{"id":38215,"date":"2025-02-12T00:01:04","date_gmt":"2025-02-11T16:01:04","guid":{"rendered":"https:\/\/17aitech.com\/?p=38215"},"modified":"2025-02-12T00:01:04","modified_gmt":"2025-02-11T16:01:04","slug":"%e5%a6%82%e4%bd%95%e4%bc%98%e5%8c%96%e6%b5%8b%e8%af%95%e6%97%b6%e8%ae%a1%e7%ae%97%ef%bc%9f%e8%a7%a3%e5%86%b3%e3%80%8c%e5%85%83%e5%bc%ba%e5%8c%96%e5%ad%a6%e4%b9%a0%e3%80%8d%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=38215","title":{"rendered":"\u5982\u4f55\u4f18\u5316\u6d4b\u8bd5\u65f6\u8ba1\u7b97\uff1f\u89e3\u51b3\u300c\u5143\u5f3a\u5316\u5b66\u4e60\u300d\u95ee\u9898"},"content":{"rendered":"<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:<a href=\"https:\/\/www.jiqizhixin.com\/articles\/2025-02-10-6\" target=\"_blank\">\u5982\u4f55\u4f18\u5316\u6d4b\u8bd5\u65f6\u8ba1\u7b97\uff1f\u89e3\u51b3\u300c\u5143\u5f3a\u5316\u5b66\u4e60\u300d\u95ee\u9898<\/a><\/p>\n<section>\u4f18\u5316\u5927\u6a21\u578b\u7684<strong>\u6d4b\u8bd5\u65f6\u8ba1\u7b97<\/strong>\u662f\u63d0\u5347\u6a21\u578b\u90e8\u7f72\u6548\u7387\u548c\u8282\u7701\u8ba1\u7b97\u8d44\u6e90\u7684\u5173\u952e\u4e00\u73af\u3002\u524d\u6bb5\u65f6\u95f4\uff0c\u9ec4\u4ec1\u52cb\u5728 CES 2025 \u7684\u6f14\u8bb2\u4e2d\u628a\u6d4b\u8bd5\u65f6 Scaling \u5f62\u5bb9\u4e3a\u5927\u6a21\u578b\u53d1\u5c55\u7684\u4e09\u6761\u66f2\u7ebf\u4e4b\u4e00\u3002\u5982\u4f55\u4f18\u5316\u6d4b\u8bd5\u65f6\u8ba1\u7b97\u6210\u4e3a\u4e1a\u754c\u5173\u6ce8\u7684\u91cd\u8981\u8bfe\u9898\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-6517f79d9d3ec6f970c9c1f0cd2a21dd.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-6517f79d9d3ec6f970c9c1f0cd2a21dd.png\"><\/a><\/section>\n<section>\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6539\u8fdb\u5927\u578b\u8bed\u8a00\u6a21\u578b (LLM) \u7684\u4e3b\u8981\u7b56\u7565\u662f\u4f7f\u7528\u8d8a\u6765\u8d8a\u591a\u7684\u9ad8\u8d28\u91cf\u6570\u636e\u8fdb\u884c\u76d1\u7763\u5fae\u8c03 (SFT) \u6216\u5f3a\u5316\u5b66\u4e60 (RL)\u3002<\/section>\n<section><\/section>\n<section>\u4e0d\u5e78\u7684\u662f\uff0c\u8fd9\u79cd\u6269\u5c55\u5f62\u5f0f\u4f3c\u4e4e\u5f88\u5feb\u5c31\u4f1a\u9047\u5230\u74f6\u9888\uff0c\u9884\u8bad\u7ec3\u7684\u6269\u5c55\u5b9a\u5f8b\u4f1a\u8d8b\u4e8e\u7a33\u5b9a\uff0c\u6709\u62a5\u544a\u79f0\uff0c\u7528\u4e8e\u8bad\u7ec3\u7684\u9ad8\u8d28\u91cf\u6587\u672c\u6570\u636e\u53ef\u80fd\u5728 2028 \u5e74\u8017\u5c3d\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u66f4\u56f0\u96be\u7684\u4efb\u52a1\uff0c\u4f8b\u5982\u89e3\u51b3\u63a8\u7406\u95ee\u9898\uff0c\u8fd9\u4f3c\u4e4e\u9700\u8981\u5c06\u5f53\u524d\u6570\u636e\u6269\u5c55\u7ea6 100 \u500d\u624d\u80fd\u770b\u5230\u4efb\u4f55\u663e\u8457\u7684\u6539\u8fdb\u3002LLM \u5728\u8fd9\u4e9b\u56f0\u96be\u4efb\u52a1\u4e2d\u7684\u95ee\u9898\u4e0a\u7684\u5f53\u524d\u8868\u73b0\u4ecd\u7136\u4e0d\u5c3d\u5982\u4eba\u610f\u3002\u56e0\u6b64\uff0c\u8feb\u5207\u9700\u8981\u6570\u636e\u9ad8\u6548\u7684\u65b9\u6cd5\u6765\u8bad\u7ec3 LLM\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u53ef\u4ee5\u8d85\u8d8a\u6570\u636e\u6269\u5c55\u5e76\u89e3\u51b3\u66f4\u590d\u6742\u7684\u6311\u6218\u3002<\/section>\n<section><\/section>\n<section>\u5728\u8fd9\u7bc7\u6587\u7ae0\u4e2d\uff0c\u6211\u4eec\u5c06\u8ba8\u8bba\u8fd9\u6837\u4e00\u79cd\u65b9\u6cd5\uff1a<strong>\u901a\u8fc7\u6539\u53d8 