{"id":91031,"date":"2026-08-06T17:24:36","date_gmt":"2026-08-06T09:24:36","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/91031.html"},"modified":"2026-08-06T17:24:36","modified_gmt":"2026-08-06T09:24:36","slug":"dpo-%e4%b8%8e-rlhf-%e6%9b%bf%e4%bb%a3%e6%96%b9%e6%a1%88%ef%bc%9a%e5%8e%9f%e7%90%86%e4%b8%8e%e5%ae%9e%e7%8e%b0","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/91031.html","title":{"rendered":"DPO \u4e0e RLHF \u66ff\u4ee3\u65b9\u6848\uff1a\u539f\u7406\u4e0e\u5b9e\u73b0"},"content":{"rendered":"<h2>DPO \u4e0e RLHF \u66ff\u4ee3\u65b9\u6848&#xff1a;\u539f\u7406\u4e0e\u5b9e\u73b0<\/h2>\n<h3>\u672c\u7ae0\u5bfc\u8bfb<\/h3>\n<p>RLHF \u867d\u7136\u6548\u679c\u663e\u8457&#xff0c;\u4f46\u5de5\u7a0b\u590d\u6742\u5ea6\u9ad8\u2014\u2014\u56db\u6a21\u578b\u67b6\u6784\u3001\u8bad\u7ec3\u4e0d\u7a33\u5b9a\u3001\u5956\u52b1\u9ed1\u5ba2\u7b49\u95ee\u9898\u8ba9\u8bb8\u591a\u56e2\u961f\u671b\u800c\u5374\u6b65\u30022023 \u5e74\u4ee5\u6765&#xff0c;\u4e00\u7cfb\u5217\u66ff\u4ee3\u65b9\u6848\u5e94\u8fd0\u800c\u751f&#xff0c;\u5176\u4e2d DPO&#xff08;Direct Preference Optimization&#xff09; \u6700\u53d7\u5173\u6ce8\u3002\u672c\u7ae0\u5c06\u6df1\u5165 DPO \u7684\u63a8\u5bfc\u8fc7\u7a0b&#xff0c;\u5bf9\u6bd4 IPO\u3001KTO\u3001ORPO \u7b49\u53d8\u4f53&#xff0c;\u63a2\u8ba8 RLAIF \u7684\u524d\u666f&#xff0c;\u5e76\u7ed9\u51fa\u65b9\u6848\u9009\u62e9\u6307\u5357\u3002<\/p>\n<p>\u524d\u7f6e\u77e5\u8bc6&#xff1a;\u7b2c 4 \u7ae0\u7684 RLHF \u539f\u7406\u3002<\/p>\n<p>\u5b66\u4e60\u76ee\u6807&#xff1a;<\/p>\n<ul>\n<li>\u7406\u89e3 DPO \u7684\u6838\u5fc3\u6d1e\u5bdf\u4e0e\u63a8\u5bfc\u8fc7\u7a0b<\/li>\n<li>\u638c\u63e1 DPO \u53d8\u4f53&#xff08;IPO\u3001KTO\u3001ORPO\u3001SimPO&#xff09;\u7684\u539f\u7406<\/li>\n<li>\u7406\u89e3 RLAIF \u7684\u6d41\u7a0b\u4e0e\u5c40\u9650<\/li>\n<li>\u80fd\u6839\u636e\u573a\u666f\u9009\u62e9\u5408\u9002\u7684\u504f\u597d\u4f18\u5316\u65b9\u6848<\/li>\n<\/ul>\n<hr \/>\n<h3>DPO&#xff08;Direct Preference Optimization&#xff09;<\/h3>\n<h4>\u6838\u5fc3\u6d1e\u5bdf<\/h4>\n<p>DPO \u7684\u6838\u5fc3\u6d1e\u5bdf\u6765\u81ea\u4e00\u4e2a\u6570\u5b66\u53d1\u73b0&#xff1a;RLHF \u7684\u6700\u4f18\u7b56\u7565\u6709\u95ed\u5f0f\u89e3&#xff0c;\u53ef\u4ee5\u7ed5\u8fc7\u5956\u52b1\u6a21\u578b&#xff0c;\u76f4\u63a5\u4ece\u504f\u597d\u6570\u636e\u4f18\u5316\u7b56\u7565\u3002<\/p>\n<p>\u56de\u5fc6 RLHF \u7684\u4f18\u5316\u76ee\u6807&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">max\u2061\u03c0Ex,y\u223c\u03c0[r(x,y)]\u2212\u03b2\u22c5DKL[\u03c0(\u22c5\u2223x)\u2225\u03c0ref(\u22c5\u2223x)]\\\\max_\\\\pi \\\\mathbb{E}_{x,y \\\\sim \\\\pi} [r(x,y)] &#8211; \\\\beta \\\\cdot D_{KL}[\\\\pi(\\\\cdot|x) \\\\| \\\\pi_{ref}(\\\\cdot|x)]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.45em;vertical-align: -0.7em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4306em\"><span class=\"\" style=\"top: -2.4em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c0<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"\"><span class=\"mop\">max<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/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\">x<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mrel mtight\">\u223c<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c0<\/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=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/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: 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: 1.0361em;vertical-align: -0.2861em\"><\/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 mathnormal mtight\" style=\"margin-right: 0.0715em\">K<\/span><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: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u22c5<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">\u2225<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/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=\"mopen\">(<\/span><span class=\"mord\">\u22c5<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)]<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8fd9\u4e2a\u4f18\u5316\u95ee\u9898\u7684\u6700\u4f18\u89e3\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0\u2217(y\u2223x)&#061;1Z(x)\u03c0ref(y\u2223x)\u22c5exp\u2061(r(x,y)\u03b2)\\\\pi^*(y|x) &#061; \\\\frac{1}{Z(x)} \\\\pi_{ref}(y|x) \\\\cdot \\\\exp\\\\left(\\\\frac{r(x,y)}{\\\\beta}\\\\right)<\/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: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7387em\"><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=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">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: 2.2574em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">Z<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/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\">1<\/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=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/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=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/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><span class=\"base\"><span class=\"strut\" style=\"height: 2.4em;vertical-align: -0.95em\"><\/span><span class=\"mop\">exp<\/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\"><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: 0.0528em\">\u03b2<\/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: 0.0278em\">r<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8804em\"><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>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Z(x)&#061;\u2211y\u03c0ref(y\u2223x)\u22c5exp\u2061(r(x,y)\/\u03b2)Z(x) &#061; \\\\sum_y \\\\pi_{ref}(y|x) \\\\cdot \\\\exp(r(x,y)\/\\\\beta)<\/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: 0.0715em\">Z<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">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: 1.1858em;vertical-align: -0.4358em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.0017em\"><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 mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4358em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/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=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/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><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mop\">exp<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">\/<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u662f\u5f52\u4e00\u5316\u5e38\u6570\u3002<\/p>\n<p>\u5173\u952e\u4e00\u6b65&#xff1a;\u4ece\u6700\u4f18\u89e3\u4e2d\u89e3\u51fa\u5956\u52b1\u51fd\u6570&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">r(x,y)&#061;\u03b2log\u2061\u03c0\u2217(y\u2223x)\u03c0ref(y\u2223x)&#043;\u03b2log\u2061Z(x)r(x,y) &#061; \\\\beta \\\\log \\\\frac{\\\\pi^*(y|x)}{\\\\pi_{ref}(y|x)} &#043; \\\\beta \\\\log Z(x)<\/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 mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/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: 2.3991em;vertical-align: -0.9721em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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=\"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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/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=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/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\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><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=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9721em\"><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\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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 mathnormal\" style=\"margin-right: 0.0715em\">Z<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8fd9\u610f\u5473\u7740&#xff1a;\u5982\u679c\u6211\u4eec\u77e5\u9053\u6700\u4f18\u7b56\u7565 