{"id":22862,"date":"2024-11-01T10:07:03","date_gmt":"2024-11-01T02:07:03","guid":{"rendered":"https:\/\/aif.amtbbs.org\/?p=22862"},"modified":"2024-11-01T10:07:03","modified_gmt":"2024-11-01T02:07:03","slug":"%e5%bc%ba%e5%8c%96%e5%ad%a6%e4%b9%a0%e4%b9%8b%e7%88%b6richard-sutton%e7%bb%99%e5%87%ba%e4%b8%80%e4%b8%aa%e7%ae%80%e5%8d%95%e6%80%9d%e8%b7%af%ef%bc%8c%e5%a4%a7%e5%b9%85%e5%a2%9e%e5%bc%ba%e6%89%80","status":"publish","type":"post","link":"https:\/\/aif.amtbbs.org\/index.php\/2024\/11\/01\/22862\/","title":{"rendered":"\u5f3a\u5316\u5b66\u4e60\u4e4b\u7236Richard Sutton\u7ed9\u51fa\u4e00\u4e2a\u7b80\u5355\u601d\u8def\uff0c\u5927\u5e45\u589e\u5f3a\u6240\u6709RL\u7b97\u6cd5"},"content":{"rendered":"<div class=\"article-desc\">\u8fd1\u65e5\uff0c\u5f3a\u5316\u5b66\u4e60\u4e4b\u7236\u3001\u963f\u5c14\u4f2f\u5854\u5927\u5b66\u6559\u6388 Richard Sutton \u7684\u56e2\u961f\u4f4e\u8c03\u66f4\u65b0\u4e86\u4e00\u7bc7\u8bba\u6587\uff0c\u5176\u4e2d\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u901a\u7528\u601d\u60f3 Reward Centering\uff0c\u5e76\u79f0\u8be5\u601d\u60f3\u9002\u7528\u4e8e\u51e0\u4e4e\u6240\u6709\u5f3a\u5316\u5b66\u4e60\u7b97\u6cd5\u3002\u8fd9\u91cc\u6211\u4eec\u5c06\u5176\u8bd1\u4e3a\u300c\u5956\u52b1\u805a\u4e2d\u300d\u3002<\/div>\n<div id=\"postspictures\" class=\"article-content\">\n<div id=\"container\" class=\"container am-engine\" data-v-1d7a5742=\"\" data-element=\"root\">\n<p>\u5728\u5f53\u4eca\u7684\u5927\u6a21\u578b\u65f6\u4ee3\uff0c\u4ee5 RLHF \u4e3a\u4ee3\u8868\u7684\u5f3a\u5316\u5b66\u4e60\u65b9\u6cd5\u5177\u6709\u65e0\u53ef\u66ff\u4ee3\u7684\u91cd\u8981\u6027\uff0c\u751a\u81f3\u6210\u4e3a\u4e86 OpenAI \u03bf1 \u7b49\u6a21\u578b\u5b9e\u73b0\u5f3a\u5927\u63a8\u7406\u80fd\u529b\u7684\u5173\u952e\u3002<\/p>\n<p>\u4f46\u8fd9\u4e9b\u5f3a\u5316\u5b66\u4e60\u65b9\u6cd5\u4ecd\u6709\u6539\u8fdb\u7a7a\u95f4\u3002\u8fd1\u65e5\uff0c\u5f3a\u5316\u5b66\u4e60\u4e4b\u7236\u3001\u963f\u5c14\u4f2f\u5854\u5927\u5b66\u6559\u6388 Richard Sutton \u7684\u56e2\u961f\u4f4e\u8c03\u66f4\u65b0\u4e86\u4e00\u7bc7\u8bba\u6587\uff0c\u5176\u4e2d\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u901a\u7528\u601d\u60f3 Reward Centering\uff0c\u5e76\u79f0\u8be5\u601d\u60f3\u9002\u7528\u4e8e\u51e0\u4e4e\u6240\u6709\u5f3a\u5316\u5b66\u4e60\u7b97\u6cd5\u3002\u8fd9\u91cc\u6211\u4eec\u5c06\u5176\u8bd1\u4e3a\u300c\u5956\u52b1\u805a\u4e2d\u300d\u3002<\/p>\n<p>\u8be5\u8bba\u6587\u662f\u9996\u5c4a\u5f3a\u5316\u5b66\u4e60\u4f1a\u8bae\uff08RLC 2024\uff09\u7684\u5165\u9009\u8bba\u6587\u4e4b\u4e00\u3002\u4e00\u4f5c Abhishek Naik \u521a\u521a\u4ece\u963f\u5c14\u4f2f\u5854\u5927\u5b66\u83b7\u5f97\u535a\u58eb\u5b66\u4f4d\uff0c\u4ed6\u662f Sutton \u6559\u6388\u7684\u7b2c 12 \u4f4d\u535a\u58eb\u6bd5\u4e1a\u751f\u3002<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s2.51cto.com\/oss\/202411\/01\/b259bd469267efb8ba0445b1f842147b22f956.