LLM \u8bad\u7ec3\u76ee\u6807\uff0c\u6211\u4eec\u53ef\u4ee5\u91cd\u7528\u73b0\u6709\u6570\u636e\u4ee5\u53ca\u66f4\u591a\u7684\u6d4b\u8bd5\u65f6\u8ba1\u7b97\u6765\u8bad\u7ec3\u6a21\u578b\u4ee5\u505a\u5f97\u66f4\u597d\u3002<\/strong><\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-9bb14a3d1ec064a3f3e74909f09eb2f9.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-9bb14a3d1ec064a3f3e74909f09eb2f9.png\"><\/a><\/section>\n<section>\u535a\u5ba2\u5730\u5740\uff1ahttps:\/\/blog.ml.cmu.edu\/2025\/01\/08\/optimizing-llm-test-time-compute-involves-solving-a-meta-rl-problem\/<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-13d151cfa70dfd6cc870fe87deab9d27.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-13d151cfa70dfd6cc870fe87deab9d27.png\"><\/a><\/section>\n<section><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u56fe 1\uff1a\u8bad\u7ec3\u6a21\u578b\u4ee5\u4f18\u5316\u6d4b\u8bd5\u65f6\u8ba1\u7b97\u5e76\u5b66\u4e60\u300c\u5982\u4f55\u53d1\u73b0\u300d\u6b63\u786e\u7b54\u6848\uff0c\u800c\u4e0d\u662f\u5b66\u4e60\u8f93\u51fa\u300c\u4ec0\u4e48\u7b54\u6848\u300d\u7684\u4f20\u7edf\u5b66<\/sup><\/em><sup><em>\u4e60\u8303\u5f0f<\/em>\u3002<\/sup><\/section>\n<section><\/section>\n<section>\u5f53\u524d\u8bad\u7ec3\u6a21\u578b\u7684\u4e3b\u8981\u539f\u5219\u662f\u76d1\u7763\u5b83\u4eec\u4e3a\u8f93\u5165\u4ea7\u751f\u7279\u5b9a\u7684\u8f93\u51fa\u3002\u4f8b\u5982\uff0c\u76d1\u7763\u5fae\u8c03\u5c1d\u8bd5\u5339\u914d\u7ed9\u5b9a\u8f93\u5165\u7684\u76f4\u63a5\u8f93\u51fa token\uff0c\u7c7b\u4f3c\u4e8e\u6a21\u4eff\u5b66\u4e60\uff0c\u800c RL \u5fae\u8c03\u8bad\u7ec3\u54cd\u5e94\u4ee5\u4f18\u5316\u5956\u52b1\u51fd\u6570\uff0c\u8be5\u51fd\u6570\u901a\u5e38\u5e94\u8be5\u5728 oracle \u54cd\u5e94\u4e0a\u53d6\u6700\u9ad8\u503c\u3002\u65e0\u8bba\u54ea\u79cd\u60c5\u51b5\uff0c\u6211\u4eec\u90fd\u5728\u8bad\u7ec3\u6a21\u578b\u4ee5\u4ea7\u751f\u5b83\u53ef\u4ee5\u8868\u793a\u7684 y* \u7684\u6700\u4f73\u8fd1\u4f3c\u503c\u3002<\/section>\n<section><\/section>\n<section>\u4ece\u62bd\u8c61\u4e0a\u8bb2\uff0c\u8fd9\u79cd\u8303\u5f0f\u8bad\u7ec3\u6a21\u578b\u4ee5\u4ea7\u751f\u5355\u4e2a\u8f93\u5165\u8f93\u51fa\u6620\u5c04\uff0c\u5f53\u76ee\u6807\u662f\u76f4\u63a5\u89e3\u51b3\u7ed9\u5b9a\u5206\u5e03\u4e2d\u7684\u4e00\u7ec4\u7c7b\u4f3c\u67e5\u8be2\u65f6\uff0c\u8fd9\u79cd\u65b9\u6cd5\u5f88\u6709\u6548\uff0c\u4f46\u65e0\u6cd5\u53d1\u73b0\u5206\u5e03\u5916\u67e5\u8be2\u7684\u89e3\u51b3\u65b9\u6848\u3002\u56fa\u5b9a\u7684\u3001\u4e00\u5200\u5207\u7684\u65b9\u6cd5\u65e0\u6cd5\u6709\u6548\u9002\u5e94\u4efb\u52a1\u7684\u5f02\u8d28\u6027\u3002\u6211\u4eec\u66f4\u5e0c\u671b\u6709\u4e00\u4e2a\u5f3a\u5927\u7684\u6a21\u578b\uff0c\u5b83\u80fd\u591f\u901a\u8fc7\u5c1d\u8bd5\u591a\u79cd\u65b9\u6cd5\u5e76\u5728\u4e0d\u540c\u7a0b\u5ea6\u4e0a\u5bfb\u6c42\u4fe1\u606f\uff0c\u6216\u8005\u5728\u65e0\u6cd5\u5b8c\u5168\u89e3\u51b3\u95ee\u9898\u65f6\u8868\u8fbe\u4e0d\u786e\u5b9a\u6027\uff0c\u4ece\u800c\u63a8\u5e7f\u5230\u65b0\u7684\u3001\u672a\u89c1\u8fc7\u7684\u95ee\u9898\u3