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0\u2217\\\\pi^*<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6887em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><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=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5c31\u53ef\u4ee5\u53cd\u63a8\u51fa\u5956\u52b1\u51fd\u6570\u3002 \u800c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Z(x)Z(x)<\/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: 0.0715em\">Z<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u662f\u5e38\u6570&#xff08;\u5bf9\u4e8e\u540c\u4e00 prompt&#xff0c;\u4e24\u4e2a\u56de\u7b54\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Z(x)Z(x)<\/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: 0.0715em\">Z<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u76f8\u540c&#xff09;&#xff0c;\u5728\u6210\u5bf9\u6bd4\u8f83\u4e2d\u4f1a\u6d88\u6389\u3002<\/p>\n<h4>DPO \u635f\u5931\u51fd\u6570\u63a8\u5bfc<\/h4>\n<p>\u5c06\u5956\u52b1\u51fd\u6570\u4ee3\u5165 Bradley-Terry \u6a21\u578b&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">P(yw\u227byl\u2223x)&#061;\u03c3(r(x,yw)\u2212r(x,yl))P(y_w \\\\succ y_l | x) &#061; \\\\sigma\\\\left(r(x,y_w) &#8211; r(x,y_l)\\\\right)<\/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: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/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\">\u227b<\/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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/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 mathnormal\">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: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/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: 0.0278em\">r<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/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 class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/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 delimcenter\" style=\"top: 0em\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">&#061;\u03c3(\u03b2log\u2061\u03c0\u2217(yw\u2223x)\u03c0ref(yw\u2223x)\u2212\u03b2log\u2061\u03c0\u2217(yl\u2223x)\u03c0ref(yl\u2223x))&#061; \\\\sigma\\\\left(\\\\beta \\\\log \\\\frac{\\\\pi^*(y_w|x)}{\\\\pi_{ref}(y_w|x)} &#8211; \\\\beta \\\\log \\\\frac{\\\\pi^*(y_l|x)}{\\\\pi_{ref}(y_l|x)}\\\\right)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.3669em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4221em;vertical-align: -0.9721em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/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 mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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=\"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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/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=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/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 mathnormal\">x<\/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\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><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=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/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 mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9721em\"><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\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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=\"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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/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=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/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 mathnormal\">x<\/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\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><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=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/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 mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9721em\"><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>\u6700\u5927\u4f3c\u7136\u4f30\u8ba1&#xff0c;\u5f97\u5230 DPO \u635f\u5931\u51fd\u6570&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">LDPO&#061;\u2212E(x,yw,yl)[log\u2061\u03c3(\u03b2log\u2061\u03c0(yw\u2223x)\u03c0ref(yw\u2223x)\u2212\u03b2log\u2061\u03c0(yl\u2223x)\u03c0ref(yl\u2223x))]\\\\mathcal{L}_{DPO} &#061; -\\\\mathbb{E}_{(x,y_w,y_l)} \\\\left[\\\\log \\\\sigma\\\\left(\\\\beta \\\\log \\\\frac{\\\\pi(y_w|x)}{\\\\pi_{ref}(y_w|x)} &#8211; \\\\beta \\\\log \\\\frac{\\\\pi(y_l|x)}{\\\\pi_{ref}(y_l|x)}\\\\right)\\\\right]<\/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 mathnormal mtight\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">O<\/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: 2.4221em;vertical-align: -0.9721em\"><\/span><span class=\"mord\">\u2212<\/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 mathnormal mtight\">x<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;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: 0.0269em\">w<\/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 mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0359em;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: 0.0197em\">l<\/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=\"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 mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/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 mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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=\"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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/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=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/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 mathnormal\">x<\/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 mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/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 mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9721em\"><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\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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=\"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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/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=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/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 mathnormal\">x<\/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 mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/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 mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9721em\"><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>\u76f4\u89c9\u89e3\u91ca&#xff1a;DPO \u76f4\u63a5\u4f18\u5316\u7b56\u7565&#xff0c;\u4f7f\u5f97&#034;\u88ab\u9009\u62e9\u7684\u56de\u7b54&#034;\u7684\u4f3c\u7136\u6bd4&#xff08;\u76f8\u5bf9\u4e8e\u53c2\u8003\u6a21\u578b&#xff09;\u9ad8\u4e8e&#034;\u88ab\u62d2\u7edd\u7684\u56de\u7b54&#034;\u3002<\/p>\n<h4>DPO vs RLHF \u7684\u7b49\u4ef7\u6027<\/h4>\n<table>\n<tr>\u7ef4\u5ea6RLHFDPO<\/tr>\n<tbody>\n<tr>\n<td>\u4f18\u5316\u76ee\u6807<\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">max\u2061\u03c0E[r(x,y)]\u2212\u03b2\u22c5KL\\\\max_\\\\pi E[r(x,y)] &#8211; \\\\beta \\\\cdot KL<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mop\"><span class=\"mop\">max<\/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-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\">\u03c0<\/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=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/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: 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: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u6700\u5c0f\u5316 DPO \u635f\u5931<\/td>\n<\/tr>\n<tr>\n<td>\u5956\u52b1\u6a21\u578b<\/td>\n<td>\u9700\u8981\u5355\u72ec\u8bad\u7ec3<\/td>\n<td>\u9690\u5f0f\u5305\u542b\u5728\u7b56\u7565\u4e2d<\/td>\n<\/tr>\n<tr>\n<td>\u8bad\u7ec3\u7a33\u5b9a\u6027<\/td>\n<td>\u4f4e&#xff08;PPO \u4e0d\u7a33\u5b9a&#xff09;<\/td>\n<td>\u9ad8&#xff08;\u6807\u51c6\u76d1\u7763\u5b66\u4e60&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>\u7406\u8bba\u6700\u4f18\u6027<\/td>\n<td>\u6700\u4f18<\/td>\n<td>\u7b49\u4ef7&#xff08;\u540c\u4e00\u4f18\u5316\u76ee\u6807&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>\u8ba1\u7b97\u6210\u672c<\/td>\n<td>\u9ad8&#xff08;\u56db\u6a21\u578b&#xff09;<\/td>\n<td>\u4f4e&#xff08;\u4e24\u6a21\u578b&#xff09;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u7b49\u4ef7\u6027\u8bf4\u660e&#xff1a;DPO \u548c RLHF \u4f18\u5316\u7684\u662f\u540c\u4e00\u4e2a\u76ee\u6807\u51fd\u6570&#xff0c;DPO \u53ea\u662f\u627e\u5230\u4e86\u4e00\u79cd\u66f4\u9ad8\u6548\u7684\u53c2\u6570\u5316\u65b9\u5f0f\u3002\u7406\u8bba\u4e0a&#xff0c;DPO \u7684\u6700\u4f18\u89e3\u4e0e RLHF \u7684\u6700\u4f18\u89e3\u76f8\u540c\u3002<\/p>\n<h4>DPO \u4ee3\u7801\u5b9e\u73b0<\/h4>\n<p><span class=\"token keyword\">from<\/span> trl <span class=\"token keyword\">import<\/span> DPOTrainer<span class=\"token punctuation\">,<\/span> DPOConfig<\/p>\n<p><span class=\"token comment\"># DPO \u914d\u7f6e<\/span><br \/>\ndpo_config <span class=\"token operator\">&#061;<\/span> DPOConfig<span class=\"token punctuation\">(<\/span><br \/>\n    output_dir<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;.\/dpo_model&#034;<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    num_train_epochs<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    per_device_train_batch_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    gradient_accumulation_steps<span class=\"token operator\">&#061;<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    learning_rate<span class=\"token operator\">&#061;<\/span><span class=\"token number\">5e-7<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    beta<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span>               <span class=\"token comment\"># DPO \u7684 \u03b2 \u53c2\u6570<\/span><br \/>\n    loss_type<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;sigmoid&#034;<\/span><span class=\"token punctuation\">,<\/span>     <span class=\"token comment\"># DPO \u635f\u5931\u7c7b\u578b<\/span><br \/>\n    max_length<span class=\"token operator\">&#061;<\/span><span class=\"token number\">512<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    bf16<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># DPO \u8bad\u7ec3<\/span><br \/>\ndpo_trainer <span class=\"token operator\">&#061;<\/span> DPOTrainer<span class=\"token punctuation\">(<\/span><br \/>\n    model<span class=\"token operator\">&#061;<\/span>model<span class=\"token punctuation\">,<\/span>                    <span class=\"token comment\"># \u5f85\u8bad\u7ec3\u7684\u7b56\u7565\u6a21\u578b<\/span><br \/>\n    ref_model<span class=\"token operator\">&#061;<\/span>ref_model<span class=\"token punctuation\">,<\/span>            <span class=\"token comment\"># \u53c2\u8003\u6a21\u578b&#xff08;\u51bb\u7ed3&#xff09;<\/span><br \/>\n    args<span class=\"token operator\">&#061;<\/span>dpo_config<span class=\"token punctuation\">,<\/span><br \/>\n    train_dataset<span class=\"token operator\">&#061;<\/span>preference_dataset<span class=\"token punctuation\">,<\/span><br \/>\n    tokenizer<span class=\"token operator\">&#061;<\/span>tokenizer<span class=\"token punctuation\">,<\/span><br \/>\n    peft_config<span class=\"token operator\">&#061;<\/span>lora_config<span class=\"token punctuation\">,<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><\/p>\n<p>dpo_trainer<span class=\"token punctuation\">.<\/span>train<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\ndpo_trainer<span class=\"token punctuation\">.<\/span>save_model<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;.\/dpo_model&#034;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<hr \/>\n<h3>DPO \u7684\u53d8\u4f53<\/h3>\n<h4>IPO&#xff08;Identity Preference Optimization&#xff09;<\/h4>\n<p>\u95ee\u9898&#xff1a;DPO \u5728\u504f\u597d\u6570\u636e\u786e\u5b9a\u6027\u9ad8\u65f6\u5bb9\u6613\u8fc7\u62df\u5408\u2014\u2014\u5982\u679c\u6240\u6709\u6807\u6ce8\u8005\u90fd\u8ba4\u4e3a A \u6bd4 B \u597d&#xff0c;DPO \u4f1a\u65e0\u9650\u589e\u5927 A \u548c B \u7684\u5dee\u8ddd\u3002<\/p>\n<p>\u89e3\u51b3\u65b9\u6848&#xff1a;IPO \u7528\u6052\u7b49\u51fd\u6570\u66ff\u4ee3 sigmoid&#xff0c;\u9650\u5236\u7b56\u7565\u504f\u79bb\u53c2\u8003\u6a21\u578b\u7684\u7a0b\u5ea6&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">LIPO&#061;E(x,yw,yl)[(log\u2061\u03c0(yw\u2223x)\u03c0ref(yw\u2223x)\u2212log\u2061\u03c0(yl\u2223x)\u03c0ref(yl\u2223x)\u22121\u03b2)2]\\\\mathcal{L}_{IPO} &#061; \\\\mathbb{E}_{(x,y_w,y_l)} \\\\left[\\\\left(\\\\log \\\\frac{\\\\pi(y_w|x)}{\\\\pi_{ref}(y_w|x)} &#8211; \\\\log \\\\frac{\\\\pi(y_l|x)}{\\\\pi_{ref}(y_l|x)} &#8211; \\\\frac{1}{\\\\beta}\\\\right)^2\\\\right]<\/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 mathnormal mtight\" style=\"margin-right: 0.0785em\">I<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">O<\/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: 3em;vertical-align: -1.25em\"><\/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 mathnormal mtight\">x<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;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: 0.0269em\">w<\/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 mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0359em;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: 0.0197em\">l<\/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=\"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=\"minner\"><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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/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=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/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 mathnormal\">x<\/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 mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/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 mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9721em\"><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\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/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=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/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 mathnormal\">x<\/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 mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/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 mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9721em\"><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\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8804em\"><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=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.654em\"><span class=\"\" style=\"top: -3.9029em;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><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5173\u952e\u533a\u522b&#xff1a;IPO \u7528\u5e73\u65b9\u635f\u5931\u66ff\u4ee3\u4e86 DPO \u7684 log-sigmoid \u635f\u5931&#xff0c;\u8fd9\u610f\u5473\u7740&#xff1a;<\/p>\n<ul>\n<li>\u5f53\u504f\u597d\u5dee\u8ddd\u8db3\u591f\u5927\u65f6&#xff0c;IPO \u4f1a\u505c\u6b62\u4f18\u5316&#xff08;\u6b63\u5219\u5316\u6548\u679c&#xff09;<\/li>\n<li>DPO \u4f1a\u6301\u7eed\u589e\u5927\u5dee\u8ddd&#xff0c;\u5bfc\u81f4\u8fc7\u62df\u5408<\/li>\n<\/ul>\n<p><span class=\"token comment\"># IPO \u8bad\u7ec3<\/span><br \/>\ndpo_config <span class=\"token operator\">&#061;<\/span> DPOConfig<span class=\"token punctuation\">(<\/span><br \/>\n    loss_type<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;ipo&#034;<\/span><span class=\"token punctuation\">,<\/span>  <span class=\"token