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u4e0b\u9762\u6211\u4eec\u7b80\u8981\u770b\u770b Reward Centering \u6709\u4f55\u521b\u65b0\u4e4b\u5904\u3002<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s9.51cto.com\/oss\/202411\/01\/b496a2410e1d5760b0b6414fcc33d6ea95e2d4.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<ul data-id=\"ua73dd4b-3cfGUW4i\">\n<li data-id=\"ld70c578-dfCgFlB9\">\u8bba\u6587\u6807\u9898\uff1aReward Centering<\/li>\n<li data-id=\"ld70c578-MjMV1L5U\">\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/arxiv.org\/pdf\/2405.09999<\/li>\n<\/ul>\n<h4>\u5956\u52b1\u805a\u4e2d\u7406\u8bba<\/h4>\n<p>\u667a\u80fd\u4f53\u548c\u73af\u5883\u4e4b\u95f4\u7684\u4ea4\u4e92\u53ef\u4ee5\u8868\u8ff0\u4e3a\u4e00\u4e2a\u6709\u9650\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\uff08MDP\uff09(S, A, R, p)\uff0c\u5176\u4e2d S \u8868\u793a\u72b6\u6001\u96c6\uff0cA \u8868\u793a\u52a8\u4f5c\u96c6\uff0cR \u8868\u793a\u5956\u52b1\u96c6\uff0cp : S \u00d7 R \u00d7 S \u00d7 A \u2192 [0, 1] \u8868\u793a\u8f6c\u6362\u7684\u52a8\u6001\u3002\u5728\u65f6\u95f4\u6b65\u9aa4 t\uff0c\u667a\u80fd\u4f53\u5904\u4e8e\u72b6\u6001 S_t\uff0c\u4f7f\u7528\u884c\u4e3a\u7b56\u7565 b : A \u00d7 S \u2192 [0, 1] \u91c7\u53d6\u884c\u52a8 A_t\uff0c\u7136\u540e\u6839\u636e\u8f6c\u6362\u52a8\u6001:<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s4.51cto.com\/oss\/202411\/01\/6504906066e366375ae0110610216e58bb58c6.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u89c2\u5bdf\u4e0b\u4e00\u4e2a\u72b6\u6001 S_{t+1} \u548c\u5956\u52b1 R_{t+1}\u3002<\/p>\n<p>\u8fd9\u91cc\u7814\u7a76\u7684\u95ee\u9898\u662f\u6301\u7eed\u6027\u95ee\u9898\uff0c\u5373\u667a\u80fd\u4f53\u548c\u73af\u5883\u7684\u4ea4\u4e92\u4f1a\u65e0\u9650\u5730\u8fdb\u884c\u3002\u667a\u80fd\u4f53\u7684\u76ee\u6807\u662f\u6700\u5927\u5316\u957f\u671f\u83b7\u5f97\u7684\u5e73\u5747\u5956\u52b1\u3002\u4e3a\u6b64\uff0c\u8be5\u56e2\u961f\u8003\u8651\u4e86\u4f30\u8ba1\u6bcf\u4e2a\u72b6\u6001\u7684\u9884\u671f\u6298\u6263\u5956\u52b1\u603b\u548c\u7684\u65b9\u6cd5\uff1a<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s3.51cto.com\/oss\/202411\/01\/66bb26b4015c42c2462890a33d46b61bc810ba.