002<\/section>\n<section><\/section>\n<section>\u6211\u4eec\u5982\u4f55\u8bad\u7ec3\u6a21\u578b\u6765\u6ee1\u8db3\u8fd9\u4e9b\u8981\u6c42\uff1f<\/section>\n<section><\/section>\n<section><strong>\u5b66\u4e60\u300c\u5982\u4f55\u56de\u7b54\u300d<\/strong><\/section>\n<section><\/section>\n<section>\u4e3a\u4e86\u89e3\u51b3\u4e0a\u8ff0\u95ee\u9898\uff0c\u4e00\u4e2a\u65b0\u60f3\u6cd5\u662f\u5141\u8bb8\u6a21\u578b\u5728\u6d4b\u8bd5\u65f6\u4f7f\u7528\u8ba1\u7b97\u8d44\u6e90\u6765\u5bfb\u627e\u300c\u5143\uff08meta\uff09\u300d\u7b56\u7565\u6216\u7b97\u6cd5\uff0c\u8fd9\u4e9b\u7b56\u7565\u6216\u7b97\u6cd5\u53ef\u4ee5\u5e2e\u52a9\u5b83\u4eec\u7406\u89e3\u300c\u5982\u4f55\u300d\u5f97\u51fa\u4e00\u4e2a\u597d\u7684\u7b54\u6848\u3002<\/section>\n<section><\/section>\n<section>\u5b9e\u73b0\u80fd\u591f\u8d4b\u4e88\u6a21\u578b\u7cfb\u7edf\u6027\u7a0b\u5e8f\u8fd0\u884c\u80fd\u529b\u7684\u5143\u7b56\u7565\uff0c\u5e94\u8be5\u80fd\u591f\u4f7f\u5176\u5728\u6d4b\u8bd5\u65f6\u5916\u63a8\u548c\u6cdb\u5316\u5230\u4e0d\u540c\u590d\u6742\u5ea6\u7684\u8f93\u5165\u67e5\u8be2\u3002\u4f8b\u5982\uff0c\u5982\u679c\u4e00\u4e2a\u6a21\u578b\u88ab\u6559\u4e86\u67ef\u897f &#8211; \u65bd\u74e6\u8328\u4e0d\u7b49\u5f0f\u7684\u542b\u4e49\uff0c\u5b83\u5c31\u5e94\u8be5\u80fd\u591f\u5728\u7b80\u5355\u548c\u56f0\u96be\u7684\u8bc1\u660e\u95ee\u9898\u4e0a\u5728\u9002\u5f53\u7684\u65f6\u5019\u8fd0\u7528\u5b83\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u6d4b\u8bd5\u67e5\u8be2\uff0c\u6211\u4eec\u5e0c\u671b\u6a21\u578b\u80fd\u591f\u6267\u884c\u5305\u542b\u591a\u4e2a\u57fa\u672c\u63a8\u7406\u6b65\u9aa4\u7684\u7b56\u7565\uff0c\u8fd9\u53ef\u80fd\u9700\u8981\u6d88\u8017\u66f4\u591a\u7684 token\u3002<\/section>\n<section><\/section>\n<section>\u56fe 2 \u5c55\u793a\u4e86\u89e3\u51b3\u4e00\u4e2a\u7ed9\u5b9a\u95ee\u9898\u7684\u4e24\u79cd\u4e0d\u540c\u7b56\u7565\u7684\u4f8b\u5b50\u3002\u6211\u4eec\u5982\u4f55\u8bad\u7ec3\u6a21\u578b\u6765\u505a\u5230\u8fd9\u4e00\u70b9\u5462\uff1f\u6211\u4eec\u5c06\u628a\u8fd9\u4e2a\u76ee\u6807\u5f62\u5f0f\u5316\u4e3a\u4e00\u4e2a\u5b66\u4e60\u95ee\u9898\uff0c\u5e76\u901a\u8fc7\u5143\u5f3a\u5316\u5b66\u4e60\u7684\u601d\u8def\u6765\u89e3\u51b3\u5b83\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-e9fafbc7cd7cec700fa63e2c6c808041.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-e9fafbc7cd7cec700fa63e2c6c808041.png\"><\/a><\/section>\n<section><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u56fe 2: \u00a0\u5c55\u793a\u4e86\u4e24\u79cd\u7b97\u6cd5\u53ca\u5176\u5404\u81ea\u751f\u6210\u7684 token \u6d41\u793a\u4f8b\u3002<\/sup><\/em><\/section>\n<section><\/section>\n<section><strong>\u5c06\u5b66\u4e60\u300c\u5982\u4f55\u505a\u300d\u5f62\u5f0f\u5316\u4e3a\u4e00\u4e2a\u76ee\u6807<\/strong><\/section>\n<section><\/section>\n<section>\u5bf9\u4e8e\u6bcf\u4e2a\u95ee\u9898 x\u2208X\uff0c\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u5956\u52b1\u51fd\u6570 r (x,\u22c5):Y\u21a6{0,1}, \u53ef\u4ee5\u9488\u5bf9\u4efb\u4f55\u8f93\u51fa token \u6d41 y \u8fdb\u884c\u67e5\u8be2\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u6570\u5b66\u63a8\u7406\u95ee\u9898 x\uff0c\u5176 token \u8f93\u51fa\u6d41\u4e3a y\uff0c\u5956\u52b1 r (x,y) \u53ef\u4ee5\u662f\u68c0\u67e5\u67d0\u4e2a token \u5b50\u5e8f\u5217\u662f\u5426\u5305\u542b\u6b63\u786e\u7b54\u6848\u7684\u51fd\u6570\u3002\u6211\u4eec\u53ea\u83b7\u5f97\u4e86\u8bad\u7ec3\u95ee\u9898\u6570\u636e\u96c6 D_train, \u56e0\u6b64\u4e5f\u53ea\u6709\u5956\u52b1\u51fd\u6570\u96c6\u5408 {r (x,\u22c5):x\u2208D_train}\u3002\u6211\u4eec\u7684\u76ee\u6807\u662f\u5728\u4e8b\u5148\u672a\u77e5\u7684\u6d4b\u8bd5\u95ee\u9898\u5206\u5e03 P_test \u4e0a\u83b7\u5f97\u9ad8\u5956\u52b1\u3002\u6d4b\u8bd5\u95ee\u9898\u7684\u96be\u5ea6\u53ef\u80fd\u4e0e\u8bad\u7ec3\u95ee\u9898\u4e0d\u540c\u3002<\/section>\n<section><\/section>\n<section>\u5bf9\u4e8e\u672a\u77e5\u7684\u6d4b\u8bd5\u95ee\u9898\u5206\u5e03 P_test \u548c\u6709\u9650\u7684\u6d4b\u8bd5\u65f6\u8ba1\u7b97\u9884\u7b97 C\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u8bad\u7ec3\u95ee\u9898\u6570\u636e\u96c6 D_train \u4e2d\u5b66\u4e60\u4e00\u4e2a\u7b97\u6cd5 A\u2208A_C (D_train), \u8fd9\u4e2a\u7b97\u6cd5\u5c5e\u4e8e\u63a8\u7406\u8ba1\u7b97\u53d7\u9650\u7684\u6d4b\u8bd5\u65f6\u7b97\u6cd5\u7c7b A_C\u3002\u8fd9\u4e2a\u7c7b\u4e2d\u7684\u6bcf\u4e2a\u7b97\u6cd5\u90fd\u4ee5\u95ee\u9898 x\u223cP_test \u4f5c\u4e3a\u8f93\u5165\uff0c\u5e76\u8f93\u51fa\u4e00\u4e2a token \u6d41\u3002<\/section>\n<section><\/section>\n<section>\u5728\u56fe 2 \u4e2d\uff0c\u6211\u4eec\u7ed9\u51fa\u4e86\u4e00\u4e9b\u4f8b\u5b50\u6765\u5e2e\u52a9\u7406\u89e3\u8fd9\u4e2a token \u6d41\u53ef\u4ee5\u662f\u4ec0\u4e48\u3002\u4f8b\u5982\uff0cA_\u03b8(x) \u53ef\u80fd\u9996\u5148\u5305\u542b\u9488\u5bf9\u95ee\u9898 x \u7684\u67d0\u4e9b\u5c1d\u8bd5 token\uff0c\u7136\u540e\u662f\u4e00\u4e9b\u7528\u4e8e\u9884\u6d4b\u5c1d\u8bd5\u6b63\u786e\u6027\u7684\u9a8c\u8bc1 token\uff0c\u5982\u679c\u9a8c\u8bc1\u4e3a\u4e0d\u6b63\u786e\uff0c\u63a5\u7740\u662f\u5bf9\u521d\u59cb\u5c1d\u8bd5\u7684\u4e00\u4e9b\u6539\u8fdb\uff0c\u6240\u6709\u8fd9\u4e9b\u90fd\u4ee5\u300c\u7ebf\u6027\u300d\u65b9\u5f0f\u4e32\u8054\u5728\u4e00\u8d77\u3002\u53e6\u4e00\u4e2a\u7b97\u6cd5 A_\u03b8(x) \u53ef\u80fd\u662f\u4ee5\u7ebf\u6027\u65b9\u5f0f\u6a21\u62df\u67d0\u79cd\u542f\u53d1\u5f0f\u5f15\u5bfc\u641c\u7d22\u7b97\u6cd5\u3002\u7b97\u6cd5\u7c7b A_C (D_train) \u5c06\u7531\u4e0a\u8ff0\u6240\u6709\u53ef\u80fd\u7684 A_\u03b8(x) \u4ea7\u751f\u7684\u4e0b\u4e00\u4e2a token \u5206\u5e03\u7ec4\u6210\u3002\u6ce8\u610f\uff0c\u5728\u8fd9\u4e9b\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u5e0c\u671b\u4f7f\u7528\u66f4\u591a\u7684 token \u6765\u5b66\u4e60\u4e00\u4e2a\u901a\u7528\u4f46\u53ef\u6cdb\u5316\u7684\u7a0b\u5e8f\uff0c\u800c\u4e0d\u662f\u53bb\u731c\u6d4b\u95ee\u9898 x \u7684\u89e3\u51b3\u65b9\u6848\u3002<\/section>\n<section><\/section>\n<section>\u6211\u4eec\u7684\u5b66\u4e60\u76ee\u6807\u662f\u5b66\u4e60\u7531\u81ea\u56de\u5f52\u5927\u8bed\u8a00\u6a21\u578b\u53c2\u6570\u5316\u7684 A_\u03b8(x)\u3002\u6211\u4eec\u5c06\u8fd9\u6574\u4e2a\u6d41 (\u5305\u62ec\u6700\u7ec8\u7b54\u6848) \u79f0\u4e3a\u54cd\u5e94 y\u223cA_\u03b8(x)\u3002\u7b97\u6cd5 A_\u03b8(x) \u7684\u6548\u7528\u7531\u5956\u52b1 r (x,y) \u8861\u91cf\u7684\u5e73\u5747\u6b63\u786e\u6027\u7ed9\u51fa\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5b66\u4e60\u7b97\u6cd5\u8868\u8ff0\u4e3a\u89e3\u51b3\u4ee5\u4e0b\u4f18\u5316\u95ee\u9898\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-30d2d7b81ab65a681b1dec2db2c76631.