{"id":39842,"date":"2025-04-02T06:02:27","date_gmt":"2025-04-01T22:02:27","guid":{"rendered":"https:\/\/17aitech.com\/?p=39842"},"modified":"2025-04-02T06:02:27","modified_gmt":"2025-04-01T22:02:27","slug":"%e5%9c%a8gsm8k%e4%b8%8a%e6%af%94grpo%e5%bf%ab8%e5%80%8d%ef%bc%81%e5%8e%a6%e5%a4%a7%e6%8f%90%e5%87%bacppo%ef%bc%8c%e8%ae%a9%e5%bc%ba%e5%8c%96%e5%ad%a6%e4%b9%a0%e5%bf%ab%e5%a6%82%e9%97%aa%e7%94%b5","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=39842","title":{"rendered":"\u5728GSM8K\u4e0a\u6bd4GRPO\u5feb8\u500d\uff01\u53a6\u5927\u63d0\u51faCPPO\uff0c\u8ba9\u5f3a\u5316\u5b66\u4e60\u5feb\u5982\u95ea\u7535"},"content":{"rendered":"<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:<a href=\"https:\/\/www.jiqizhixin.com\/articles\/2025-04-01-4\" target=\"_blank\">\u5728GSM8K\u4e0a\u6bd4GRPO\u5feb8\u500d\uff01\u53a6\u5927\u63d0\u51faCPPO\uff0c\u8ba9\u5f3a\u5316\u5b66\u4e60\u5feb\u5982\u95ea\u7535<\/a><\/p>\n<p>DeepSeek-R1 \u7684\u6210\u529f\u79bb\u4e0d\u5f00\u4e00\u79cd\u5f3a\u5316\u5b66\u4e60\u7b97\u6cd5\uff1aGRPO\uff08\u7ec4\u76f8\u5bf9\u7b56\u7565\u4f18\u5316\uff09\u3002<\/p>\n<p>\u4e0d\u540c\u4e8e PPO\uff08\u8fd1\u7aef\u7b56\u7565\u4f18\u5316\uff09\uff0cGRPO \u662f\u76f4\u63a5\u6839\u636e\u7ec4\u5206\u6570\u4f30\u8ba1\u57fa\u7ebf\uff0c\u56e0\u6b64\u6d88\u9664\u4e86\u5bf9 critic \u6a21\u578b\u7684\u9700\u6c42\u3002\u4f46\u662f\uff0c\u8fd9\u53c8\u9700\u8981\u4e3a\u6bcf\u4e2a\u95ee\u9898\u90fd\u91c7\u6837\u4e00\u7ec4\u5b8c\u6210\u7ed3\u679c\uff0c\u8fdb\u800c\u8ba9\u8bad\u7ec3\u8fc7\u7a0b\u7684\u8ba1\u7b97\u6210\u672c\u8f83\u9ad8\u3002<\/p>\n<p>\u4e4b\u540e\uff0cGRPO \u4f1a\u4f7f\u7528\u4e00\u4e2a\u57fa\u4e8e\u89c4\u5219\u7684\u5956\u52b1\u51fd\u6570\u6765\u8ba1\u7b97\u6bcf\u4e2a\u5b8c\u6210\u7ed3\u679c\u7684\u5956\u52b1\uff0c\u5e76\u8ba1\u7b97\u6bcf\u4e2a\u5b8c\u6210\u7ed3\u679c\u7684\u76f8\u5bf9\u4f18\u52bf\u3002<\/p>\n<p>\u4e3a\u4e86\u4fdd\u8bc1\u8bad\u7ec3\u7684\u7a33\u5b9a\u6027\uff0cGRPO \u8fd8\u4f1a\u8ba1\u7b97\u4e00\u7ec4\u5b8c\u6210\u7ed3\u679c\u7684\u7b56\u7565\u6a21\u578b\u3001\u53c2\u8003\u6a21\u578b\u548c\u65e7\u7b56\u7565\u6a21\u578b\u7684\u9884\u6d4b\u6982\u7387\u4e4b\u6bd4\u4f5c\u4e3a\u7b56\u7565\u76ee\u6807\u51fd\u6570\u7684\u4e00\u90e8\u5206\uff0c\u8fd9\u53c8\u4f1a\u8fdb\u4e00\u6b65\u63d0\u5347\u5f3a\u5316\u5b66\u4e60\u7684\u8bad\u7ec3\u5f00\u9500\u3002GRPO \u5de8\u5927\u7684\u8bad\u7ec3\u5f00\u9500\u9650\u5236\u4e86\u5176\u8bad\u7ec3\u6548\u7387\u548c\u53ef\u6269\u5c55\u6027\u3002\u800c\u5728\u5b9e\u8df5\u4e2d\uff0c\u63d0\u9ad8\u8bad\u7ec3\u6548\u7387\u662f\u975e\u5e38\u91cd\u8981\u7684\u3002<\/p>\n<p>\u603b\u7ed3\u8d77\u6765\uff0cGRPO \u8bad\u7ec3\u7684\u8ba1\u7b97\u6210\u672c\u4e3b\u8981\u6e90\u81ea\u5176\u6838\u5fc3\u8bbe\u8ba1\uff1a\u4e3a\u4e86\u8fdb\u884c\u7ec4\u5185\u6bd4\u8f83\uff0c\u4f1a\u4e3a\u6bcf\u4e2a\u63d0\u793a\u8bcd\u751f\u6210\u4e00\u5927\u7ec4\u5b8c\u6210\u7ed3\u679c\u3002\u6b64\u5916\uff0cGRPO \u7684\u524d\u5411\u8ba1\u7b97\u4f1a\u4ee5\u5b8c\u6210\u6570\u91cf\u7684 3 \u500d\u7684\u5c3a\u5ea6\u6269\u5c55\u3002<\/p>\n<p>\u90a3\u4e48\uff0c\u95ee\u9898\u6765\u4e86\uff1a\u5728\u8fd9\u4e2a\u5f3a\u5316\u5b66\u4e60\u8fc7\u7a0b\u4e2d\uff0c\u6bcf\u4e2a\u5b8c\u6210\u7ed3\u679c\u7684\u8d21\u732e\u90fd\u4e00\u6837\u5417\uff1f<\/p>\n<p>\u8fd1\u65e5\uff0c\u53a6\u95e8\u5927\u5b66\u7eaa\u8363\u5d58\u56e2\u961f\u7814\u7a76\u53d1\u73b0\uff0c\u6bcf\u4e2a\u5b8c\u6210\u7ed3\u679c\u7684\u8d21\u732e\u4e0e\u5176\u76f8\u5bf9\u4f18\u52bf\u6709\u5173\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6bcf\u4e2a\u5b8c\u6210\u7ed3\u679c\u5bf9\u7b56\u7565\u6a21\u578b\u8bad\u7ec3\u7684\u8d21\u732e\u5e76\u4e0d\u76f8\u7b49\u3002\u5982\u56fe 1 \u6240\u793a\uff0c\u5b8c\u6210\u7ed3\u679c\u7684\u6570\u91cf\u589e\u5927\u65f6\uff0c\u51c6\u786e\u5ea6\u63d0\u5347\u5e76\u4e0d\u975e\u5e38\u663e\u8457\uff0c\u4f46\u8bad\u7ec3\u65f6\u95f4\u5374\u4f1a\u8fc5\u901f\u589e\u957f\u3002<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-2a964811e3dc127e0d39fd2c53a36efd.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-2a964811e3dc127e0d39fd2c53a36efd.png\"><\/a><\/section>\n<section>\u57fa\u4e8e\u8fd9\u4e00\u89c1\u89e3\uff0c\u4ed6\u4eec\u53d1\u73b0\u53ef\u4ee5\u901a\u8fc7\u5bf9\u5b8c\u6210\u7ed3\u679c\u8fdb\u884c\u526a\u679d\u6765\u52a0\u901f GRPO\u3002\u7136\u540e\uff0c\u4ed6\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u52a0\u901f\u7248\u7684 GRPO\uff1a<strong>CPPO<\/strong>\uff08Completion Pruning Policy Optimization \/ \u5b8c\u6210\u526a\u679d\u7b56\u7565\u4f18\u5316\uff09\u3002\u5e76\u4e14\u4ed6\u4eec\u4e5f\u5df2\u7ecf\u5f00\u6e90\u53d1\u5e03\u4e86\u8be5\u7b97\u6cd5\u7684\u4ee3\u7801\u3002<\/section>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-2c6d3823658ef3ce0a9855d00470b24c.