comment\"># \u4f7f\u7528 IPO \u635f\u5931<\/span><br \/>\n    beta<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><\/p>\n<h4>KTO&#xff08;Kahneman-Tversky Optimization&#xff09;<\/h4>\n<p>\u95ee\u9898&#xff1a;DPO \u9700\u8981\u6210\u5bf9\u504f\u597d\u6570\u636e (prompt, chosen, rejected)&#xff0c;\u4f46\u5b9e\u9645\u4e2d\u6210\u5bf9\u6570\u636e\u6536\u96c6\u6210\u672c\u9ad8\u3002<\/p>\n<p>\u89e3\u51b3\u65b9\u6848&#xff1a;KTO \u53ea\u9700\u8981&#034;\u597d\/\u574f&#034;\u6807\u7b7e&#xff0c;\u4e0d\u9700\u8981\u6210\u5bf9\u6bd4\u8f83&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">LKTO&#061;E(x,y)[\u03bbw\u22c5(1\u2212v(x,y))\u22c51[y\u00a0is\u00a0good]&#043;\u03bbl\u22c5v(x,y)\u22c51[y\u00a0is\u00a0bad]]\\\\mathcal{L}_{KTO} &#061; \\\\mathbb{E}_{(x,y)} \\\\left[\\\\lambda_w \\\\cdot (1 &#8211; v(x,y)) \\\\cdot \\\\mathbb{1}[y \\\\text{ is good}] &#043; \\\\lambda_l \\\\cdot v(x,y) \\\\cdot \\\\mathbb{1}[y \\\\text{ is bad}]\\\\right]<\/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 mathnormal mtight\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">O<\/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: 1.1052em;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 mathnormal mtight\">x<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/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><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: 0.1514em\"><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 mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/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\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/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 class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/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\">1<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord text\"><span class=\"mord\">\u00a0is\u00a0good<\/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\"><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><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: 0.0197em\">l<\/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\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/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\">1<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord text\"><span class=\"mord\">\u00a0is\u00a0bad<\/span><\/span><span class=\"mclose\">]<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">v(x,y)&#061;\u03c3(\u03b2log\u2061\u03c0(y\u2223x)\u03c0ref(y\u2223x)\u2212zref)v(x,y) &#061; \\\\sigma(\\\\beta \\\\log \\\\frac{\\\\pi(y|x)}{\\\\pi_{ref}(y|x)} &#8211; z_{ref})<\/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\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/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: 1.5581em;vertical-align: -0.5481em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.01em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0359em;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\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord mtight\">\u2223<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mclose mtight\">)<\/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: -3.485em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord mtight\">\u2223<\/span><span class=\"mord mathnormal mtight\">x<\/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: 0.5481em\"><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\">\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: 0.044em\">z<\/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: -0.044em;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: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/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=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">zrefz_{ref}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7167em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/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: -0.044em;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: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/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> \u662f\u53c2\u8003\u6a21\u578b\u7684\u671f\u671b\u5956\u52b1\u3002<\/p>\n<p>KTO \u7684\u4f18\u52bf&#xff1a;<\/p>\n<ul>\n<li>\u6570\u636e\u9700\u6c42\u4f4e&#xff1a;\u53ea\u9700\u597d\/\u574f\u6807\u7b7e&#xff0c;\u4e0d\u9700\u8981\u6210\u5bf9\u6bd4\u8f83<\/li>\n<li>\u6570\u636e\u91cf\u5927&#xff1a;\u7528\u6237 &#x1f44d;\/&#x1f44e; \u5c31\u53ef\u4ee5\u4f5c\u4e3a\u8bad\u7ec3\u6570\u636e<\/li>\n<li>\u635f\u5931\u51fd\u6570\u4e0d\u5bf9\u79f0&#xff1a;\u501f\u9274\u524d\u666f\u7406\u8bba&#xff0c;\u574f\u6837\u672c\u7684\u60e9\u7f5a\u6bd4\u597d\u6837\u672c\u7684\u5956\u52b1\u5927<\/li>\n<\/ul>\n<p><span class=\"token comment\"># KTO \u8bad\u7ec3<\/span><br \/>\ndpo_config <span class=\"token operator\">&#061;<\/span> DPOConfig<span class=\"token punctuation\">(<\/span><br \/>\n    loss_type<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;kto&#034;<\/span><span class=\"token punctuation\">,<\/span>  <span class=\"token comment\"># \u4f7f\u7528 KTO \u635f\u5931<\/span><br \/>\n    beta<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><\/p>\n<h4>ORPO&#xff08;Odds Ratio Preference Optimization&#xff09;<\/h4>\n<p>\u95ee\u9898&#xff1a;DPO \u9700\u8981\u53c2\u8003\u6a21\u578b&#xff0c;\u589e\u52a0\u4e86\u663e\u5b58\u6d88\u8017\u3002<\/p>\n<p>\u89e3\u51b3\u65b9\u6848&#xff1a;ORPO \u7528\u80dc\u7387\u6bd4&#xff08;Odds Ratio&#xff09;\u66ff\u4ee3\u5bf9\u6570\u4f3c\u7136\u6bd4&#xff0c;\u4e0d\u9700\u8981\u53c2\u8003\u6a21\u578b&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">LORPO&#061;LSFT&#043;\u03bb\u22c5LOR\\\\mathcal{L}_{ORPO} &#061; \\\\mathcal{L}_{SFT} &#043; \\\\lambda \\\\cdot \\\\mathcal{L}_{OR}<\/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 mathnormal mtight\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">O<\/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: 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 mathnormal mtight\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">F<\/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=\"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: 0.6944em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/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: 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 mathnormal mtight\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0077em\">R<\/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><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">LOR\\\\mathcal{L}_{OR}<\/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 mathnormal mtight\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0077em\">R<\/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> \u662f\u57fa\u4e8e\u80dc\u7387\u6bd4\u7684\u504f\u597d\u635f\u5931&#xff0c;\u76f4\u63a5\u5728 SFT \u635f\u5931\u4e0a\u6dfb\u52a0\u504f\u597d\u4f18\u5316\u9879\u3002<\/p>\n<p>\u4f18\u52bf&#xff1a;\u4e0d\u9700\u8981\u53c2\u8003\u6a21\u578b&#xff0c;\u663e\u5b58\u6d88\u8017\u51cf\u534a\u3002<\/p>\n<h4>SimPO&#xff08;Simple Preference Optimization&#xff09;<\/h4>\n<p>\u95ee\u9898&#xff1a;DPO \u7684\u53c2\u8003\u6a21\u578b\u4f9d\u8d56\u589e\u52a0\u4e86\u5b9e\u73b0\u590d\u6742\u5ea6\u3002<\/p>\n<p>\u89e3\u51b3\u65b9\u6848&#xff1a;SimPO \u7528\u5e8f\u5217\u957f\u5ea6\u5f52\u4e00\u5316\u7684\u5e73\u5747\u5bf9\u6570\u6982\u7387\u66ff\u4ee3\u5bf9\u6570\u4f3c\u7136\u6bd4&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">LSimPO&#061;\u2212E[log\u2061\u03c3(\u03b2\u2223yw\u2223log\u2061\u03c0(yw\u2223x)\u2212\u03b2\u2223yl\u2223log\u2061\u03c0(yl\u2223x)\u2212\u03b3)]\\\\mathcal{L}_{SimPO} &#061; -\\\\mathbb{E}\\\\left[\\\\log \\\\sigma\\\\left(\\\\frac{\\\\beta}{|y_w|} \\\\log \\\\pi(y_w|x) &#8211; \\\\frac{\\\\beta}{|y_l|} \\\\log \\\\pi(y_l|x) &#8211; \\\\gamma\\\\right)\\\\right]<\/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 mathnormal mtight\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord mathnormal