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-30d2d7b81ab65a681b1dec2db2c76631.png\"><\/a><\/section>\n<section><strong>\u5c06 (Op-How) \u89e3\u91ca\u4e3a\u5143\u5f3a\u5316\u5b66\u4e60\u95ee\u9898<\/strong><\/section>\n<section><\/section>\n<section>\u63a5\u4e0b\u6765\u7684\u95ee\u9898\u662f\uff1a\u6211\u4eec\u5982\u4f55\u89e3\u51b3\u7531\u8bed\u8a00\u6a21\u578b\u53c2\u6570\u5316\u7684\u3001\u5728\u8ba1\u7b97\u53d7\u9650\u7b97\u6cd5\u7c7b A_c \u4e0a\u7684\u4f18\u5316\u95ee\u9898 (Op-How)\uff1f<\/section>\n<section><\/section>\n<section>\u663e\u7136\uff0c\u6211\u4eec\u65e2\u4e0d\u77e5\u9053\u6d4b\u8bd5\u95ee\u9898\u7684\u7ed3\u679c\uff0c\u4e5f\u6ca1\u6709\u4efb\u4f55\u76d1\u7763\u4fe1\u606f\u3002\u56e0\u6b64\uff0c\u8ba1\u7b97\u5916\u90e8\u671f\u671b\u662f\u5f92\u52b3\u7684\u3002\u5bf9\u95ee\u9898 x \u731c\u6d4b\u6700\u4f73\u53ef\u80fd\u54cd\u5e94\u7684\u300c\u6807\u51c6\u300d\u5927\u8bed\u8a00\u6a21\u578b\u7b56\u7565\u4f3c\u4e4e\u4e5f\u4e0d\u662f\u6700\u4f18\u7684\uff0c\u56e0\u4e3a\u5982\u679c\u5145\u5206\u5229\u7528\u8ba1\u7b97\u9884\u7b97 C\uff0c\u5b83\u53ef\u80fd\u4f1a\u505a\u5f97\u66f4\u597d\u3002<\/section>\n<section><\/section>\n<section>\u4e3b\u8981\u601d\u8def\u662f\u4f18\u5316 (Op-How) \u7684\u7b97\u6cd5 A_\u03b8(x)\u2208A_c\uff0c\u7c7b\u4f3c\u4e8e\u5f3a\u5316\u5b66\u4e60\u4e2d\u7684\u81ea\u9002\u5e94\u7b56\u7565\uff0c\u5b83\u4f7f\u7528\u989d\u5916\u7684 token \u9884\u7b97\u6765\u5b9e\u73b0\u67d0\u79cd\u7b97\u6cd5\u7b56\u7565\u6765\u89e3\u51b3\u8f93\u5165\u95ee\u9898 x\u3002\u6709\u4e86\u8fd9\u4e2a\u8054\u7cfb\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u7c7b\u4f3c\u95ee\u9898\u901a\u5e38\u7684\u89e3\u51b3\u65b9\u5f0f\u4e2d\u83b7\u5f97\u542f\u53d1\uff1a\u901a\u8fc7\u5143\u5b66\u4e60\u7684\u89c6\u89d2\u6765\u770b\u5f85 (Op-How)\uff0c\u5177\u4f53\u6765\u8bf4\u662f\u5143\u5f3a\u5316\u5b66\u4e60\uff1a\u300c\u5143\u300d\u662f\u56e0\u4e3a\u6211\u4eec\u5e0c\u671b\u5b66\u4e60\u7b97\u6cd5\u800c\u4e0d\u662f\u76f4\u63a5\u56de\u7b54\u7ed9\u5b9a\u95ee\u9898\uff0c\u800c\u300c\u5f3a\u5316\u5b66\u4e60\u300d\u662f\u56e0\u4e3a (Op-How) \u662f\u4e00\u4e2a\u5956\u52b1\u6700\u5927\u5316\u95ee\u9898\u3002<\/section>\n<section><\/section>\n<section><strong>\u4e00\u4e2a\u975e\u5e38\u7b80\u77ed\u7684\u5143\u5f3a\u5316\u5b66\u4e60\u5165\u95e8<\/strong><\/section>\n<section><\/section>\n<section>\u901a\u5e38\uff0c\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\u4e00\u4e2a\u7b56\u7565\u6765\u6700\u5927\u5316\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b (MDP) \u4e2d\u7684\u7ed9\u5b9a\u5956\u52b1\u51fd\u6570\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u5143\u5f3a\u5316\u5b66\u4e60\u95ee\u9898\u8bbe\u5b9a\u5047\u8bbe\u53ef\u4ee5\u8bbf\u95ee\u4efb\u52a1\u5206\u5e03 (\u6bcf\u4e2a\u4efb\u52a1\u90fd\u6709\u4e0d\u540c\u7684\u5956\u52b1\u51fd\u6570\u548c\u52a8\u6001\u7279\u6027)\u3002\u5728\u8fd9\u79cd\u8bbe\u5b9a\u4e0b\uff0c\u76ee\u6807\u662f\u5728\u6765\u81ea\u8bad\u7ec3\u5206\u5e03\u7684\u4efb\u52a1\u4e0a\u8bad\u7ec3\u7b56\u7565\uff0c\u4f7f\u5176\u80fd\u591f\u5728\u4ece\u76f8\u540c\u6216\u4e0d\u540c\u6d4b\u8bd5\u5206\u5e03\u62bd\u53d6\u7684\u6d4b\u8bd5\u4efb\u52a1\u4e0a\u8868\u73b0\u826f\u597d\u3002<\/section>\n<section><\/section>\n<section>\u6b64\u5916\uff0c\u8fd9\u79cd\u8bbe\u5b9a\u4e0d\u662f\u6839\u636e\u7b56\u7565\u5728\u6d4b\u8bd5\u4efb\u52a1\u4e0a\u7684\u96f6\u6837\u672c\u8868\u73b0\u6765\u8bc4\u4f30\u5b83\uff0c\u800c\u662f\u8ba9\u5b83\u901a\u8fc7\u5728\u6d4b\u8bd5\u65f6\u6267\u884c\u51e0\u4e2a\u300c\u8bad\u7ec3\u300d\u56de\u5408\u6765\u9002\u5e94\u6d4b\u8bd5\u4efb\u52a1\uff0c\u5728\u6267\u884c\u8fd9\u4e9b\u56de\u5408\u4e4b\u540e\u518d\u8bc4\u4f30\u7b56\u7565\u3002<\/section>\n<section><\/section>\n<section>\u56de\u5230\u6211\u4eec\u7684\u8bbe\u5b9a\uff0c\u4f60\u53ef\u80fd\u4f1a\u60f3\u77e5\u9053\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\uff08MDP\uff09\u548c\u591a\u4e2a\u4efb\u52a1 (\u7528\u4e8e\u5143\u5f3a\u5316\u5b66\u4e60) \u662f\u5982\u4f55\u4f53\u73b0\u7684\u3002\u6bcf\u4e2a\u95ee\u9898 x\u2208X \u90fd\u4f1a\u5f15\u53d1\u4e00\u4e2a\u65b0\u7684\u5f3a\u5316\u5b66\u4e60\u4efb\u52a1\uff0c\u8fd9\u4e2a\u4efb\u52a1\u88ab\u5f62\u5f0f\u5316\u4e3a\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b (MDP) M_x\uff0c\u5176\u4e2d\u95ee\u9898 x \u4e2d\u7684 token \u96c6\u5408\u4f5c\u4e3a\u521d\u59cb\u72b6\u6001\uff0c\u6211\u4eec\u7684\u5927\u8bed\u8a00\u6a21\u578b A_\u03b8(x) \u4ea7\u751f\u7684\u6bcf\u4e2a token \u4f5c\u4e3a\u4e00\u4e2a\u52a8\u4f5c\uff0c\u800c\u7b80\u5355\u7684\u786e\u5b9a\u6027\u52a8\u6001\u5219\u901a\u8fc7\u5c06\u65b0\u7684 token \u2208T \u4e0e\u5230\u76ee\u524d\u4e3a\u6b62\u7684 token \u5e8f\u5217\u8fde\u63a5\u6765\u5b9a\u4e49\u3002\u6ce8\u610f\uff0c\u6240\u6709 MDP \u5171\u4eab\u52a8\u4f5c\u96c6\u5408\u548c\u72b6\u6001\u96c6\u5408\u00a0<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-3d6803ede3129c255c75a55e604eff83.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-3d6803ede3129c255c75a55e604eff83.png\"><\/a>\u00a0\uff0c\u8fd9\u4e9b\u5bf9\u5e94\u4e8e\u8bcd\u6c47\u8868\u4e2d\u53ef\u80fd\u51fa\u73b0\u7684\u53d8\u957f token \u5e8f\u5217\u3002\u7136\u800c\uff0c\u6bcf\u4e2a MDP M_x \u90fd\u6709\u4e00\u4e2a\u4e0d\u540c\u7684\u672a\u77e5\u5956\u52b1\u51fd\u6570\uff0c\u7531\u6bd4\u8f83\u5668 r (x,\u22c5) \u7ed9\u51fa\u3002<\/section>\n<section><\/section>\n<section>\u90a3\u4e48\u89e3\u51b3 (Op-How) \u5c31\u5bf9\u5e94\u7740\u627e\u5230\u4e00\u4e2a\u7b56\u7565\uff0c\u8be5\u7b56\u7565\u80fd\u591f\u5728\u8ba1\u7b97\u9884\u7b97 C \u5185\u5feb\u901f\u9002\u5e94\u6d4b\u8bd5\u95ee\u9898 (\u6216\u6d4b\u8bd5\u72b6\u6001) \u7684\u5206\u5e03\u3002\u4ece\u8ba4\u77e5 POMDP \u7684\u89c6\u89d2\u6765\u770b\u8fd9\u79cd\u6d4b\u8bd5\u65f6\u6cdb\u5316\u7684\u6982\u5ff5\u662f\u53e6\u4e00\u79cd\u65b9\u5f0f\uff0c\u8fd9\u662f\u4e00\u4e2a\u5c06\u5728 M_x \u65cf\u4e0a\u5b66\u4e60\u7b56\u7565\u89c6\u4e3a\u90e8\u5206\u89c2\u5bdf\u5f3a\u5316\u5b66\u4e60\u95ee\u9898\u7684\u6784\u9020\u3002\u8fd9\u4e2a\u89c6\u89d2\u63d0\u4f9b\u4e86\u53e6\u4e00\u79cd\u6fc0\u53d1\u81ea\u9002\u5e94\u7b56\u7565\u548c\u5143\u5f3a\u5316\u5b66\u4e60\u9700\u6c42\u7684\u65b9\u5f0f\uff1a\u5bf9\u4e8e\u90a3\u4e9b\u6709\u5f3a\u5316\u5b66\u4e60\u80cc\u666f\u7684\u4eba\u6765\u8bf4\uff0c\u89e3\u51b3 