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u8fd9\u91cc\uff0c\u6298\u6263\u56e0\u5b50\u4e0d\u662f\u95ee\u9898\u7684\u4e00\u90e8\u5206\uff0c\u800c\u662f\u4e00\u4e2a\u7b97\u6cd5\u53c2\u6570\u3002<\/p>\n<p>\u5956\u52b1\u805a\u4e2d\u601d\u60f3\u5f88\u7b80\u5355\uff1a\u4ece\u5956\u52b1\u4e2d\u51cf\u53bb\u5b9e\u9645\u89c2\u5bdf\u5230\u7684\u5956\u52b1\u7684\u5e73\u5747\u503c\u3002\u8fd9\u6837\u505a\u4f1a\u8ba9\u4fee\u6539\u540e\u7684\u5956\u52b1\u770b\u8d77\u6765\u4ee5\u5747\u503c\u4e3a\u4e2d\u5fc3\u3002<\/p>\n<p>\u8fd9\u79cd\u4ee5\u5747\u503c\u4e3a\u4e2d\u5fc3\u7684\u5956\u52b1\u5728 bandit \u8bbe\u7f6e\u4e2d\u5f88\u5e38\u89c1\u3002\u4e3e\u4e2a\u4f8b\u5b50\uff0cSutton \u548c Barto \u5728 2018 \u5e74\u7684\u4e00\u7bc7\u8bba\u6587\u4e2d\u8868\u660e\uff0c\u6839\u636e\u89c2\u5bdf\u5230\u7684\u5956\u52b1\u4f30\u8ba1\u548c\u51cf\u53bb\u5e73\u5747\u5956\u52b1\u53ef\u4ee5\u663e\u7740\u63d0\u9ad8\u5b66\u4e60\u901f\u5ea6\u3002<\/p>\n<p>\u800c\u8fd9\u91cc\uff0c\u8be5\u56e2\u961f\u8bc1\u660e\u6240\u6709\u5f3a\u5316\u5b66\u4e60\u7b97\u6cd5\u90fd\u80fd\u4eab\u53d7\u5230\u8fd9\u79cd\u597d\u5904\uff0c\u5e76\u4e14\u5f53\u6298\u73b0\u56e0\u5b50 \u03b3 \u63a5\u8fd1 1 \u65f6\uff0c\u597d\u5904\u4f1a\u66f4\u5927\u3002<\/p>\n<p>\u5956\u52b1\u805a\u4e2d\u4e4b\u6240\u4ee5\u8fd9\u4e48\u597d\uff0c\u4e00\u4e2a\u5e95\u5c42\u539f\u56e0\u53ef\u901a\u8fc7\u6298\u73b0\u4ef7\u503c\u51fd\u6570\u7684\u7f57\u6717\u7ea7\u6570\uff08Laurent Series\uff09\u5206\u89e3\u6765\u63ed\u793a\u3002<\/p>\n<p>\u6298\u73b0\u4ef7\u503c\u51fd\u6570\u53ef\u88ab\u5206\u89e3\u6210\u4e24\u90e8\u5206\u3002\u5176\u4e2d\u4e00\u90e8\u5206\u662f\u4e00\u4e2a\u5e38\u6570\uff0c\u5e76\u4e0d\u4f9d\u8d56\u72b6\u6001\u6216\u52a8\u4f5c\uff0c\u56e0\u6b64\u5e76\u4e0d\u53c2\u4e0e\u52a8\u4f5c\u9009\u53d6\u3002<\/p>\n<p>\u7528\u6570\u5b66\u8868\u793a\u7684\u8bdd\uff0c\u5bf9\u4e8e\u4e0e\u6298\u73b0\u56e0\u5b50 \u03b3 \u5bf9\u5e94\u7684\u7b56\u7565 \u03c0 \u7684\u8868\u683c\u6298\u73b0\u4ef7\u503c\u51fd\u6570<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s3.51cto.com\/oss\/202411\/01\/64c579723eadde2ad2e8029f4c74de7b0a28aa.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\uff1a<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s7.51cto.com\/oss\/202411\/01\/880958a102bac279032381103a3c5cc42585b4.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u5176\u4e2d r(\u03c0) \u662f\u7b56\u7565 \u03c0 \u83b7\u5f97\u7684\u72ec\u7acb\u4e8e\u72b6\u6001\u7684\u5e73\u5747\u5956\u52b1\uff0c<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s7.51cto.com\/oss\/202411\/01\/a7e2d1a629070fc3ec70177102f381b482679d.