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-2c6d3823658ef3ce0a9855d00470b24c.png\"><\/a><\/section>\n<ul>\n<li>\n<p>\u8bba\u6587\u6807\u9898\uff1aCPPO: Accelerating the Training of Group Relative Policy Optimization-Based Reasoning Models<\/p>\n<\/li>\n<li>\n<p>\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/arxiv.org\/pdf\/2503.22342<\/p>\n<\/li>\n<li>\n<p>\u9879\u76ee\u5730\u5740\uff1ahttps:\/\/github.com\/lzhxmu\/CPPO<\/p>\n<\/li>\n<\/ul>\n<p>\u987e\u540d\u601d\u4e49\uff0cCPPO \u4f1a\u6839\u636e\u4f18\u52bf\u5bf9\u5b8c\u6210\u7ed3\u679c\u8fdb\u884c\u526a\u679d\uff0c\u8fd9\u6837\u4e00\u6765\u5c31\u53ef\u4ee5\u63d0\u5347\u5f3a\u5316\u5b66\u4e60\u8fc7\u7a0b\u7684\u901f\u5ea6\u3002<\/p>\n<p>\u5177\u4f53\u6765\u8bf4\uff0c\u4e00\u5f00\u59cb\uff0c\u7b56\u7565\u6a21\u578b\u4f1a\u9488\u5bf9\u6bcf\u4e2a\u95ee\u9898\u91c7\u6837\u4e00\u7ec4\u5b8c\u6210\u7ed3\u679c\u3002\u968f\u540e\uff0c\u901a\u8fc7\u5956\u52b1\u51fd\u6570\u8ba1\u7b97\u6bcf\u4e2a\u5b8c\u6210\u7ed3\u679c\u7684\u76f8\u5bf9\u4f18\u52bf\u3002\u7136\u540e\uff0cCPPO \u4f1a\u4fee\u526a\u6389\u7edd\u5bf9\u4f18\u52bf\u503c\u8f83\u4f4e\u7684\u5b8c\u6210\u7ed3\u679c\uff0c\u4ec5\u4fdd\u7559\u7edd\u5bf9\u4f18\u52bf\u8f83\u9ad8\u7684\u5b8c\u6210\u7ed3\u679c\u6765\u8ba1\u7b97\u635f\u5931\u3002\u6b64\u8fc7\u7a0b\u53ef\u5927\u5927\u51cf\u5c11\u8bad\u7ec3\u6240\u9700\u7684\u5b8c\u6210\u7ed3\u679c\u6570\u91cf\uff0c\u4ece\u800c\u52a0\u5feb\u8bad\u7ec3\u8fc7\u7a0b\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u4ed6\u4eec\u8fd8\u89c2\u5bdf\u5230\uff0c\u7531\u4e8e\u5b8c\u6210\u526a\u679d\u4f1a\u5bfc\u81f4 GPU \u8d44\u6e90\u5229\u7528\u7387\u4e0d\u8db3\uff0c\u4ece\u800c\u5bfc\u81f4\u8d44\u6e90\u6d6a\u8d39\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u4ed6\u4eec\u5f15\u5165\u4e86\u4e00\u79cd\u52a8\u6001\u5b8c\u6210\u7ed3\u679c\u5206\u914d\u7b56\u7565\u3002\u8be5\u7b56\u7565\u4f1a\u7528\u65b0\u95ee\u9898\u7684\u5b8c\u6210\u7ed3\u679c\u586b\u5145\u6bcf\u4e2a\u8bbe\u5907\uff0c\u4ece\u800c\u5145\u5206\u5229\u7528 GPU \u8d44\u6e90\u5e76\u8fdb\u4e00\u6b65\u63d0\u9ad8\u8bad\u7ec3\u6548\u7387\u3002<\/p>\n<p>\u5b9e\u9a8c\u8bc1\u660e\uff0c\u4ed6\u4eec\u7684\u65b9\u6cd5\u662f\u6709\u6548\u7684\u3002\u5f53\u4f7f\u7528 Qwen-2.5 \u7cfb\u5217\u6a21\u578b\u65f6\uff08\u5305\u62ec Qwen-2.5-1.5B-Instruct \u548c Qwen-2.5-7B-Instruct\uff09\uff0c\u5728\u4fdd\u8bc1\u4e86\u51c6\u786e\u5ea6\u76f8\u5f53\u7684\u57fa\u7840\u4e0a\uff0cCPPO \u5728 GSM8K \u57fa\u51c6\u4e0a\u7684\u901f\u5ea6\u6bd4 GRPO \u5feb <strong>8.32 <\/strong>\u500d\uff0c\u5728 MATH \u57fa\u51c6\u4e0a\u5feb <strong>3.51 <\/strong>\u500d\u3002<\/p>\n<p>\u6216\u8005\u7528\u7f51\u53cb\u7684\u8bdd\u6765\u8bf4\uff0c\u5feb\u5982\u95ea\u7535\uff01<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-7ed7c13d6a5db0b62e1beb17a423ee8f.gif\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-7ed7c13d6a5db0b62e1beb17a423ee8f.gif\"><\/a><\/section>\n<p><strong>CPPO\uff1a\u5b8c\u6210\u526a\u679d\u7b56\u7565\u4f18\u5316<\/strong><\/p>\n<ul>\n<li>\u8981\u4e86\u89e3 CPPO\uff0c\u9996\u5148\u5fc5\u987b\u77e5\u9053 GRPO\uff0c\u5176\u516c\u5f0f\u5982\u4e0b\uff1a<\/li>\n<\/ul>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-036680b78f7141f173119e1d8f7aabd1.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-036680b78f7141f173119e1d8f7aabd1.png\"><\/a><\/section>\n<p>\u5176\u4e2d\uff0cq \u662f\u4ece\u6570\u636e\u96c6\u5206\u5e03 P (Q) \u4e2d\u91c7\u6837\u7684\u95ee\u9898\uff0c{o_1, o_2, &#8230; , o_G} \u662f G \u4e2a\u5b8c\u6210\u7ed3\u679c\uff0c\u03c0_\u03b8 \u662f\u7b56\u7565\u6a21\u578b\uff0c\u03c0_\u03b8_old \u662f\u65e7\u7b56\u7565\u6a21\u578b\uff0c\u03c0_\u03b8_ref \u662f\u53c2\u8003\u6a21\u578b\uff0c\u03f5 \u548c \u03b2 \u662f\u8d85\u53c2\u6570\uff0cA_i \u662f\u4f7f\u7528\u4e00\u7ec4\u5956\u52b1 {r_1, r_2, &#8230; , r_G} \u8ba1\u7b97\u7684\u4f18\u52bf\u3002<\/p>\n<p>\u76f8\u6bd4\u4e8e GRPO\uff0cCPPO \u5f15\u5165\u4e86\u4e00\u4e2a\u9009\u62e9\u6027\u6761\u4ef6\uff0c\u8be5\u6761\u4ef6\u4ec5\u4f1a\u5305\u62ec\u8868\u73b0\u51fa\u8db3\u591f\u9ad8\u4f18\u52bf\u7684\u5b8c\u6210\u7ed3\u679c\u3002CPPO \u7684\u76ee\u6807\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-05edec21a80b44d400d46690c58c431e.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-05edec21a80b44d400d46690c58c431e.png\"><\/a><\/section>\n<p>\u5176\u4e2d \u03b3 \u662f\u4e00\u4e2a\u9884\u5b9a\u4e49\u7684\u9608\u503c\uff0c\u7528\u4e8e\u786e\u4fdd\u5728\u68af\u5ea6\u66f4\u65b0\u4e2d\u4ec5\u4fdd\u7559\u7edd\u5bf9\u4f18\u52bf\u9ad8\u4e8e \u03b3 \u7684\u5b8c\u6210\u7ed3\u679c\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5f53<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-53aa99b2c57cb4e52432796147c833fc.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-53aa99b2c57cb4e52432796147c833fc.png\"><\/a>\uff0c\u6216\u8005 <a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-87f081ca058f5b63a6f83339eaf56ea1.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-87f081ca058f5b63a6f83339eaf56ea1.png\"><\/a>\u00a0\u65f6\uff0cclip \u51fd\u6570\u4f1a\u88ab\u6fc0\u6d3b\u3002<\/p>\n<p>\u56fe 2 \u5c55\u793a\u4e86 CPPO \u7684\u6982\u51b5\uff1a<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-cb6f66d78c749bd086d4905f2976926c.