class=\"mord mathnormal\">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: 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 text mtight\"><span class=\"mord mtight\">ref<\/span><\/span><\/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><\/span><\/p>\n<h4>4.5 \u67b6\u6784\u65e0\u5173\u6027\u7684\u7406\u8bba\u4fdd\u8bc1<\/h4>\n<p>TraceRL \u6846\u67b6\u7684\u8bbe\u8ba1\u4e0d\u4f9d\u8d56\u4e8e\u7279\u5b9a\u7684\u6269\u6563\u6ce8\u610f\u529b\u673a\u5236\u3002\u8bbe\u6ce8\u610f\u529b\u673a\u5236\u62bd\u8c61\u4e3a\u4e00\u4e2a\u51fd\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        Attn<\/p>\n<p>        :<\/p>\n<p>         R<\/p>\n<p>          L<\/p>\n<p>          \u00d7<\/p>\n<p>          d<\/p>\n<p>        \u2192<\/p>\n<p>         R<\/p>\n<p>          L<\/p>\n<p>          \u00d7<\/p>\n<p>          d<\/p>\n<p>       \\\\text{Attn}: \\\\mathbb{R}^{L \\\\times d} \\\\rightarrow \\\\mathbb{R}^{L \\\\times d}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">Attn<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">:<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/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 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/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: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/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 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u7b56\u7565\u7f51\u7edc\u7684\u4e00\u822c\u5f62\u5f0f\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          p<\/p>\n<p>          \u03b8<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          \u220f<\/p>\n<p>           i<\/p>\n<p>           \u2208<\/p>\n<p>           M<\/p>\n<p>           (<\/p>\n<p>            x<\/p>\n<p>            t<\/p>\n<p>           )<\/p>\n<p>         Softmax<\/p>\n<p>          (<\/p>\n<p>          W<\/p>\n<p>          \u22c5<\/p>\n<p>           Attn<\/p>\n<p>           \u03b8<\/p>\n<p>          (<\/p>\n<p>          Emb<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           t<\/p>\n<p>          )<\/p>\n<p>           )<\/p>\n<p>           i<\/p>\n<p>          &#043;<\/p>\n<p>          b<\/p>\n<p>          )<\/p>\n<p>         p_\\\\theta(\\\\mathbf{x}_{t-1} | \\\\mathbf{x}_t) &#061; \\\\prod_{i \\\\in \\\\mathcal{M}(\\\\mathbf{x}_t)} \\\\text{Softmax}\\\\left( W \\\\cdot \\\\text{Attn}_\\\\theta(\\\\text{Emb}(\\\\mathbf{x}_t))_i &#043; b \\\\right) <\/p>\n<p>     <\/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\">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: 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: 0.0278em\">\u03b8<\/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 mathbf\">x<\/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: 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\">t<\/span><span class=\"mbin mtight\">\u2212<\/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=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"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: 2.566em;vertical-align: -1.516em\"><\/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: -1.809em;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 mathcal mtight\">M<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">x<\/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 class=\"mclose mtight\">)<\/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\">\u220f<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.516em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord text\"><span class=\"mord\">Softmax<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/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 class=\"mord\"><span class=\"mord text\"><span class=\"mord\">Attn<\/span><\/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-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: 0.0278em\">\u03b8<\/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 text\"><span class=\"mord\">Emb<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/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=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/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=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5bf9\u4e8e\u4e0d\u540c\u7684\u6ce8\u610f\u529b\u67b6\u6784\u2014\u2014\u5168\u6ce8\u610f\u529b\u3001\u5757\u6ce8\u610f\u529b\u6216\u7a00\u758f\u6ce8\u610f\u529b\u2014\u2014\u53ea\u8981\u6ce8\u610f\u529b\u6a21\u5757\u53ef\u5fae&#xff0c;\u7b56\u7565\u68af\u5ea6\u5373\u53ef\u6b63\u786e\u4f20\u64ad\u3002\u56e0\u6b64&#xff0c;TraceRL \u5bf9\u4efb\u4f55\u53ef\u5fae\u5206\u7684\u6ce8\u610f\u529b\u67b6\u6784\u5747\u9002\u7528\u3002<\/p>\n<h4>4.6 \u8bfe\u7a0b\u5b66\u4e60\u4e0e\u957f\u601d\u7ef4\u94fe\u63a8\u7406\u7684\u5f62\u5f0f\u5316\u5206\u6790<\/h4>\n<p>\u4e3a\u8fdb\u4e00\u6b65\u63d0\u5347\u590d\u6742\u63a8\u7406\u80fd\u529b&#xff0c;\u7814\u7a76\u56e2\u961f\u5f15\u5165\u8bfe\u7a0b\u5b66\u4e60\u7b56\u7565\u3002\u8bbe\u4efb\u52a1\u96be\u5ea6\u7531\u51fd\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        d<\/p>\n<p>        :<\/p>\n<p>        X<\/p>\n<p>        \u2192<\/p>\n<p>        [<\/p>\n<p>        0<\/p>\n<p>        ,<\/p>\n<p>        1<\/p>\n<p>        ]<\/p>\n<p>       d: \\\\mathcal{X} \\\\rightarrow [0,1]<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">:<\/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: 0.1464em\">X<\/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: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">0<\/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> \u5ea6\u91cf\u3002\u8bfe\u7a0b\u8c03\u5ea6\u51fd\u6570\u5b9a\u4e49\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         C<\/p>\n<p>         (<\/p>\n<p>         k<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>         min<\/p>\n<p>         \u2061<\/p>\n<p>          (<\/p>\n<p>          1<\/p>\n<p>          ,<\/p>\n<p>          max<\/p>\n<p>          \u2061<\/p>\n<p>           (<\/p>\n<p>           0<\/p>\n<p>           ,<\/p>\n<p>             k<\/p>\n<p>             \u2212<\/p>\n<p>              k<\/p>\n<p>              warmup<\/p>\n<p>             k<\/p>\n<p>             anneal<\/p>\n<p>           )<\/p>\n<p>          )<\/p>\n<p>         \\\\mathcal{C}(k) &#061; \\\\min\\\\left(1, \\\\max\\\\left(0, \\\\frac{k &#8211; k_{\\\\text{warmup}}}{k_{\\\\text{anneal}}}\\\\right)\\\\right) <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathcal\" style=\"margin-right: 0.0583em\">C<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/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: 2.4em;vertical-align: -0.95em\"><\/span><span class=\"mop\">min<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">(<\/span><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">max<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">(<\/span><\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/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: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/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: -0.0315em;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 text mtight\"><span class=\"mord mtight\">anneal<\/span><\/span><\/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 mathnormal\" style=\"margin-right: 0.0315em\">k<\/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 class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0315em;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 text mtight\"><span class=\"mord mtight\">warmup<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><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: 0.836em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        k<\/p>\n<p>       k<\/p>\n<p>    <\/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> \u4e3a\u5f53\u524d\u8bad\u7ec3\u6b65\u6570\u3002\u5728\u6bcf\u4e2a epoch&#xff0c;\u53ea\u6709\u6ee1\u8db3 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        d<\/p>\n<p>        (<\/p>\n<p>        T<\/p>\n<p>        )<\/p>\n<p>        \u2264<\/p>\n<p>        C<\/p>\n<p>        (<\/p>\n<p>        k<\/p>\n<p>        )<\/p>\n<p>       d(\\\\mathcal{T}) \\\\leq \\\\mathcal{C}(k)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathcal\" style=\"margin-right: 0.2542em\">T<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/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 mathcal\" style=\"margin-right: 0.0583em\">C<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u7684\u4efb\u52a1 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        T<\/p>\n<p>       \\\\mathcal{T}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathcal\" style=\"margin-right: 0.2542em\">T<\/span><\/span><\/span><\/span><\/span> \u88ab\u91c7\u6837\u7528\u4e8e\u8bad\u7ec3\u3002\u8be5\u7b56\u7565\u6700\u7ec8\u6210\u529f\u8bad\u7ec3\u51fa\u9996\u4e2a\u652f\u6301\u957f\u601d\u7ef4\u94fe\u63a8\u7406\u7684\u6269\u6563\u8bed\u8a00\u6a21\u578b\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260831230010-6a96077a8f43a.