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u662f\u72b6\u6001 s \u7684\u5fae\u5206\u503c\u3002\u5b83\u4eec\u5404\u81ea\u5bf9\u4e8e\u904d\u5386 MDP \u7684\u5b9a\u4e49\u4e3a\uff1a<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s5.51cto.com\/oss\/202411\/01\/45a9e6c445eb46745774553ce5154487e129e7.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s2.51cto.com\/oss\/202411\/01\/3691c7d03ddd8101c660298252f97a73b193fe.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u5219\u662f\u4e00\u4e2a\u8bef\u5dee\u9879\uff0c\u5f53\u6298\u73b0\u56e0\u5b50\u53d8\u4e3a 1 \u65f6\u53d8\u4e3a\u96f6\u3002\u72b6\u6001\u503c\u7684\u8fd9\u79cd\u5206\u89e3\u4e5f\u610f\u5473\u7740\u72b6\u6001-\u52a8\u4f5c\u503c\u6709\u7c7b\u4f3c\u7684\u5206\u89e3\u3002<\/p>\n<p>\u8fd9\u79cd Laurent \u7ea7\u6570\u5206\u89e3\u80fd\u89e3\u91ca\u5956\u52b1\u805a\u4e2d\u4e3a\u4f55\u6709\u52a9\u4e8e\u89e3\u51b3 bandit \u95ee\u9898\u3002<\/p>\n<p>\u5728\u5b8c\u6574\u7684\u5f3a\u5316\u5b66\u4e60\u95ee\u9898\u4e2d\uff0c\u4e0e\u72b6\u6001\u65e0\u5173\u7684\u504f\u79fb\u53ef\u80fd\u4f1a\u76f8\u5f53\u5927\u3002\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u56fe 2 \u4e2d\u5c55\u793a\u7684\u4e09\u72b6\u6001\u9a6c\u5c14\u79d1\u592b\u5956\u52b1\u8fc7\u7a0b\u3002\u5982\u679c\u72b6\u6001\u4ece A \u53d8\u6210 B\uff0c\u5219\u5956\u52b1\u662f +3\uff0c\u5426\u5219\u90fd\u662f 0\u3002\u5e73\u5747\u5956\u52b1\u4e3a r(\u03c0) = 1\u3002\u53f3\u4fa7\u8868\u4e2d\u7ed9\u51fa\u4e86\u4e09\u4e2a\u6298\u73b0\u56e0\u5b50\u7684\u6298\u73b0\u72b6\u6001\u503c\u3002<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s3.51cto.com\/oss\/202411\/01\/898d1ac9129fbc1e7a96748e56f11ed807ed23.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u73b0\u5728\uff0c\u4ece\u6bcf\u4e2a\u72b6\u6001\u4e2d\u51cf\u53bb\u5e38\u6570\u504f\u79fb\u7684\u6298\u73b0\u503c<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s7.51cto.com\/oss\/202411\/01\/68295f71159dc8e9a5a155b65a3f621f79481e.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\uff0c\u4e5f\u88ab\u79f0\u4e3a\u805a\u4e2d\u6298\u73b0\u503c\u3002<\/p>\n<p>\u53ef\u4ee5\u770b\u5230\uff0c\u8fd9\u4e2a\u5df2\u7ecf\u805a\u4e2d\u7684\u503c\u5728\u5e45\u5ea6\u4e0a\u8981\u5c0f\u5f97\u591a\uff0c\u5e76\u4e14\u5f53\u6298\u73b0\u56e0\u5b50\u589e\u5927\u65f6\uff0c\u4e5f\u53ea\u4f1a\u53d1\u751f\u8f7b\u5fae\u53d8\u5316\u3002\u8fd9\u91cc\u8fd8\u7ed9\u51fa\u4e86\u5fae\u5206\u503c\u4ee5\u4f9b\u53c2\u8003\u3002<\/p>\n<p>\u8fd9\u4e9b\u8d8b\u52bf\u666e\u904d\u6210\u7acb\uff1a\u5bf9\u4e8e\u4efb\u610f\u95ee\u9898\uff0c\u6298\u73b0\u503c\u7684\u5e45\u5ea6\u90fd\u4f1a\u968f\u7740\u6298\u73b0\u56e0\u5b50\u63a5\u8fd1 1 \u800c\u6025\u5267\u589e\u52a0\uff0c\u800c\u805a\u4e2d\u6298\u73b0\u503c\u5219\u53d8\u5316\u4e0d\u5927\uff0c\u5e76\u63a5\u8fd1\u5fae\u5206\u503c\u3002<\/p>\n<p>\u4ece\u6570\u5b66\u4e0a\u770b\uff0c\u805a\u4e2d\u6298\u73b0\u503c\u662f\u5e73\u5747\u805a\u4e2d\u5956\u52b1\u7684\u9884\u671f\u6298\u73b0\u548c\uff1a<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s2.51cto.com\/oss\/202411\/01\/84c167264085ea0168a9212479fad55b7bae6e.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u5176\u4e2d \u03b3 \u2208 [0, 1]\u3002\u5f53 \u03b3 = 1 \u65f6\uff0c\u805a\u4e2d\u6298\u73b0\u503c\u4e0e\u5fae\u5206\u503c\u76f8\u540c\u3002\u66f4\u4e00\u822c\u5730\u8bf4\uff0c\u805a\u4e2d\u6298\u73b0\u503c\u662f\u5fae\u5206\u503c\u52a0\u4e0a\u6765\u81ea\u7f57\u6717\u7ea7\u6570\u5206\u89e3\u7684\u8bef\u5dee\u9879\uff0c\u5982\u4e0a\u56fe\u53f3\u4fa7\u6240\u793a\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u5956\u52b1\u805a\u4e2d\u80fd\u591f\u901a\u8fc7\u4e24\u4e2a\u7ec4\u4ef6\uff08\u6052\u5b9a\u5e73\u5747\u5956\u52b1\u548c\u805a\u4e2d\u6298\u73b0\u503c\u51fd\u6570\uff09\u6355\u83b7\u6298\u73b0\u503c\u51fd\u6570\u4e2d\u7684\u6240\u6709\u4fe1\u606f\u3002\u8fd9\u79cd\u5206\u89e3\u975e\u5e38\u6709\u4ef7\u503c\uff1a<\/p>\n<ul data-id=\"ua73dd4b-nO12b2GA\">\n<li data-id=\"ld70c578-m5dfQD7g\">\u5f53\u03b3\u21921\u65f6\uff0c\u6298\u73b0\u503c\u8d8b\u4e8e\u7206\u70b8\uff0c\u4f46\u805a\u4e2d\u6298\u73b0\u503c\u4ecd\u7136\u5f88\u5c0f\u4e14\u6613\u4e8e\u5904\u7406\u3002<\/li>\n<li data-id=\"ld70c578-TOZHA3gP\">\u5982\u679c\u95ee\u9898\u7684\u5956\u52b1\u504f\u79fb\u4e86\u4e00\u4e2a\u5e38\u6570 c\uff0c\u90a3\u4e48\u6298\u73b0\u503c\u7684\u5e45\u5ea6\u5c31\u4f1a\u589e\u52a0 c\/(1 \u2212 \u03b3)\uff0c\u4f46\u805a\u4e2d\u6298\u73b0\u503c\u4f1a\u4fdd\u6301\u4e0d\u53d8\uff0c\u56e0\u4e3a\u5e73\u5747\u5956\u52b1\u4e5f\u4f1a\u589e\u52a0 c\u3002<\/li>\n<\/ul>\n<p>\u4f7f\u7528\u5956\u52b1\u805a\u4e2d\u65f6\uff0c\u8fd8\u53ef\u4ee5\u8bbe\u8ba1\u51fa\u5728\u667a\u80fd\u4f53\u7684\u751f\u547d\u5468\u671f\u5185\u53ef\u4ee5\u6539\u53d8\u6298\u73b0\u56e0\u5b50\uff08\u7b97\u6cd5\u53c2\u6570\uff09\u7684\u7b97\u6cd5\u3002\u5bf9\u4e8e\u6807\u51c6\u6298\u73b0\u7b97\u6cd5\u6765\u8bf4\uff0c\u8fd9\u901a\u5e38\u662f\u4f4e\u6548\u6216\u65e0\u6548\u7684\uff0c\u56e0\u4e3a\u5b83\u4eec\u7684\u975e\u805a\u4e2d\u503c\u53ef\u80fd\u4f1a\u53d1\u751f\u5de8\u5927\u53d8\u5316\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u805a\u4e2d\u503c\u53ef\u80fd\u53d8\u5316\u4e0d\u5927\uff0c\u5f53\u6298\u73b0\u56e0\u5b50\u63a5\u8fd1 1 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src=\"https:\/\/s5.51cto.com\/oss\/202411\/01\/e786c0875642d251a7b090406ae6b1138059b0.