POMDP \u7b49\u540c\u4e8e\u8fd0\u884c\u5143\u5f3a\u5316\u5b66\u4e60\u8fd9\u4e00\u70b9\u5e94\u8be5\u4e0d\u8db3\u4e3a\u5947\u3002\u56e0\u6b64\uff0c\u901a\u8fc7\u89e3\u51b3\u5143\u5f3a\u5316\u5b66\u4e60\u76ee\u6807\uff0c\u6211\u4eec\u6b63\u5728\u5bfb\u6c42\u8fd9\u4e2a\u8ba4\u77e5 POMDP \u7684\u6700\u4f18\u7b56\u7565\u5e76\u5b9e\u73b0\u6cdb\u5316\u3002<\/section>\n<section><\/section>\n<section><strong>\u9002\u5e94\u6027\u7b56\u7565\u5982\u4f55\u9002\u5e94\u6d4b\u8bd5\u95ee\u9898\uff1f<\/strong><\/section>\n<section><\/section>\n<section>\u5728\u5143\u5f3a\u5316\u5b66\u4e60\u4e2d\uff0c\u5bf9\u4e8e\u6bcf\u4e2a\u6d4b\u8bd5 MDP M_x\uff0c\u7b56\u7565 A_\u03b8 \u5728\u901a\u8fc7 A_\u03b8 \u751f\u6210\u6700\u7ec8\u54cd\u5e94\u8fdb\u884c\u8bc4\u4f30\u4e4b\u524d\uff0c\u53ef\u4ee5\u901a\u8fc7\u6d88\u8017\u6d4b\u8bd5\u65f6\u8ba1\u7b97\u6765\u83b7\u53d6\u4fe1\u606f\u3002\u5728\u5143\u5f3a\u5316\u5b66\u4e60\u672f\u8bed\u4e2d\uff0c\u83b7\u5f97\u7684\u5173\u4e8e\u6d4b\u8bd5 MDP M_x \u7684\u4fe1\u606f\u53ef\u4ee5\u88ab\u89c6\u4e3a\u5728\u6d4b\u8bd5\u95ee\u9898 x \u5f15\u53d1\u7684 MDP 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\u6d41\u8fdb\u884c\u8fc7\u7a0b\u4e2d\u4e0d\u9700\u8981\u6d89\u53ca\u5916\u90e8\u5de5\u5177\u4e5f\u80fd\u83b7\u5f97\u4fe1\u606f\u3002\u6d41\u4e2d\u7684\u6bcf\u4e2a\u56de\u5408\u90fd\u53ef\u4ee5\u6709\u610f\u4e49\u5730\u589e\u52a0\u66f4\u591a\u4fe1\u606f\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u6d88\u8017\u66f4\u591a\u7684\u6d4b\u8bd5\u65f6\u8ba1\u7b97\u89c6\u4e3a\u4ece\u6a21\u578b\u5bf9\u6700\u4f18\u89e3\u7684\u540e\u9a8c\u8fd1\u4f3c P (\u22c5|x,\u03b8) \u4e2d\u91c7\u6837\u7684\u4e00\u79cd\u65b9\u5f0f\uff0c\u5176\u4e2d\u6bcf\u4e2a\u56de\u5408 (\u6216\u8f93\u51fa\u6d41\u4e2d\u7684 token) \u90fd\u5728\u6539\u8fdb\u8fd9\u4e2a\u8fd1\u4f3c\u3002\u56e0\u6b64\uff0c\u663e\u5f0f\u5730\u8c03\u6574\u5148\u524d\u751f\u6210\u7684 token \u53ef\u4ee5\u63d0\u4f9b\u4e00\u79cd\u8ba1\u7b97\u53ef\u884c\u7684\u65b9\u5f0f\uff0c\u7528\u56fa\u5b9a\u5927\u5c0f\u7684\u5927\u8bed\u8a00\u6a21\u578b\u6765\u8868\u5f81\u8fd9\u4e2a\u540e\u9a8c\u3002<\/section>\n<section><\/section>\n<section>\u7efc\u4e0a\u6240\u8ff0\uff0c\u5f53\u88ab\u89c6\u4e3a\u5143\u5f3a\u5316\u5b66\u4e60\u95ee\u9898\u65f6\uff0cA (\u22c5|\u22c5) \u6210\u4e3a\u4e00\u4e2a\u5386\u53f2\u6761\u4ef6 (\u300c\u81ea\u9002\u5e94\u300d) \u7b56\u7565\uff0c\u901a\u8fc7\u5728\u7ed9\u5b9a\u6d4b\u8bd5\u95ee\u9898\u4e0a\u82b1\u8d39\u6700\u591a C \u7684\u8ba1\u7b97\u6765\u4f18\u5316\u5956\u52b1 r\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-41a9e2b7c92e923bfc0c7436c3e52eec.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-41a9e2b7c92e923bfc0c7436c3e52eec.png\"><\/a><\/section>\n<section><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u56fe 3\uff1a\u667a\u80fd\u4f53 &#8211; \u73af\u5883\u4ea4\u4e92\u534f\u8bae\u3002\u56fe\u6e90\uff1ahttps:\/\/arxiv.org\/pdf\/1611.02779<\/sup><\/em><\/section>\n<section><\/section>\n<section><strong>\u5b66\u4e60\u81ea\u9002\u5e94\u7b56\u7565\u7684\u5143\u5f3a\u5316\u5b66\u4e60<\/strong><\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-06b112665cf563e799af2775d6de7a05.