mtight\">im<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">O<\/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\">\u2212<\/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 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 mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/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\"><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\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><span 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: 0.0528em\">\u03b2<\/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=\"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 mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/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 mathnormal\">x<\/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 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\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><span 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: 0.0528em\">\u03b2<\/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=\"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 mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/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 mathnormal\">x<\/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 class=\"mord mathnormal\" style=\"margin-right: 0.0556em\">\u03b3<\/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\">\u03b3\\\\gamma<\/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> \u662f\u76ee\u6807\u5956\u52b1\u8fb9\u754c\u3002<\/p>\n<p>\u4f18\u52bf&#xff1a;\u4e0d\u9700\u8981\u53c2\u8003\u6a21\u578b&#xff0c;\u957f\u5ea6\u5f52\u4e00\u5316\u907f\u514d\u957f\u5ea6\u504f\u597d\u3002<\/p>\n<hr \/>\n<h3>RLAIF&#xff08;RL from AI Feedback&#xff09;<\/h3>\n<h4>Constitutional AI<\/h4>\n<p>\u6838\u5fc3\u601d\u60f3&#xff1a;\u7528 AI \u539f\u5219\u66ff\u4ee3\u4eba\u7c7b\u53cd\u9988&#xff0c;\u8ba9 AI \u81ea\u5df1\u5224\u65ad&#034;\u4ec0\u4e48\u662f\u5bf9\u7684&#034;\u3002<\/p>\n<p>\u6d41\u7a0b&#xff1a;<\/p>\n<li>\u5b9a\u4e49\u4e00\u7ec4&#034;\u5baa\u6cd5\u539f\u5219&#034;&#xff08;Constitutional Principles&#xff09;<\/li>\n<li>\u6a21\u578b\u751f\u6210\u56de\u7b54<\/li>\n<li>AI \u8bc4\u4f30\u5668\u6839\u636e\u539f\u5219\u8bc4\u4f30\u56de\u7b54<\/li>\n<li>AI \u751f\u6210\u504f\u597d\u6570\u636e<\/li>\n<li>\u7528\u504f\u597d\u6570\u636e\u8bad\u7ec3\u5956\u52b1\u6a21\u578b\u6216\u76f4\u63a5\u7528 DPO<\/li>\n<h4>RLAIF \u6d41\u7a0b<\/h4>\n<p>1. \u751f\u6210\u56de\u7b54 \u2192 2. AI \u8bc4\u4f30 \u2192 3. \u751f\u6210\u504f\u597d \u2192 4. \u8bad\u7ec3<\/p>\n<p>\u4ee3\u7801\u5b9e\u73b0&#xff1a;LLM-as-Judge \u504f\u597d\u6570\u636e\u751f\u6210<\/p>\n<p><span class=\"token keyword\">from<\/span> openai <span class=\"token keyword\">import<\/span> OpenAI<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">generate_preference_data_with_ai<\/span><span class=\"token punctuation\">(<\/span><br \/>\n    prompts<span class=\"token punctuation\">,<\/span> model_a_responses<span class=\"token punctuation\">,<\/span> model_b_responses<span class=\"token punctuation\">,<\/span> judge_model<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;gpt-4&#034;<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token triple-quoted-string string\">&#034;&#034;&#034;<br \/>\n    \u7528 LLM-as-Judge \u751f\u6210\u504f\u597d\u6570\u636e<br \/>\n    &#034;&#034;&#034;<\/span><br \/>\n    client <span class=\"token operator\">&#061;<\/span> OpenAI<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    preference_data <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><\/p>\n<p>    <span class=\"token keyword\">for<\/span> prompt<span class=\"token punctuation\">,<\/span> resp_a<span class=\"token punctuation\">,<\/span> resp_b <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">zip<\/span><span class=\"token punctuation\">(<\/span>prompts<span class=\"token punctuation\">,<\/span> model_a_responses<span class=\"token punctuation\">,<\/span> model_b_responses<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        judge_prompt <span class=\"token operator\">&#061;<\/span> <span class=\"token string-interpolation\"><span class=\"token string\">f&#034;&#034;&#034;You are a helpful AI judge. Given the following prompt and two responses, determine which response is better.<\/p>\n<p>Prompt: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>prompt<span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\"><\/p>\n<p>Response A: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>resp_a<span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\"><\/p>\n<p>Response B: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>resp_b<span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\"><\/p>\n<p>Which response is better? Answer with &#034;A&#034; or &#034;B&#034; and explain your reasoning.&#034;&#034;&#034;<\/span><\/span><\/p>\n<p>        response <span class=\"token operator\">&#061;<\/span> client<span class=\"token punctuation\">.<\/span>chat<span class=\"token punctuation\">.<\/span>completions<span class=\"token punctuation\">.<\/span>create<span class=\"token punctuation\">(<\/span><br \/>\n            model<span class=\"token operator\">&#061;<\/span>judge_model<span class=\"token punctuation\">,<\/span><br \/>\n            messages<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">{<\/span><span class=\"token string\">&#034;role&#034;<\/span><span class=\"token punctuation\">:<\/span> <span class=\"token string\">&#034;user&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;content&#034;<\/span><span class=\"token punctuation\">:<\/span> judge_prompt<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n            temperature<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span><br \/>\n        <span class=\"token punctuation\">)<\/span><\/p>\n<p>        judgment <span class=\"token operator\">&#061;<\/span> response<span class=\"token punctuation\">.<\/span>choices<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>message<span class=\"token punctuation\">.<\/span>content<br \/>\n        winner <span class=\"token operator\">&#061;<\/span> <span class=\"token string\">&#034;A&#034;<\/span> <span class=\"token keyword\">if<\/span> <span class=\"token string\">&#034;A&#034;<\/span> <span class=\"token keyword\">in<\/span> judgment<span class=\"token punctuation\">.<\/span>split<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\\\\n&#034;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token keyword\">else<\/span> <span class=\"token string\">&#034;B&#034;<\/span><\/p>\n<p>        preference_data<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token string\">&#034;prompt&#034;<\/span><span class=\"token punctuation\">:<\/span> prompt<span class=\"token punctuation\">,<\/span><br \/>\n            <span class=\"token string\">&#034;chosen&#034;<\/span><span class=\"token punctuation\">:<\/span> resp_a <span class=\"token keyword\">if<\/span> winner <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#034;A&#034;<\/span> <span class=\"token keyword\">else<\/span> resp_b<span class=\"token punctuation\">,<\/span><br \/>\n            <span class=\"token string\">&#034;rejected&#034;<\/span><span class=\"token punctuation\">:<\/span> resp_b <span class=\"token keyword\">if<\/span> winner <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#034;A&#034;<\/span> <span class=\"token keyword\">else<\/span> resp_a<span class=\"token punctuation\">,<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token keyword\">return<\/span> preference_data<\/p>\n<h4>RLAIF \u7684\u5c40\u9650<\/h4>\n<table>\n<tr>\u95ee\u9898\u539f\u56e0\u5f71\u54cd<\/tr>\n<tbody>\n<tr>\n<td>AI \u504f\u89c1\u4f20\u64ad<\/td>\n<td>AI \u8bc4\u4f30\u5668\u672c\u8eab\u6709\u504f\u89c1<\/td>\n<td>\u6a21\u578b\u81ea\u6211\u5f3a\u5316<\/td>\n<\/tr>\n<tr>\n<td>\u8bc4\u4f30\u8d28\u91cf\u4e0a\u9650<\/td>\n<td>AI \u65e0\u6cd5\u8d85\u8d8a\u81ea\u8eab\u80fd\u529b<\/td>\n<td>\u5bf9\u9f50\u4e0a\u9650\u53d7\u9650\u4e8e\u8bc4\u4f30\u5668<\/td>\n<\/tr>\n<tr>\n<td>\u4f4d\u7f6e\u504f\u89c1<\/td>\n<td>AI \u8bc4\u4f30\u5668\u504f\u597d\u7b2c\u4e00\u4e2a\u56de\u7b54<\/td>\n<td>\u504f\u597d\u6570\u636e\u4e0d\u53ef\u9760<\/td>\n<\/tr>\n<tr>\n<td>\u957f\u5ea6\u504f\u89c1<\/td>\n<td>AI \u8bc4\u4f30\u5668\u504f\u597d\u957f\u56de\u7b54<\/td>\n<td>\u5956\u52b1\u6a21\u578b\u504f\u5dee<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h3>\u65b9\u6848\u5bf9\u6bd4\u4e0e\u9009\u62e9<\/h3>\n<h4>\u7efc\u5408\u5bf9\u6bd4\u8868<\/h4>\n<table>\n<tr>\u7ef4\u5ea6RLHFDPOIPOKTORLAIF<\/tr>\n<tbody>\n<tr>\n<td>\u662f\u5426\u9700\u8981\u5956\u52b1\u6a21\u578b<\/td>\n<td>\u2705<\/td>\n<td>\u274c<\/td>\n<td>\u274c<\/td>\n<td>\u274c<\/td>\n<td>\u2705<\/td>\n<\/tr>\n<tr>\n<td>\u662f\u5426\u9700\u8981\u53c2\u8003\u6a21\u578b<\/td>\n<td>\u2705<\/td>\n<td>\u2705<\/td>\n<td>\u2705<\/td>\n<td>\u2705<\/td>\n<td>\u2705<\/td>\n<\/tr>\n<tr>\n<td>\u6570\u636e\u9700\u6c42<\/td>\n<td>\u6210\u5bf9\u504f\u597d<\/td>\n<td>\u6210\u5bf9\u504f\u597d<\/td>\n<td>\u6210\u5bf9\u504f\u597d<\/td>\n<td>\u597d\/\u574f\u6807\u7b7e<\/td>\n<td>AI \u751f\u6210\u504f\u597d<\/td>\n<\/tr>\n<tr>\n<td>\u8bad\u7ec3\u7a33\u5b9a\u6027<\/td>\n<td>\u4f4e<\/td>\n<td>\u4e2d<\/td>\n<td>\u9ad8<\/td>\n<td>\u9ad8<\/td>\n<td>\u4f4e<\/td>\n<\/tr>\n<tr>\n<td>\u7406\u8bba\u6700\u4f18\u6027<\/td>\n<td>\u6700\u4f18<\/td>\n<td>\u7b49\u4ef7<\/td>\n<td>\u6539\u8fdb<\/td>\n<td>\u8fd1\u4f3c<\/td>\n<td>\u4f9d\u8d56 AI \u8d28\u91cf<\/td>\n<\/tr>\n<tr>\n<td>\u8ba1\u7b97\u6210\u672c<\/td>\n<td>\u9ad8<\/td>\n<td>\u4f4e<\/td>\n<td>\u4f4e<\/td>\n<td>\u4f4e<\/td>\n<td>\u9ad8<\/td>\n<\/tr>\n<tr>\n<td>\u5b9e\u73b0\u590d\u6742\u5ea6<\/td>\n<td>\u9ad8<\/td>\n<td>\u4f4e<\/td>\n<td>\u4f4e<\/td>\n<td>\u4f4e<\/td>\n<td>\u4e2d<\/td>\n<\/tr>\n<tr>\n<td>\u9002\u5408\u573a\u666f<\/td>\n<td>\u5927\u89c4\u6a21\u5bf9\u9f50<\/td>\n<td>\u4e2d\u5c0f\u89c4\u6a21\u5bf9\u9f50<\/td>\n<td>\u504f\u597d\u786e\u5b9a\u6027\u9ad8<\/td>\n<td>\u53ea\u6709\u597d\/\u574f\u6807\u7b7e<\/td>\n<td>\u6807\u6ce8\u6210\u672c\u6781\u9ad8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>\u9009\u62e9\u51b3\u7b56\u6811<\/h4>\n<p>\u5f00\u59cb<br \/>\n\u2502<br \/>\n\u251c\u2500 \u662f\u5426\u6709\u6210\u5bf9\u504f\u597d\u6570\u636e&#xff1f;<br \/>\n\u2502   \u251c\u2500 \u662f \u2192 \u504f\u597d\u786e\u5b9a\u6027\u9ad8&#xff1f;<br \/>\n\u2502   \u2502       \u251c\u2500 \u662f \u2192 IPO&#xff08;\u9632\u6b62\u8fc7\u62df\u5408&#xff09;<br \/>\n\u2502   \u2502       \u2514\u2500 \u5426 \u2192 DPO&#xff08;\u901a\u7528\u9009\u62e9&#xff09;<br \/>\n\u2502   \u2514\u2500 \u5426 \u2192 \u53ea\u6709\u597d\/\u574f\u6807\u7b7e&#xff1f;<br \/>\n\u2502           \u251c\u2500 \u662f \u2192 KTO<br \/>\n\u2502           \u2514\u2500 \u5426 \u2192 \u6807\u6ce8\u6210\u672c\u53ef\u63a5\u53d7&#xff1f;<br \/>\n\u2502                   \u251c\u2500 \u662f \u2192 \u6536\u96c6\u6210\u5bf9\u504f\u597d \u2192 DPO<br \/>\n\u2502                   \u2514\u2500 \u5426 \u2192 RLAIF&#xff08;\u7528 AI \u751f\u6210\u504f\u597d&#xff09;<br \/>\n\u2502<br \/>\n\u251c\u2500 \u8ba1\u7b97\u8d44\u6e90\u5145\u8db3&#xff1f;<br \/>\n\u2502   \u251c\u2500 \u662f \u2192 \u8003\u8651 RLHF&#xff08;\u7406\u8bba\u6700\u4f18&#xff09;<br \/>\n\u2502   \u2514\u2500 \u5426 \u2192 DPO\/IPO\/KTO<br \/>\n\u2502<br \/>\n\u2514\u2500 \u662f\u5426\u9700\u8981\u53c2\u8003\u6a21\u578b&#xff1f;<br \/>\n    \u251c\u2500 \u662f \u2192 DPO\/IPO\/KTO<br \/>\n    \u2514\u2500 \u5426 \u2192 ORPO\/SimPO<\/p>\n<h4>DPO \u5b9e\u6218<\/h4>\n<p><span class=\"token comment\"># \u5b8c\u6574\u7684 DPO \u8bad\u7ec3\u6d41\u7a0b<\/span><br \/>\n<span class=\"token keyword\">from<\/span> transformers <span class=\"token keyword\">import<\/span> AutoModelForCausalLM<span class=\"token punctuation\">,<\/span> AutoTokenizer<br \/>\n<span class=\"token keyword\">from<\/span> trl <span class=\"token keyword\">import<\/span> DPOTrainer<span class=\"token punctuation\">,<\/span> DPOConfig<br \/>\n<span class=\"token keyword\">from<\/span> peft <span class=\"token keyword\">import<\/span> LoraConfig<br \/>\n<span class=\"token keyword\">from<\/span> datasets <span class=\"token keyword\">import<\/span> load_dataset<\/p>\n<p><span class=\"token comment\"># \u52a0\u8f7d\u6a21\u578b<\/span><br \/>\nmodel_name <span class=\"token operator\">&#061;<\/span> <span class=\"token string\">&#034;meta-llama\/Llama-3-8B&#034;<\/span><br \/>\nmodel <span class=\"token operator\">&#061;<\/span> AutoModelForCausalLM<span class=\"token punctuation\">.<\/span>from_pretrained<span class=\"token punctuation\">(<\/span>model_name<span class=\"token punctuation\">)<\/span><br \/>\nref_model <span class=\"token operator\">&#061;<\/span> AutoModelForCausalLM<span class=\"token punctuation\">.<\/span>from_pretrained<span class=\"token punctuation\">(<\/span>model_name<span class=\"token punctuation\">)<\/span><br \/>\ntokenizer <span class=\"token operator\">&#061;<\/span> AutoTokenizer<span class=\"token punctuation\">.<\/span>from_pretrained<span class=\"token punctuation\">(<\/span>model_name<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u52a0\u8f7d\u504f\u597d\u6570\u636e<\/span><br \/>\ndataset <span class=\"token operator\">&#061;<\/span> load_dataset<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Anthropic\/hh-rlhf&#034;<\/span><span class=\"token punctuation\">,<\/span> split<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;train&#034;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># LoRA \u914d\u7f6e<\/span><br \/>\nlora_config <span class=\"token operator\">&#061;<\/span> LoraConfig<span class=\"token punctuation\">(<\/span><br \/>\n    r<span class=\"token operator\">&#061;<\/span><span class=\"token number\">16<\/span><span class=\"token punctuation\">,<\/span> lora_alpha<span class=\"token operator\">&#061;<\/span><span class=\"token number\">32<\/span><span class=\"token punctuation\">,<\/span> lora_dropout<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.05<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    target_modules<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span><span class=\"token string\">&#034;q_proj&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;v_proj&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;k_proj&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;o_proj&#034;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    task_type<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;CAUSAL_LM&#034;<\/span><span class=\"token punctuation\">,<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># DPO \u8bad\u7ec3<\/span><br \/>\ndpo_config <span class=\"token operator\">&#061;<\/span> DPOConfig<span class=\"token punctuation\">(<\/span><br \/>\n    output_dir<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;.\/dpo_output&#034;<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    beta<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    loss_type<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;sigmoid&#034;<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    num_train_epochs<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    per_device_train_batch_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    learning_rate<span class=\"token operator\">&#061;<\/span><span class=\"token number\">5e-7<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    bf16<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><\/p>\n<p>trainer <span class=\"token operator\">&#061;<\/span> DPOTrainer<span class=\"token punctuation\">(<\/span><br \/>\n    model<span class=\"token operator\">&#061;<\/span>model<span class=\"token punctuation\">,<\/span><br \/>\n    ref_model<span class=\"token operator\">&#061;<\/span>ref_model<span class=\"token punctuation\">,<\/span><br \/>\n    args<span class=\"token operator\">&#061;<\/span>dpo_config<span class=\"token punctuation\">,<\/span><br \/>\n    train_dataset<span class=\"token operator\">&#061;<\/span>dataset<span class=\"token punctuation\">,<\/span><br \/>\n    tokenizer<span class=\"token operator\">&#061;<\/span>tokenizer<span class=\"token punctuation\">,<\/span><br \/>\n    peft_config<span class=\"token operator\">&#061;<\/span>lora_config<span class=\"token punctuation\">,<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><\/p>\n<p>trainer<span class=\"token punctuation\">.