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>5. \u5b9e\u9a8c\u8bbe\u8ba1\u4e0e\u4e3b\u8981\u7ed3\u679c<\/h3>\n<h4>5.1 \u8bc4\u4f30\u57fa\u51c6\u4e0e\u6570\u636e\u96c6<\/h4>\n<p>\u8bc4\u4f30\u57fa\u51c6\u5305\u62ec&#xff1a;<\/p>\n<ul>\n<li>MATH500&#xff1a;\u5305\u542b 500 \u9053\u6570\u5b66\u7ade\u8d5b\u9898\u76ee&#xff0c;\u7528\u4e8e\u8bc4\u4f30\u6570\u5b66\u63a8\u7406\u80fd\u529b\u3002<\/li>\n<li>LiveCodeBench-V2&#xff1a;\u7528\u4e8e\u8bc4\u4f30\u4ee3\u7801\u751f\u6210\u4e0e\u5b9e\u9645\u6267\u884c\u80fd\u529b\u7684\u57fa\u51c6\u3002<\/li>\n<\/ul>\n<p>\u5bf9\u6bd4\u6a21\u578b\u9009\u53d6\u4e3b\u6d41\u7684\u81ea\u56de\u5f52\u5927\u8bed\u8a00\u6a21\u578b&#xff1a;Qwen2.5-7B\u3001Llama3.1-8B \u7b49\u3002<\/p>\n<h4>5.2 \u5b9e\u73b0\u7ec6\u8282\u4e0e\u8d85\u53c2\u6570\u8bbe\u7f6e<\/h4>\n<p>\u6839\u636e\u8bba\u6587&#xff0c;\u5173\u952e\u8d85\u53c2\u6570\u8bbe\u7f6e\u5982\u4e0b&#xff1a;<\/p>\n<table>\n<tr>\u53c2\u6570\u503c<\/tr>\n<tbody>\n<tr>\n<td>\u6269\u6563\u6b65\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           T<\/p>\n<p>          T<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>128<\/td>\n<\/tr>\n<tr>\n<td>\u5b66\u4e60\u7387<\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           5<\/p>\n<p>           \u00d7<\/p>\n<p>            10<\/p>\n<p>             \u2212<\/p>\n<p>             6<\/p>\n<p>          5 \\\\times 10^{-6}<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><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\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>\u6279\u6b21\u5927\u5c0f<\/td>\n<td>64<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           \u03b3<\/p>\n<p>          \\\\gamma<\/p>\n<p>       <\/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: 0.0556em\">\u03b3<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>0.99<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            \u03bb<\/p>\n<p>            GAE<\/p>\n<p>          \\\\lambda_{\\\\text{GAE}}<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bb<\/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 text mtight\"><span class=\"mord mtight\">GAE<\/span><\/span><\/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><\/td>\n<td>0.95<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           \u03b2<\/p>\n<p>          \\\\beta<\/p>\n<p>       <\/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: 0.0528em\">\u03b2<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>0.01<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>5.3 \u4e3b\u5b9e\u9a8c\u7ed3\u679c<\/h4>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260831230010-6a96077a9f1aa.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260831230010-6a96077aabc35.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>5.4 \u6d88\u878d\u5b9e\u9a8c\u4e0e\u654f\u611f\u6027\u5206\u6790<\/h4>\n<p>\u6839\u636e\u8bba\u6587\u5185\u5bb9&#xff0c;\u6d88\u878d\u5b9e\u9a8c\u9a8c\u8bc1\u4e86\u4ee5\u4e0b\u8bbe\u8ba1\u9009\u62e9\u7684\u6709\u6548\u6027&#xff1a;<\/p>\n<li>\n<p>\u5bc6\u96c6\u5956\u52b1\u7684\u5f71\u54cd&#xff1a;\u5e26\u6709\u4e2d\u95f4\u72b6\u6001\u5956\u52b1&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          \u03bb<\/p>\n<p>          &gt;<\/p>\n<p>          0<\/p>\n<p>         \\\\lambda &gt; 0<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7335em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/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\u914d\u7f6e\u76f8\u6bd4\u4ec5\u4f7f\u7528\u6700\u7ec8\u5956\u52b1&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          \u03bb<\/p>\n<p>          &#061;<\/p>\n<p>          0<\/p>\n<p>         \\\\lambda &#061; 0<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/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;\u5728\u51c6\u786e\u7387\u548c\u6536\u655b\u901f\u5ea6\u4e0a\u5747\u6709\u63d0\u5347\u3002<\/p>\n<\/li>\n<li>\n<p>KL \u7ea6\u675f\u7684\u5f71\u54cd&#xff1a;\u9002\u4e2d\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          \u03b2<\/p>\n<p>         \\\\beta<\/p>\n<p>      <\/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: 0.0528em\">\u03b2<\/span><\/span><\/span><\/span><\/span> \u503c&#xff08;\u7ea6 0.01&#xff09;\u5728\u9632\u6b62\u7b56\u7565\u5d29\u584c\u548c\u4fdd\u6301\u63a2\u7d22\u80fd\u529b\u4e4b\u95f4\u53d6\u5f97\u6700\u4f73\u5e73\u8861\u3002<\/p>\n<\/li>\n<h3>6. \u5c40\u9650\u6027\u4e0e\u672a\u6765\u7814\u7a76\u65b9\u5411<\/h3>\n<p>\u5c3d\u7ba1 TraceRL 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