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-06b112665cf563e799af2775d6de7a05.png\"><\/a><\/section>\n<section><em><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u56fe 4\uff1aA_\u03b8(x) \u7684\u54cd\u5e94\u5305\u62ec\u4e00\u4e32 token\u3002<\/sup><\/em><\/section>\n<section><\/section>\n<section>\u6211\u4eec\u5982\u4f55\u89e3\u51b3\u8fd9\u6837\u4e00\u4e2a\u5143\u5f3a\u5316\u5b66\u4e60\u95ee\u9898\uff1f\u4e5f\u8bb8\u89e3\u51b3\u5143\u5f3a\u5316\u5b66\u4e60\u95ee\u9898\u6700\u660e\u663e\u7684\u65b9\u6cd5\u662f\u91c7\u7528<strong>\u9ed1\u76d2\u5143\u5f3a\u5316\u5b66\u4e60\u65b9\u6cd5<\/strong>\u3002\u8fd9\u5c06\u6d89\u53ca\u6700\u5927\u5316\u8f93\u51fa\u8f68\u8ff9 A_\u03b8(x) \u4e2d\u60f3\u8c61\u7684\u300cepisodes\u300d\u7684\u5956\u52b1\u603b\u548c\u3002\u4f8b\u5982\uff0c\u5982\u679c A_\u03b8(x) \u5bf9\u5e94\u4e8e\u4f7f\u7528\u81ea\u6211\u7ea0\u6b63\u7b56\u7565\uff0c\u90a3\u4e48\u6bcf\u4e2a episode \u7684\u5956\u52b1\u5c06\u5bf9\u8f68\u8ff9\u4e2d\u51fa\u73b0\u7684\u5355\u4e2a\u54cd\u5e94\u8fdb\u884c\u8bc4\u5206\u3002\u5982\u679c A_\u03b8(x) \u89c4\u5b9a\u4e86\u4e00\u79cd\u5728\u751f\u6210\u548c\u751f\u6210\u9a8c\u8bc1\u4e4b\u95f4\u4ea4\u66ff\u7684\u7b56\u7565\uff0c\u90a3\u4e48\u5956\u52b1\u5c06\u5bf9\u5e94\u4e8e\u751f\u6210\u548c\u9a8c\u8bc1\u7684\u6210\u529f\u3002\u7136\u540e\u6211\u4eec\u53ef\u4ee5\u4f18\u5316\uff1a<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-b886a29f271273a07e6b75da5fe69271.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/02\/frc-b886a29f271273a07e6b75da5fe69271.png\"><\/a><\/section>\n<section>\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c\u8f93\u51fa token 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(Obj-2)\u3002\u5b9e\u9645\u4e0a\uff0c\u53ea\u8981\u80fd\u591f\u4f7f\u7528\u67d0\u79cd\u6267\u884c\u5b9a\u671f\u5728\u7ebf\u7b56\u7565\u91c7\u6837\u7684\u5f3a\u5316\u5b66\u4e60\u7b97\u6cd5\u6765\u89e3\u51b3\u4f18\u5316\u95ee\u9898\uff0c\u5f3a\u5316\u5b66\u4e60\u65b9\u6cd5\u7684\u9009\u62e9 (\u57fa\u4e8e\u4ef7\u503c\u8fd8\u662f\u57fa\u4e8e\u7b56\u7565) \u53ef\u80fd\u5e76\u4e0d\u91cd\u8981\u3002<\/section>\n<section><\/section>\n<section>\u6211\u4eec\u8fd8\u53ef\u4ee5\u8003\u8651\u53e6\u4e00\u79cd\u5236\u5b9a\u5143\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\u76ee\u6807\u7684\u65b9\u6cd5\uff1a\u53ea\u4f18\u5316\u6d4b\u8bd5\u56de\u5408\u83b7\u5f97\u7684\u5956\u52b1\uff0c\u800c\u4e0d\u662f\u8bad\u7ec3\u56de\u5408\u7684\u5956\u52b1\uff0c\u4ece\u800c\u907f\u514d\u91cf\u5316\u4fe1\u606f\u589e\u76ca\u7684\u9700\u8981\u3002<\/section>\n<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:<a href=\"https:\/\/www.jiqizhixin.com\/articles\/2025-02-10-6\" target=\"_blank\">\u5982\u4f55\u4f18\u5316\u6d4b\u8bd5\u65f6\u8ba1\u7b97\uff1f\u89e3\u51b3\u300c\u5143\u5f3a\u5316\u5b66\u4e60\u300d\u95ee\u9898<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:\u5982\u4f55\u4f18\u5316\u6d4b\u8bd5\u65f6\u8ba1\u7b97\uff1f\u89e3 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