{"id":2337,"date":"2025-01-15T14:37:36","date_gmt":"2025-01-15T06:37:36","guid":{"rendered":"https:\/\/www.15zhi.net\/blog\/?p=2337"},"modified":"2025-01-15T14:50:57","modified_gmt":"2025-01-15T06:50:57","slug":"202501-%e8%ae%ba%e6%96%87%e7%a0%94%e8%af%bb-online-minimax-q-network-learning-for-two-player-zero-sum-markov-games","status":"publish","type":"post","link":"https:\/\/www.15zhi.net\/blog\/202501-%e8%ae%ba%e6%96%87%e7%a0%94%e8%af%bb-online-minimax-q-network-learning-for-two-player-zero-sum-markov-games\/","title":{"rendered":"202501 \u8bba\u6587\u7814\u8bfb-Online Minimax Q Network Learning for Two-Player Zero-Sum Markov Games"},"content":{"rendered":"\n<p>\u6765\u6e90\uff1aIEEE Transactions on Neural Networks and Learning Systems\u00a0<\/p>\n\n\n\n<p>\u4f5c\u8005\uff1aYuanHeng Zhu, Dongbin Zhao<\/p>\n\n\n\n<p>\u5355\u4f4d\uff1a\u4e2d\u56fd\u79d1\u5b66\u9662\u81ea\u52a8\u5316\u7814\u7a76\u6240<\/p>\n\n\n\n<p>\u65f6\u95f4\uff1a2020<\/p>\n\n\n\n<p><strong>\u4e00\u3001\u80cc\u666f<\/strong><\/p>\n\n\n\n<p>\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\uff08MDP\uff09\u662f\u63cf\u8ff0\u667a\u80fd\u4f53\u4e0e\u73af\u5883\u4e4b\u95f4\u4ea4\u4e92\u8fc7\u7a0b\u7684\u5e38\u7528\u5de5\u5177\u3002\u8fd1\u5e74\u6765\uff0c\u57fa\u4e8eMDP\u7684\u5f3a\u5316\u5b66\u4e60\uff08RL\uff09\u5728\u89e3\u51b3\u5355\u667a\u80fd\u4f53\u6700\u4f18\u51b3\u7b56\u95ee\u9898\u65b9\u9762\u5f97\u5230\u4e86\u5145\u5206\u53d1\u5c55\u3002\u7136\u800c\uff0c\u5728\u8bb8\u591a\u73b0\u5b9e\u573a\u666f\u4e2d\uff0c\u540c\u4e00\u73af\u5883\u4e2d\u5b58\u5728\u591a\u4e2a\u667a\u80fd\u4f53\u5e76\u5171\u540c\u5f71\u54cd\u7cfb\u7edf\u7684\u6f14\u5316\u3002 <\/p>\n\n\n\n<p>\u9a6c\u5c14\u53ef\u592b\u535a\u5f08 (MG)\u88ab\u89c6\u4e3a MDP \u5bf9\u535a\u5f08\u573a\u666f\u7684\u6269\u5c55\u3002\u5728 MG \u4e2d\uff0c\u591a\u4e2a\u4ee3\u7406\u505a\u51fa\u4e00\u7cfb\u5217\u51b3\u7b56\u4ee5\u6700\u5927\u5316\u5171\u540c\u6216\u4e2a\u4eba\u5229\u76ca\u3002\u4e24\u4eba\u96f6\u548c\u535a\u5f08\uff08TZMG\uff09\u662f\u5176\u4e2d\u4e00\u79cd\u7279\u6b8a\u60c5\u51b5\uff0c\u5176\u5305\u62ec\u4e24\u4e2a\u5229\u76ca\u5b8c\u5168\u76f8\u53cd\u7684\u53c2\u4e0e\u8005\u3002<\/p>\n\n\n\n<p>TZMG\u53ef\u63cf\u8ff0\u4e3a\u4e00\u4e2a\u516d\u5143\u7ec4\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"345\" height=\"57\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-81.png\" alt=\"\" class=\"wp-image-2356\" style=\"width:157px;height:auto\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-81.png 345w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-81-300x50.png 300w\" sizes=\"auto, (max-width: 345px) 100vw, 