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/>\u3002\u66f4\u4e00\u822c\u5730\uff0c\u53ef\u4ee5\u4f7f\u7528\u6b65\u957f\u53c2\u6570 \u03b2t \u6765\u66f4\u65b0\u8be5\u4f30\u8ba1\uff1a<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s2.51cto.com\/oss\/202411\/01\/09fdb5934be26506e34680ca9a20f7a1323766.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u8be5\u56e2\u961f\u8868\u793a\uff0c\u8fd9\u79cd\u7b80\u5355\u7684\u805a\u4e2d\u65b9\u6cd5\u9002\u7528\u4e8e\u51e0\u4e4e\u4efb\u4f55\u5f3a\u5316\u5b66\u4e60\u7b97\u6cd5\u3002\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u5956\u52b1\u805a\u4e2d\u53ef\u4ee5\u4e0e\u4f20\u7edf\u7684\u65f6\u95f4\u5dee\u5206\uff08TD\uff09\u5b66\u4e60\u7ec4\u5408\u8d77\u6765\u5b66\u4e60\u4e00\u4e2a\u72b6\u6001-\u4ef7\u503c\u51fd\u6570\u4f30\u8ba1\uff1a<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s6.51cto.com\/oss\/202411\/01\/32407e1658c7b2f2153849e87b33593b5d5db7.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u6b64\u5916\uff0c\u4ed6\u4eec\u8fd8\u63d0\u51fa\u4e86\u57fa\u4e8e\u4ef7\u503c\u7684\u5956\u52b1\u805a\u4e2d\u3002\u8fd9\u79cd\u65b9\u6cd5\u7684\u7075\u611f\u6765\u81ea\u5f3a\u5316\u5b66\u4e60\u7684\u5e73\u5747\u5956\u52b1\u516c\u5f0f\u3002Wan et al. (2021) \u8868\u660e\uff0c\u4f7f\u7528\u65f6\u95f4\u5dee\u5206\uff08TD\uff09\u8bef\u5dee\uff08\u800c\u4e0d\u662f (4) \u4e2d\u7684\u4f20\u7edf\u8bef\u5dee\uff09\u53ef\u4ee5\u5bf9\u8868\u683c\u79bb\u7b56\u7565\u8bbe\u7f6e\u4e2d\u7684\u5956\u52b1\u7387\u8fdb\u884c\u65e0\u504f\u4f30\u8ba1\u3002\u4e8b\u5b9e\u8bc1\u660e\uff0c\u5e73\u5747\u5956\u52b1\u516c\u5f0f\u4e2d\u7684\u8fd9\u4e2a\u601d\u8def\u5728\u6298\u6263\u5956\u52b1\u516c\u5f0f\u4e2d\u4e5f\u975e\u5e38\u6709\u6548\u3002<\/p>\n<p>\u8be5\u56e2\u961f\u8868\u660e\uff0c\u5982\u679c\u884c\u4e3a\u7b56\u7565\u91c7\u53d6\u76ee\u6807\u7b56\u7565\u6240\u505a\u7684\u6240\u6709\u64cd\u4f5c\uff0c\u90a3\u4e48\u53ef\u4ee5\u4f7f\u7528 TD \u8bef\u5dee\u5f88\u597d\u5730\u8fd1\u4f3c\u76ee\u6807\u7b56\u7565\u7684\u5e73\u5747\u5956\u52b1\uff1a<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s7.51cto.com\/oss\/202411\/01\/45bdfc7836c118a565563271043a50398e4fb6.