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-cb6f66d78c749bd086d4905f2976926c.png\"><\/a><\/section>\n<p><strong>\u7edf\u4e00\u5355\/\u591a GPU \u8bbe\u7f6e<\/strong><\/p>\n<p>\u5728\u591a GPU \u8bad\u7ec3\u573a\u666f\u4e2d\uff0c\u8be5\u56e2\u961f\u89c2\u5bdf\u5230\u5177\u6709\u663e\u8457\u4f18\u52bf\u7684\u5b8c\u6210\u7ed3\u679c\u7684\u6570\u91cf\u56e0\u8bbe\u5907\u800c\u5f02\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6574\u4f53\u8bad\u7ec3\u6548\u7387\u4f1a\u6709\u8bbe\u5907\u5904\u7406\u6700\u591a\u5b8c\u6210\u7ed3\u679c\u6570\u91cf\u7684\u74f6\u9888 \u2014\u2014 \u8fd9\u79cd\u73b0\u8c61\u79f0\u4e3a\u300c\u6728\u6876\u6548\u5e94\uff08bucket effect\uff09\u300d\u3002\u4e3a\u4e86\u7f13\u89e3\u8fd9\u79cd\u60c5\u51b5\uff0c\u5bf9\u4e8e\u6bcf\u53f0 GPU\uff0c\u8be5\u56e2\u961f\u7684\u9009\u62e9\u662f\u53ea\u4fdd\u7559\u6bcf\u4e2a\u95ee\u9898\u5177\u6709\u6700\u5927\u7edd\u5bf9\u4f18\u52bf\u7684 k \u4e2a\u5b8c\u6210\u7ed3\u679c\uff0c\u5176\u4e2d<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-5552cf4bb6141f2f5cf6e7b98759d620.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-5552cf4bb6141f2f5cf6e7b98759d620.png\"><\/a><\/section>\n<p>\u5176\u4e2d P \u2208 (0, 1] \u8868\u793a\u526a\u679d\u7387\u3002\u5728\u6b64\u7b56\u7565\u4e0b\u4fee\u6539\u540e\u7684 CPPO \u4e3a\uff1a<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-b4aa3ca48f6096a4f90c1466f5fd9c7f.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-b4aa3ca48f6096a4f90c1466f5fd9c7f.png\"><\/a><\/section>\n<p>\u5176\u4e2d\u4ec5\u5728\u5177\u6709\u6700\u9ad8\u7edd\u5bf9\u4f18\u52bf\u503c\u7684 k \u4e2a\u5b8c\u6210\u7ed3\u679c\u5bf9\u5e94\u7684\u7d22\u5f15\u96c6 I \u4e0a\u8fdb\u884c\u6c42\u548c\uff0c\u5373<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-92c1425189e15aea205e8ec261dc7d9a.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-92c1425189e15aea205e8ec261dc7d9a.png\"><\/a><\/section>\n<p>CPPO \u7b97\u6cd5\u7684\u6d41\u7a0b\u5982\u4e0b<\/p>\n<ol>\n<li>\n<p>\u65e7\u7b56\u7565\u6a21\u578b\u4e3a\u6bcf\u4e2a\u95ee\u9898\u91c7\u6837\u4e00\u7ec4\u5b8c\u6210\u7ed3\u679c\uff1b<\/p>\n<\/li>\n<li>\n<p>\u5956\u52b1\u51fd\u6570\u8ba1\u7b97\u6bcf\u4e2a\u5b8c\u6210\u7ed3\u679c\u7684\u5956\u52b1\uff1b<\/p>\n<\/li>\n<li>\n<p>\u8ba1\u7b97\u6bcf\u4e2a\u5b8c\u6210\u7ed3\u679c\u7684\u76f8\u5bf9\u4f18\u52bf\uff1b<\/p>\n<\/li>\n<li>\n<p>CPPO \u4fdd\u7559 k \u4e2a\u5177\u6709\u6700\u9ad8\u7edd\u5bf9\u4f18\u52bf\u7684\u5b8c\u6210\u7ed3\u679c\uff1b<\/p>\n<\/li>\n<li>\n<p>\u6839\u636e\u9009\u5b9a\u7684\u5b8c\u6210\u7ed3\u679c\u66f4\u65b0\u7b56\u7565\u6a21\u578b\u3002<\/p>\n<\/li>\n<\/ol>\n<p>CPPO \u548c GRPO \u4e4b\u95f4\u7684\u5173\u952e\u533a\u522b\u662f\uff1aCPPO \u4e0d\u4f1a\u5c06\u6240\u6709\u5b8c\u6210\u7ed3\u679c\u7528\u4e8e\u7b56\u7565\u6a21\u578b\u3001\u53c2\u8003\u6a21\u578b\u548c\u65e7\u7b56\u7565\u6a21\u578b\u7684\u524d\u5411\u8ba1\u7b97\u3002\u76f8\u53cd\uff0c<strong>\u901a\u8fc7\u4ec5\u4fdd\u7559\u5177\u6709\u9ad8\u7edd\u5bf9\u4f18\u52bf\u7684\u5b8c\u6210\u7ed3\u679c\u8fdb\u884c\u68af\u5ea6\u66f4\u65b0\uff0cCPPO \u53ef\u663e\u8457\u964d\u4f4e\u524d\u5411\u4f20\u9012\u671f\u95f4\u7684\u8ba1\u7b97\u5f00\u9500\uff0c\u4ece\u800c\u52a0\u901f\u4e86\u8bad\u7ec3\u8fc7\u7a0b\u3002<\/strong><\/p>\n<p><strong>\u901a\u8fc7\u52a8\u6001\u5b8c\u6210\u7ed3\u679c\u5206\u914d\u8fdb\u884c\u5e76\u884c\u5904\u7406<\/strong><\/p>\n<p>\u8be5\u56e2\u961f\u8fd8\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684<strong>\u52a8\u6001\u5b8c\u6210\u7ed3\u679c\u5206\u914d\u7b56\u7565<\/strong>\uff0c\u4ee5\u8fdb\u4e00\u6b65\u4f18\u5316 CPPO \u7684\u8bad\u7ec3\u6548\u7387\u3002<\/p>\n<p>\u7531\u4e8e GPU \u5185\u5b58\u9650\u5236\uff0c\u4f20\u7edf\u65b9\u6cd5\uff08\u5982 GRPO \u91c7\u7528\u7684\u65b9\u6cd5\uff09\u9762\u4e34\u56fa\u6709\u7684\u5c40\u9650\u6027\u3002\u5177\u4f53\u800c\u8a00\uff0c\u5355\u53f0\u8bbe\u5907\u6bcf\u6279\u6700\u591a\u53ef\u4ee5\u5904\u7406 B \u4e2a\u95ee\u9898\uff0c\u6bcf\u4e2a\u95ee\u9898\u751f\u6210 G \u4e2a\u5019\u9009\u5b8c\u6210\u7ed3\u679c\u3002\u526a\u679d\u64cd\u4f5c\u4e4b\u540e\uff0c\u6bcf\u53f0\u8bbe\u5907\u4fdd\u7559\u7684\u5b8c\u6210\u7ed3\u679c\u603b\u6570\u51cf\u5c11\u5230 B \u00d7 k\uff0c\u8fdb\u800c\u5bfc\u81f4 GPU \u5229\u7528\u7387\u4e0d\u7406\u60f3\uff0c\u5e76\u884c\u8ba1\u7b97\u80fd\u529b\u672a\u5f97\u5230\u5145\u5206\u5229\u7528\u3002<\/p>\n<p>\u4e3a\u4e86\u89e3\u51b3\u8fd9\u79cd\u4f4e\u6548\u7387\u95ee\u9898\uff0c\u8be5\u56e2\u961f\u7684\u65b9\u6cd5\u662f\u5c06\u6765\u81ea\u5176\u4ed6\u95ee\u9898\u7684\u526a\u679d\u540e\u7684\u5b8c\u6210\u7ed3\u679c\u52a8\u6001\u5206\u914d\u5230\u8bbe\u5907\u7684\u5904\u7406\u7ba1\u9053\u4e2d\uff0c\u5982\u56fe 3 \u6240\u793a\u3002<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-0cd5cab8787ef163820503f2bbe22529.