345px\" \/><\/figure>\n\n\n\n<p>\u5176\u4e2d\uff0cS\u662f\u6e38\u620f\u72b6\u6001\u96c6\uff0cA\u662f\u52a8\u4f5c\u96c6\uff0cP\u662f\u72b6\u6001\u8f6c\u79fb\u51fd\u6570\uff0cR\u662f\u5956\u52b1\u51fd\u6570\uff0c\u03b3\u662f\u6298\u6263\u56e0\u5b50\uff0c\u6b64\u5916\uff0c\u76f8\u8f83\u4e8e\u4f20\u7edf\u7684\u9a6c\u5c14\u53ef\u592b\u4e94\u5143\u7ec4\uff0cTZMG\u589e\u52a0\u4e86\u53e6\u5916\u4e00\u4e2a\u73a9\u5bb6\u7684\u52a8\u4f5c\u96c6O\u3002\u5728\u6bcf\u4e00\u6b65\uff0c\u4e24\u540d\u73a9\u5bb6\u5728\u535a\u5f08\u4e2d\u540c\u65f6\u51b3\u5b9a\u5e76\u6267\u884c\u4ed6\u4eec\u7684\u52a8\u4f5c\uff0c\u65b0\u72b6\u6001\u6ee1\u8db3\u5206\u5e03\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"277\" height=\"54\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-82.png\" alt=\"\" class=\"wp-image-2357\" style=\"width:144px;height:auto\"\/><\/figure>\n\n\n\n<p>\u5b83\u4eec\u5171\u4eab\u76f8\u540c\u7684\u5956\u52b1\u51fd\u6570\uff0c\u4f46\u4e00\u4e2a\u7684\u76ee\u6807\u662f\u6700\u5927\u5316\u672a\u6765\u5956\u52b1\u7684\u603b\u548c\uff0c\u800c\u53e6\u4e00\u4e2a\u5219\u6700\u5c0f\u5316\u5b83\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"286\" height=\"36\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-83.png\" alt=\"\" class=\"wp-image-2358\" style=\"width:177px;height:auto\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"268\" height=\"106\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-84.png\" alt=\"\" class=\"wp-image-2359\" style=\"width:152px;height:auto\"\/><\/figure>\n\n\n\n<p>\u73b0\u6709\u7684\u7814\u7a76\u5bf9\u56de\u5408\u5236\u6e38\u620f\u7ed9\u4e88\u4e86\u8f83\u591a\u5173\u6ce8\uff0c\u5e76\u53d6\u5f97\u4e86\u8f83\u5927\u8fdb\u5c55\u3002\u5728\u8fd9\u4e9b\u6e38\u620f\u4e2d\uff0c\u73a9\u5bb6\u4e00\u4e2a\u63a5\u4e00\u4e2a\u5730\u505a\u51fa\u51b3\u5b9a\uff0c\u56e0\u6b64\u73a9\u5bb6\u603b\u662f\u77e5\u9053\u53e6\u4e00\u65b9\u7684\u884c\u52a8\u3002\u800c\u4e0e\u56de\u5408\u5236\u6e38\u620f\u76f8\u6bd4\uff0c\u540c\u6b65\u6e38\u620f\u9700\u8981\u53cc\u65b9\u540c\u65f6\u505a\u51fa\u51b3\u5b9a\u3002 \u73a9\u5bb6\u4e0d\u77e5\u9053\u5bf9\u624b\u7684\u5373\u65f6\u51b3\u7b56\uff0c\u56e0\u6b64\u51b3\u7b56\u7b56\u7565\u53ef\u80fd\u4f1a\u66f4\u52a0\u68d8\u624b\u548c\u4e0d\u53ef\u9884\u6d4b\u3002\u6587\u7ae0\u5373\u901a\u8fc7\u7814\u7a76\u8fd9\u79cd\u7c7b\u578b\u7684 TZMG\uff0c\u7ed9\u51fa\u4e86\u6781\u5c0f\u6781\u5927Q\u7f51\u7edc\u7b97\u6cd5\u3002<\/p>\n\n\n\n<p><strong>\u4e8c\u3001\u8d21\u732e<\/strong><\/p>\n\n\n\n<p>\u63d0\u51fa\u4e86\u6781\u5c0f\u6781\u5927 Q \u7f51\u7edc\uff08M2QN\uff09\u7b97\u6cd5\uff0c\u4ee5\u65e0\u6a21\u578b\u7684\u65b9\u5f0f\u5728\u7ebf\u5b66\u4e60\u7eb3\u4ec0\u5747\u8861\u3002      \u7279\u70b9\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u8be5\u7b97\u6cd5\u6e90\u4e8e\u5e7f\u4e49\u7b56\u7565\u8fed\u4ee3\uff08GPI\uff09\uff0c\u5e76\u4e0eDRL\u6280\u672f\u76f8\u7ed3\u5408\uff0c\u4ee5\u6539\u5584\u5b66\u4e60\u8fc7\u7a0b\u3002<\/li>\n<\/ol>\n\n\n\n<p>2. Q\u51fd\u6570\u4e0e\u795e\u7ecf\u7f51\u7edc\uff08NN\uff09\u76f8\u7ed3\u5408\uff0c\u4ee5\u89e3\u51b3\u5927\u89c4\u6a21\u72b6\u6001\u7a7a\u95f4\u95ee\u9898\uff0c\u5e76\u7528\u535a\u5f08\u6570\u636e\u8bad\u7ec3\u53ef\u5b66\u4e60\u7684\u6743\u91cd\u3002<\/p>\n\n\n\n<p>3. \u5f15\u5165\u7ecf\u9a8c\u56de\u653e\u4ee5\u63d0\u9ad8\u6570\u636e\u6548\u7387\u5e76\u52a0\u5feb\u5b66\u4e60\u8fc7\u7a0b\u3002<\/p>\n\n\n\n<p>\u4e0eself-play\u7b97\u6cd5\u76f8\u6bd4\uff0cM2QN\u7684\u4f18\u70b9\