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u7531\u4e8e\u8fd9\u79cd\u805a\u4e2d\u65b9\u6cd5\u9664\u4e86\u5956\u52b1\u4e4b\u5916\u8fd8\u6d89\u53ca\u4ef7\u503c\uff0c\u56e0\u6b64\u4ed6\u4eec\u5c06\u5176\u79f0\u4e3a\u57fa\u4e8e\u4ef7\u503c\u7684\u805a\u4e2d\u3002\u4e0d\u540c\u4e8e\u7b80\u5355\u7684\u5956\u52b1\u805a\u4e2d\uff0c\u73b0\u5728\u5e73\u5747\u5956\u52b1\u4f30\u8ba1\u548c\u4ef7\u503c\u4f30\u8ba1\u7684\u6536\u655b\u662f\u76f8\u4e92\u4f9d\u8d56\u7684\u3002<\/p>\n<h4>\u5b9e\u9a8c<\/h4>\n<p>\u8be5\u56e2\u961f\u5b9e\u9a8c\u4e86 (5) \u5f0f\u7684\u56db\u79cd\u7b97\u6cd5\u53d8\u4f53\u7248\u672c\uff0c\u5e76\u6d4b\u8bd5\u4e86\u4e0d\u540c\u7684\u6298\u73b0\u56e0\u5b50\u3002\u8be6\u7ec6\u8fc7\u7a0b\u8bf7\u9605\u8bfb\u539f\u8bba\u6587\uff0c\u8fd9\u91cc\u6211\u4eec\u7b80\u5355\u770b\u770b\u7ed3\u679c\u3002<img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s9.51cto.com\/oss\/202411\/01\/92adbcc804f97dee7ae642290847d891557f16.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u5982\u56fe 3 \u6240\u793a\uff0c\u5f53\u5956\u52b1\u7531\u4e00\u4e2a oracle \u8fdb\u884c\u805a\u4e2d\u5904\u7406\u65f6\uff0c\u5b66\u4e60\u66f2\u7ebf\u7684\u8d77\u70b9\u4f1a\u4f4e\u5f97\u591a\u3002\u5bf9\u4e8e\u5176\u5b83\u7b97\u6cd5\uff0c\u7b2c\u4e00\u4e2a\u8bef\u5dee\u90fd\u5728 r(\u03c0)\/(1 \u2212 \u03b3) \u91cf\u7ea7\u3002<\/p>\n<p>\u65e0\u805a\u4e2d\u7684 TD \u5b66\u4e60\uff08\u84dd\u8272\uff09\u6700\u7ec8\u8fbe\u5230\u4e86\u4e0e oracle \u805a\u4e2d\u7b97\u6cd5\uff08\u6a59\u8272\uff09\u76f8\u540c\u7684\u8bef\u5dee\u7387\uff0c\u8fd9\u7b26\u5408\u9884\u671f\u3002<\/p>\n<p>\u7b80\u5355\u805a\u4e2d\u65b9\u6cd5\uff08\u7eff\u8272\uff09\u786e\u5b9e\u6709\u52a9\u4e8e\u66f4\u5feb\u5730\u964d\u4f4e RMSVE\uff0c\u4f46\u5176\u6700\u7ec8\u8bef\u5dee\u7387\u4f1a\u7a0d\u5fae\u9ad8\u4e00\u70b9\u3002\u8fd9\u4e5f\u7b26\u5408\u9884\u671f\uff0c\u56e0\u4e3a\u5e73\u5747\u5956\u52b1\u4f30\u8ba1\u4f1a\u968f\u65f6\u95f4\u800c\u53d8\u5316\uff0c\u5bfc\u81f4\u4e0e\u975e\u805a\u4e2d\u6216 oracle \u805a\u4e2d\u7248\u672c\u76f8\u6bd4\uff0c\u66f4\u65b0\u7684\u53d8\u6570\u66f4\u5927\u3002\u5f53 \u03b3 \u66f4\u5927\u65f6\u4e5f\u6709\u7c7b\u4f3c\u7684\u8d8b\u52bf\u3002\u8fd9\u4e9b\u5b9e\u9a8c\u8868\u660e\uff0c\u7b80\u5355\u7684\u5956\u52b1\u805a\u4e2d\u6280\u672f\u5728\u5728\u7b56\u7565\u8bbe\u7f6e\u4e2d\u975e\u5e38\u6709\u6548\uff0c\u5e76\u4e14\u5bf9\u4e8e\u8f83\u5927\u7684\u6298\u6263\u56e0\u5b50\uff0c\u6548\u679c\u66f4\u4e3a\u660e\u663e\u3002<\/p>\n<p>\u5728\u5b66\u4e60\u7387\u548c\u6e10\u8fd1\u8bef\u5dee\u65b9\u9762\uff0c\u57fa\u4e8e\u4ef7\u503c\u7684\u5956\u52b1\u805a\u4e2d\uff08\u7ea2\u8272\uff09\u5728\u5728\u7b56\u7565\u95ee\u9898\u4e0a\u4e0e\u7b80\u5355\u805a\u4e2d\u5dee\u4e0d\u591a\u3002\u4f46\u5728\u79bb\u7b56\u7565\u95ee\u9898\u4e0a\uff0c\u57fa\u4e8e\u4ef7\u503c\u7684\u805a\u4e2d\u80fd\u4ee5\u66f4\u5feb\u7684\u901f\u5ea6\u5f97\u5230\u66f4\u4f4e\u7684 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