<\/span>train<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h4>DPO \u7684\u5e38\u89c1\u9677\u9631<\/h4>\n<table>\n<tr>\u9677\u9631\u539f\u56e0\u89e3\u51b3\u65b9\u6848<\/tr>\n<tbody>\n<tr>\n<td>\u53c2\u8003\u6a21\u578b\u9009\u62e9\u4e0d\u5f53<\/td>\n<td>ref_model \u592a\u5f31\u6216\u592a\u5f3a<\/td>\n<td>\u4f7f\u7528 SFT \u6a21\u578b\u4f5c\u4e3a\u53c2\u8003<\/td>\n<\/tr>\n<tr>\n<td>\u03b2 \u8c03\u53c2\u4e0d\u5f53<\/td>\n<td>\u03b2 \u592a\u5927\/\u592a\u5c0f<\/td>\n<td>\u4ece 0.1 \u5f00\u59cb&#xff0c;\u76ee\u6807 KL 3-10<\/td>\n<\/tr>\n<tr>\n<td>\u6570\u636e\u8d28\u91cf\u5dee<\/td>\n<td>\u504f\u597d\u6807\u6ce8\u4e0d\u4e00\u81f4<\/td>\n<td>\u6e05\u6d17\u6570\u636e&#xff0c;\u8fc7\u6ee4\u4f4e\u8d28\u91cf\u504f\u597d<\/td>\n<\/tr>\n<tr>\n<td>\u8fc7\u62df\u5408<\/td>\n<td>\u8bad\u7ec3\u592a\u591a epochs<\/td>\n<td>1 epoch \u901a\u5e38\u8db3\u591f<\/td>\n<\/tr>\n<tr>\n<td>\u957f\u5ea6\u504f\u597d<\/td>\n<td>\u6a21\u578b\u504f\u597d\u957f\u56de\u7b54<\/td>\n<td>\u4f7f\u7528 SimPO \u6216\u957f\u5ea6\u5f52\u4e00\u5316<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h3>\u672c\u7ae0\u5c0f\u7ed3<\/h3>\n<ul>\n<li>DPO \u6838\u5fc3\u6d1e\u5bdf&#xff1a;RLHF \u7684\u6700\u4f18\u7b56\u7565\u6709\u95ed\u5f0f\u89e3&#xff0c;\u53ef\u4ee5\u7ed5\u8fc7\u5956\u52b1\u6a21\u578b\u76f4\u63a5\u4f18\u5316<\/li>\n<li>DPO \u635f\u5931&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">L&#061;\u2212E[log\u2061\u03c3(\u03b2log\u2061\u03c0(yw)\u03c0ref(yw)\u2212\u03b2log\u2061\u03c0(yl)\u03c0ref(yl))]\\\\mathcal{L} &#061; -\\\\mathbb{E}[\\\\log \\\\sigma(\\\\beta \\\\log \\\\frac{\\\\pi(y_w)}{\\\\pi_{ref}(y_w)} &#8211; \\\\beta \\\\log \\\\frac{\\\\pi(y_l)}{\\\\pi_{ref}(y_l)})]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathcal\">L<\/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: 1.5581em;vertical-align: -0.5481em\"><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord mathbb\">E<\/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 mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.01em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0359em;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\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;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: 0.0269em\">w<\/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: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.485em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;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: 0.0269em\">w<\/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: 0.5481em\"><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\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.5581em;vertical-align: -0.5481em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.01em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0359em;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\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0359em;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: 0.0197em\">l<\/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=\"mclose mtight\">)<\/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: -3.485em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0359em;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: 0.0197em\">l<\/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=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5481em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose\">)]<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>IPO&#xff1a;\u89e3\u51b3 DPO \u8fc7\u62df\u5408&#xff0c;\u7528\u5e73\u65b9\u635f\u5931\u66ff\u4ee3 log-sigmoid<\/li>\n<li>KTO&#xff1a;\u53ea\u9700\u597d\/\u574f\u6807\u7b7e&#xff0c;\u4e0d\u9700\u8981\u6210\u5bf9\u504f\u597d\u6570\u636e<\/li>\n<li>ORPO\/SimPO&#xff1a;\u4e0d\u9700\u8981\u53c2\u8003\u6a21\u578b&#xff0c;\u964d\u4f4e\u663e\u5b58\u6d88\u8017<\/li>\n<li>RLAIF&#xff1a;\u7528 AI \u66ff\u4ee3\u4eba\u7c7b\u53cd\u9988&#xff0c;\u53ef\u6269\u5c55\u4f46\u6709\u504f\u89c1\u4f20\u64ad\u98ce\u9669<\/li>\n<li>\u65b9\u6848\u9009\u62e9&#xff1a;\u6839\u636e\u6570\u636e\u7c7b\u578b\u548c\u8ba1\u7b97\u8d44\u6e90\u9009\u62e9&#xff0c;DPO \u662f\u6700\u901a\u7528\u7684\u8d77\u70b9<\/li>\n<\/ul>\n<hr \/>\n<h3>\u9762\u8bd5\u8003\u70b9\u901f\u67e5<\/h3>\n<p>Q: DPO \u7684\u63a8\u5bfc\u601d\u8def&#xff1f;<\/p>\n<p>\u4ece RLHF \u7684\u6700\u4f18\u89e3 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0\u2217&#061;1Z\u03c0ref\u22c5exp\u2061(r\/\u03b2)\\\\pi^* &#061; \\\\frac{1}{Z} \\\\pi_{ref} \\\\cdot \\\\exp(r\/\\\\beta)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6887em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><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=\"mbin mtight\">\u2217<\/span><\/span><\/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: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0715em\">Z<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/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: 0.2222em\"><\/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=\"mop\">exp<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord\">\/<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u51fa\u53d1&#xff0c;\u89e3\u51fa\u5956\u52b1\u51fd\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">r&#061;\u03b2log\u2061(\u03c0\u2217\/\u03c0ref)&#043;\u03b2log\u2061Zr &#061; \\\\beta \\\\log(\\\\pi^*\/\\\\pi_{ref}) &#043; \\\\beta \\\\log Z<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/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: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/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=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><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=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\/<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/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=\"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: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0528em\">\u03b2<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/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 mathnormal\" style=\"margin-right: 0.0715em\">Z<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4ee3\u5165 Bradley-Terry \u6a21\u578b\u540e&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ZZ<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">Z<\/span><\/span><\/span><\/span><\/span> \u5728\u6210\u5bf9\u6bd4\u8f83\u4e2d\u6d88\u6389&#xff0c;\u5f97\u5230\u76f4\u63a5\u4f18\u5316\u7b56\u7565\u7684 DPO \u635f\u5931\u3002\u6838\u5fc3\u6d1e\u5bdf&#xff1a;\u4e0d\u9700\u8981\u663e\u5f0f\u8bad\u7ec3\u5956\u52b1\u6a21\u578b&#xff0c;\u7b56\u7565\u672c\u8eab\u9690\u5f0f\u5305\u542b\u4e86\u5956\u52b1\u4fe1\u606f\u3002<\/p>\n<p>Q: DPO vs RLHF \u7684\u53d6\u820d&#xff1f;<\/p>\n<p>DPO \u7684\u4f18\u52bf&#xff1a;\u5b9e\u73b0\u7b80\u5355\u3001\u8bad\u7ec3\u7a33\u5b9a\u3001\u8ba1\u7b97\u6210\u672c\u4f4e&#xff08;\u4e24\u6a21\u578b vs \u56db\u6a21\u578b&#xff09;\u3002RLHF \u7684\u4f18\u52bf&#xff1a;\u7406\u8bba\u4e0a\u66f4\u7075\u6d3b&#xff08;\u53ef\u4ee5\u5728\u7ebf\u66f4\u65b0\u5956\u52b1\u6a21\u578b&#xff09;\u3001\u9002\u5408\u5927\u89c4\u6a21\u5bf9\u9f50\u3002\u5b9e\u8df5\u4e2d&#xff1a;\u4e2d\u5c0f\u89c4\u6a21\u7528 DPO&#xff0c;\u5927\u89c4\u6a21\u5bf9\u9f50\u7528 RLHF\u3002DPO \u7684\u6548\u679c\u901a\u5e38\u63a5\u8fd1 RLHF \u7684 80-90%\u3002<\/p>\n<p>Q: KTO \u7684\u9002\u7528\u573a\u666f&#xff1f;<\/p>\n<p>KTO \u9002\u7528\u4e8e\u53ea\u6709\u597d\/\u574f\u6807\u7b7e&#xff08;\u800c\u975e\u6210\u5bf9\u504f\u597d&#xff09;\u7684\u573a\u666f&#xff0c;\u5982\u7528\u6237 &#x1f44d;\/&#x1f44e; \u53cd\u9988\u3002KTO \u501f\u9274\u524d\u666f\u7406\u8bba&#xff0c;\u574f\u6837\u672c\u7684\u60e9\u7f5a\u6bd4\u597d\u6837\u672c\u7684\u5956\u52b1\u5927&#xff0c;\u66f4\u7b26\u5408\u4eba\u7c7b\u5fc3\u7406\u3002\u6570\u636e\u91cf\u5927\u65f6 KTO \u6548\u679c\u63a5\u8fd1 DPO\u3002<\/p>\n<p>Q: RLAIF \u7684\u524d\u666f&#xff1f;<\/p>\n<p>RLAIF \u7684\u4f18\u52bf\u662f\u53ef\u6269\u5c55\u6027\u2014\u2014\u7528 AI \u66ff\u4ee3\u4eba\u7c7b\u53cd\u9988&#xff0c;\u6210\u672c\u5927\u5e45\u964d\u4f4e\u3002\u4f46\u5f53\u524d\u5c40\u9650\u662f&#xff1a;AI \u8bc4\u4f30\u5668\u672c\u8eab\u6709\u504f\u89c1&#xff08;\u4f4d\u7f6e\u504f\u89c1\u3001\u957f\u5ea6\u504f\u89c1&#xff09;&#xff0c;\u53ef\u80fd\u5bfc\u81f4\u504f\u89c1\u4f20\u64ad\u548c\u81ea\u6211\u5f3a\u5316\u3002\u672a\u6765\u65b9\u5411&#xff1a;\u66f4\u597d\u7684 AI \u8bc4\u4f30\u5668\u3001\u81ea\u4e00\u81f4\u6027\u68c0\u9a8c\u3001\u4eba\u673a\u6df7\u5408\u53cd\u9988\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>DPO \u4e0e RLHF \u66ff\u4ee3\u65b9\u6848&#xff1a;\u539f\u7406\u4e0e\u5b9e\u73b0<br \/>\n\u672c\u7ae0\u5bfc\u8bfb<br \/>\nRLHF \u867d\u7136\u6548\u679c\u663e\u8457&#xff0c;\u4f46\u5de5\u7a0b\u590d\u6742\u5ea6\u9ad8\u2014\u2014\u56db\u6a21\u578b\u67b6\u6784\u3001\u8bad\u7ec3\u4e0d\u7a33\u5b9a\u3001\u5956\u52b1\u9ed1\u5ba2\u7b49\u95ee\u9898\u8ba9\u8bb8\u591a\u56e2\u961f\u671b\u800c\u5374\u6b65\u30022023 \u5e74\u4ee5\u6765&#xff0c;\u4e00\u7cfb\u5217\u66ff\u4ee3\u65b9\u6848\u5e94\u8fd0\u800c\u751f&#xff0c;\u5176\u4e2d DPO&#xff08;Direct Preference Optimization&#xff09; \u6700\u53d7\u5173\u6ce8\u3002\u672c\u7ae0\u5c06\u6df1\u5165 DPO \u7684\u63a8\u5bfc\u8fc7\u7a0b&#xff0c;\u5bf9\u6bd4 IPO\u3001KTO\u3001ORPO \u7b49\u53d8\u4f53&#xff0c;\u63a2\u8ba8 RLA<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[207],"topic":[],"class_list":["post-91031","post","type-post","status-publish","format-standard","hentry","category-server","tag-207"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>DPO \u4e0e RLHF \u66ff\u4ee3\u65b9\u6848\uff1a\u539f\u7406\u4e0e\u5b9e\u73b0 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/91031.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"DPO \u4e0e RLHF \u66ff\u4ee3\u65b9\u6848\uff1a\u539f\u7406\u4e0e\u5b9e\u73b0 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"DPO \u4e0e RLHF \u66ff\u4ee3\u65b9\u6848&#xff1a;\u539f\u7406\u4e0e\u5b9e\u73b0 \u672c\u7ae0\u5bfc\u8bfb RLHF \u867d\u7136\u6548\u679c\u663e\u8457&#xff0c;\u4f46\u5de5\u7a0b\u590d\u6742\u5ea6\u9ad8\u2014\u2014\u56db\u6a21\u578b\u67b6\u6784\u3001\u8bad\u7ec3\u4e0d\u7a33\u5b9a\u3001\u5956\u52b1\u9ed1\u5ba2\u7b49\u95ee\u9898\u8ba9\u8bb8\u591a\u56e2\u961f\u671b\u800c\u5374\u6b65\u30022023 \u5e74\u4ee5\u6765&#xff0c;\u4e00\u7cfb\u5217\u66ff\u4ee3\u65b9\u6848\u5e94\u8fd0\u800c\u751f&#xff0c;\u5176\u4e2d DPO&#xff08;Direct Preference Optimization&#xff09; \u6700\u53d7\u5173\u6ce8\u3002\u672c\u7ae0\u5c06\u6df1\u5165 DPO \u7684\u63a8\u5bfc\u8fc7\u7a0b&#xff0c;\u5bf9\u6bd4 IPO\u3001KTO\u3001ORPO \u7b49\u53d8\u4f53&#xff0c;\u63a2\u8ba8 RLA\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/91031.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-08-06T09:24:36+00:00\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"8 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/91031.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/91031.html\",\"name\":\"DPO \u4e0e RLHF \u66ff\u4ee3\u65b9\u6848\uff1a\u539f\u7406\u4e0e\u5b9e\u73b0 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"isPartOf\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\"},\"datePublished\":\"2026-08-06T09:24:36+00:00\",\"dateModified\":\"2026-08-06T09:24:36+00:00\",\"author\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\"},\"breadcrumb\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/91031.html#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.wsisp.com\/helps\/91031.html\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/91031.html#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9875\",\"item\":\"https:\/\/www.wsisp.com\/helps\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"DPO \u4e0e RLHF \u66ff\u4ee3\u65b9\u6848\uff1a\u539f\u7406\u4e0e\u5b9e\u73b0\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\",\"url\":\"https:\/\/www.wsisp.com\/helps\/\",\"name\":\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"description\":\"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"contentUrl\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"caption\":\"admin\"},\"sameAs\":[\"http:\/\/wp.wsisp.com\"],\"url\":\"https:\/\/www.wsisp.com\/helps\/author\/admin\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"DPO \u4e0e RLHF \u66ff\u4ee3\u65b9\u6848\uff1a\u539f\u7406\u4e0e\u5b9e\u73b0 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.wsisp.com\/helps\/91031.html","og_locale":"zh_CN","og_type":"article","og_title":"DPO \u4e0e RLHF \u66ff\u4ee3\u65b9\u6848\uff1a\u539f\u7406\u4e0e\u5b9e\u73b0 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","og_description":"DPO \u4e0e RLHF \u66ff\u4ee3\u65b9\u6848&#xff1a;\u539f\u7406\u4e0e\u5b9e\u73b0 \u672c\u7ae0\u5bfc\u8bfb RLHF \u867d\u7136\u6548\u679c\u663e\u8457&#xff0c;\u4f46\u5de5\u7a0b\u590d\u6742\u5ea6\u9ad8\u2014\u2014\u56db\u6a21\u578b\u67b6\u6784\u3001\u8bad\u7ec3\u4e0d\u7a33\u5b9a\u3001\u5956\u52b1\u9ed1\u5ba2\u7b49\u95ee\u9898\u8ba9\u8bb8\u591a\u56e2\u961f\u671b\u800c\u5374\u6b65\u30022023 \u5e74\u4ee5\u6765&#xff0c;\u4e00\u7cfb\u5217\u66ff\u4ee3\u65b9\u6848\u5e94\u8fd0\u800c\u751f&#xff0c;\u5176\u4e2d DPO&#xff08;Direct Preference Optimization&#xff09; \u6700\u53d7\u5173\u6ce8\u3002\u672c\u7ae0\u5c06\u6df1\u5165 DPO \u7684\u63a8\u5bfc\u8fc7\u7a0b&#xff0c;\u5bf9\u6bd4 IPO\u3001KTO\u3001ORPO \u7b49\u53d8\u4f53&#xff0c;\u63a2\u8ba8 RLA","og_url":"https:\/\/www.wsisp.com\/helps\/91031.html","og_site_name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","article_published_time":"2026-08-06T09:24:36+00:00","author":"admin","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"admin","\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4":"8 \u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.wsisp.com\/helps\/91031.html","url":"https:\/\/www.wsisp.com\/helps\/91031.html","name":"DPO \u4e0e RLHF \u66ff\u4ee3\u65b9\u6848\uff1a\u539f\u7406\u4e0e\u5b9e\u73b0 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","isPartOf":{"@id":"https:\/\/www.wsisp.com\/helps\/#website"},"datePublished":"2026-08-06T09:24:36+00:00","dateModified":"2026-08-06T09:24:36+00:00","author":{"@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41"},"breadcrumb":{"@id":"https:\/\/www.wsisp.com\/helps\/91031.html#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.wsisp.com\/helps\/91031.html"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.wsisp.com\/helps\/91031.html#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9875","item":"https:\/\/www.wsisp.com\/helps"},{"@type":"ListItem","position":2,"name":"DPO \u4e0e RLHF \u66ff\u4ee3\u65b9\u6848\uff1a\u539f\u7406\u4e0e\u5b9e\u73b0"}]},{"@type":"WebSite","@id":"https:\/\/www.wsisp.com\/helps\/#website","url":"https:\/\/www.wsisp.com\/helps\/","name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","description":"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41","name":"admin","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/","url":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","contentUrl":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","caption":"admin"},"sameAs":["http:\/\/wp.wsisp.com"],"url":"https:\/\/www.wsisp.com\/helps\/author\/admin"}]}},"_links":{"self":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/91031","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/comments?post=91031"}],"version-history":[{"count":0,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/91031\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media?parent=91031"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/categories?post=91031"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/tags?post=91031"},{"taxonomy":"topic","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/topic?post=91031"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}