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-0cd5cab8787ef163820503f2bbe22529.png\"><\/a><\/section>\n<p>\u6b64\u7b56\u7565\u901a\u8fc7\u4e0d\u65ad\u7528\u6765\u81ea\u539f\u59cb\u95ee\u9898\u548c\u65b0\u5f15\u5165\u95ee\u9898\u7684\u9ad8\u8d28\u91cf\u5b8c\u6210\u7ed3\u679c\u586b\u5145\u5176\u5185\u5b58\uff0c\u786e\u4fdd\u6bcf\u4e2a\u8bbe\u5907\u90fd\u80fd\u4ee5\u6ee1\u8d1f\u8377\u8fd0\u884c\u3002\u81f3\u5173\u91cd\u8981\u7684\u662f\uff0c\u6240\u6709\u65b0\u5408\u5e76\u7684\u5b8c\u6210\u7ed3\u679c\u90fd\u7ecf\u8fc7\u76f8\u540c\u7684\u4e25\u683c\u526a\u679d\u8fc7\u7a0b\uff0c\u4ee5\u4fdd\u6301\u4e00\u81f4\u6027\u548c\u76f8\u5173\u6027\u3002<\/p>\n<p>\u8fd9\u79cd\u65b9\u6cd5\u7684\u597d\u5904\u6709\u4e24\u4e2a\uff1a<\/p>\n<ul>\n<li>\n<p>\u901a\u8fc7\u5145\u5206\u5229\u7528\u8bbe\u5907\u7684\u5e76\u884c\u8ba1\u7b97\u6f5c\u529b\uff0c\u5b83\u80fd\u6700\u5927\u5316 GPU \u5229\u7528\u7387\u3002<\/p>\n<\/li>\n<li>\n<p>\u5b83\u80fd\u4f7f\u6bcf\u53f0\u8bbe\u5907\u6bcf\u6279\u5904\u7406\u66f4\u591a\u7684\u95ee\u9898\uff0c\u4ece\u800c\u51cf\u5c11\u5b9e\u73b0\u6536\u655b\u6240\u9700\u7684\u603b\u8bad\u7ec3\u6b65\u9aa4\u6570\u3002<\/p>\n<\/li>\n<\/ul>\n<p>\u6709\u8fd9\u4e24\u5927\u4f18\u52bf\uff0cCPPO \u4fbf\u53ef\u5728\u4fdd\u8bc1\u8bad\u7ec3\u8d28\u91cf\u7684\u540c\u65f6\u63d0\u9ad8\u8bad\u7ec3\u6548\u7387\u3002<\/p>\n<p><strong>CPPO \u7684\u5b9e\u9a8c\u6548\u679c<\/strong><\/p>\n<p>\u4f7f\u7528 Qwen2.5-1.5B-Instruct \u548c Qwen2.5-7B-Instruct \u6a21\u578b\uff0c\u8be5\u56e2\u961f\u5728 GSM8K \u548c MATH \u6570\u636e\u96c6\u4e0a\u5bf9 CPPO \u8fdb\u884c\u4e86\u5b9e\u9a8c\u8bc4\u4f30\u3002\u6b64\u5916\uff0c\u4e3a\u4e86\u8bc4\u4f30\u6a21\u578b\u7684\u5206\u5e03\u5916\u63a8\u7406\u80fd\u529b\uff0c\u4ed6\u4eec\u8fd8\u5f15\u5165\u4e86 AMC2023 \u548c AIME2024 \u4f5c\u4e3a\u6d4b\u8bd5\u57fa\u51c6\u3002<\/p>\n<p>\u5728 GSM8K \u4e0a\u7684\u7ed3\u679c\u5982\u8868 1 \u6240\u793a\uff0cCPPO \u5728\u51c6\u786e\u5ea6\u548c\u52a0\u901f\u6bd4\u4e0a\u90fd\u660e\u663e\u4f18\u4e8e GRPO\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0cCPPO \u5728\u5404\u79cd\u526a\u679d\u7387\u4e0b\u90fd\u8fbe\u5230\u4e86\u4e0e GRPO \u76f8\u5f53\u751a\u81f3\u66f4\u9ad8\u7684\u51c6\u786e\u5ea6\u3002\u5728 87.50% \u7684\u526a\u679d\u7387\u4e0b\uff0cCPPO \u7684\u51c6\u786e\u5ea6\u8fbe\u5230 80.41%\uff0c\u6bd4 GRPO \u7684 77.05% \u9ad8\u51fa 3.36%\u3002<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-6b9b1716ce5d1565984f90f76d5afc19.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-6b9b1716ce5d1565984f90f76d5afc19.png\"><\/a><\/section>\n<p>\u5728\u6548\u7387\u65b9\u9762\uff0cCPPO \u5927\u5927\u52a0\u5feb\u4e86\u8bad\u7ec3\u901f\u5ea6\u3002\u5728 93.75% \u7684\u526a\u679d\u7387\u4e0b\uff0c\u5176\u52a0\u901f\u6bd4\u8fbe\u5230 8.32 \u500d\u3002\u8fd9\u4e9b\u7ed3\u679c\u8868\u660e\uff0cCPPO \u4e0d\u4ec5\u80fd\u4fdd\u6301\u6216\u63d0\u9ad8\u51c6\u786e\u5ea6\uff0c\u8fd8\u53ef\u663e\u8457\u63d0\u9ad8\u8bad\u7ec3\u6548\u7387\u3002\u56e0\u6b64\uff0cCPPO \u6709\u6f5c\u529b\u6210\u4e3a\u5927\u89c4\u6a21\u63a8\u7406\u6a21\u578b\u8bad\u7ec3\u7684\u5b9e\u7528\u6709\u6548\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n<p>\u5728 MATH \u4e0a\u7684\u8868\u73b0\u89c1\u8868 2\u3002\u53ef\u4ee5\u770b\u5230\uff0cCPPO \u53ef\u4ee5\u5f88\u597d\u5730\u6269\u5c55\u5230\u66f4\u5927\u7684\u6a21\u578b \u2014\u2014 \u5728\u4e0d\u727a\u7272\u51c6\u786e\u5ea6\u7684\u60c5\u51b5\u4e0b\u5728 MATH \u4e0a\u5b9e\u73b0\u4e86\u9ad8\u8fbe <strong>3.51\u00a0<\/strong>\u500d\u7684\u52a0\u901f\u3002\u4f8b\u5982\uff0c\u5728 87.5% \u7684\u4fee\u526a\u7387\u4e0b\uff0cCPPO \u4fdd\u6301\u4e86\u4e0e GRPO (75.20%) \u76f8\u5f53\u7684\u51c6\u786e\u5ea6\uff0c\u540c\u65f6\u8fd8\u5c06\u8bad\u7ec3\u65f6\u95f4\u51cf\u5c11\u4e86 3.51 \u500d\u3002<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-3d15907401d672d007c1badccec684c2.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-3d15907401d672d007c1badccec684c2.png\"><\/a><\/section>\n<p>\u6b64\u5916\uff0c\u5728 AMC2023 \u548c AIME2024 \u57fa\u51c6\u4e0a\u7684\u8bc4\u4f30\u8868\u660e\uff0c\u5c3d\u7ba1 CPPO \u4ec5\u5728\u9ad8\u7edd\u5bf9\u4f18\u52bf\u5b8c\u6210\u7ed3\u679c\u4e0a\u8fdb\u884c\u8bad\u7ec3\uff0c\u4f46\u5b83\u4ecd\u4fdd\u7559\u4e86\u6a21\u578b\u5728\u5206\u5e03\u5916\u4efb\u52a1\u4e0a\u7684\u6cdb\u5316\u80fd\u529b\u3002\u56e0\u6b64\uff0cCPPO \u4e0d\u4ec5\u5728\u589e\u5f3a\u63a8\u7406\u80fd\u529b\u65b9\u9762\u5339\u654c\u751a\u81f3\u8d85\u8d8a\u4e86 GRPO\uff0c\u800c\u4e14\u8fd8\u5f88\u597d\u5730\u51cf\u5c11\u4e86\u8bad\u7ec3\u65f6\u95f4\uff0c\u4f7f\u5176\u6210\u4e3a\u4e00\u79cd\u66f4\u6709\u6548\u7684\u66ff\u4ee3\u65b9\u6848\u3002<\/p>\n<p>\u8be5\u56e2\u961f\u4e5f\u7814\u7a76\u4e86 CPPO \u7684\u7a33\u5b9a\u6027\u548c\u6536\u655b\u6027\u3002\u56fe 4 \u5c55\u793a\u4e86\u5728 GSM8K \u548c MATH \u6570\u636e\u96c6\u4e0a\u8bad\u7ec3\u65f6\u7684\u5956\u52b1\u66f2\u7ebf\u3002<\/p>\n<section><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-b5547d0a024bc437e51961163bc0950e.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2025\/04\/frc-b5547d0a024bc437e51961163bc0950e.png\"><\/a><\/section>\n<p>\u603b\u4f53\u800c\u8a00\uff0c\u5956\u52b1\u66f2\u7ebf\u8bc1\u660e CPPO \u5728\u63d0\u9ad8\u6536\u655b\u901f\u5ea6\u7684\u540c\u65f6\u53ef\u4fdd\u8bc1 GRPO \u7684\u8bad\u7ec3\u7a33\u5b9a\u6027\uff1aCPPO 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