u662f\u6536\u655b\u5230\u7eb3\u4ec0\u5747\u8861\u7684\u7406\u8bba\u57fa\u7840\u4ee5\u53ca\u5bf9\u5bf9\u79f0\u548c<strong>\u975e\u5bf9\u79f0\u535a\u5f08<\/strong>\u7684\u9002\u7528\u6027\u3002<\/p>\n\n\n\n<p><strong>\u4e09\u3001\u65b9\u6cd5<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u7eb3\u4ec0\u5747\u8861<\/li>\n<\/ol>\n\n\n\n<p>\u5728MGs\u4e2d\uff0c\u6ca1\u6709\u4e00\u4e2a\u53c2\u4e0e\u8005\u7684\u7b56\u7565\u603b\u662f\u6700\u4f18\u7684\uff0c\u56e0\u4e3a\u5176\u56de\u62a5\u53d6\u51b3\u4e8e\u5176\u4ed6\u884c\u4e3a\u3002\u8861\u91cf\u4e00\u4e2a\u73a9\u5bb6\u76f8\u5bf9\u4e8e\u5176\u4ed6\u73a9\u5bb6\u8868\u73b0\u7684\u4e24\u4e2a\u8457\u540d\u6982\u5ff5\u662f\u6700\u4f73\u5e94\u5bf9\u548c\u7eb3\u4ec0\u5747\u8861\u3002\u7ed9\u5b9a\u5df1\u65b9\u7b56\u7565\u03c0\uff0c\u5bf9\u65b9\u7b56\u7565\u03bc\uff0c\u5219\u7eb3\u4ec0\u5747\u8861\u5bf9\u5e94\u4e8e\u4e00\u5bf9\uff08\u03c0\u2217,\u03bc\u2217)\u8fd9\u4e24\u8005\u90fd\u662f\u5bf9\u5f7c\u6b64\u6700\u597d\u7684\u56de\u5e94\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"590\" height=\"44\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-85.png\" alt=\"\" class=\"wp-image-2360\" style=\"width:429px;height:auto\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-85.png 590w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-85-300x22.png 300w\" sizes=\"auto, (max-width: 590px) 100vw, 590px\" \/><\/figure>\n\n\n\n<p>\u5728TZMGs\u4e2d\uff0c\u603b\u662f\u5b58\u5728\u7eb3\u4ec0\u5747\u8861\uff0c\u5b83\u7b49\u4ef7\u4e8e\u6781\u5927\u6781\u5c0f\u89e3\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"656\" height=\"57\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-86.png\" alt=\"\" class=\"wp-image-2361\" style=\"width:439px;height:auto\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-86.png 656w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-86-300x26.png 300w\" sizes=\"auto, (max-width: 656px) 100vw, 656px\" \/><\/figure>\n\n\n\n<p>\u7eb3\u4ec0\u5747\u8861\u89c4\u5b9a\u4e86\u73a9\u5bb6\u5728\u6700\u5dee\u7684\u5bf9\u624b\u9762\u524d\u53ef\u4ee5\u83b7\u5f97\u7684\u6700\u5927\u56de\u62a5\uff0c\u5f53\u6211\u4eec\u4e0d\u77e5\u9053\u5bf9\u624b\u6216\u5bf9\u624b\u662f\u4e00\u4e2a\u53ef\u5b66\u4e60\u7684\u4e3b\u4f53\u5e76\u6839\u636e\u6211\u4eec\u7684\u7b56\u7565\u66f4\u65b0\u5176\u884c\u4e3a\u65f6\uff0c\u7eb3\u4ec0\u5747\u8861\u662f\u6709\u610f\u4e49\u7684\u3002<\/p>\n\n\n\n<p>2. \u6781\u5927\u6781\u5c0f\u503c\u65b9\u7a0b<\/p>\n\n\n\n<p>\u72b6\u6001\u4ef7\u503c-\u8d1d\u5c14\u66fc\u6781\u5927\u6781\u5c0f\u65b9\u7a0b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"622\" height=\"175\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-87.png\" alt=\"\" class=\"wp-image-2362\" style=\"width:427px;height:auto\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-87.png 622w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-87-300x84.png 300w\" sizes=\"auto, (max-width: 622px) 100vw, 622px\" \/><\/figure>\n\n\n\n<p>\u52a8\u4f5c\u4ef7\u503c-\u8d1d\u5c14\u66fc\u6781\u5927\u6781\u5c0f\u65b9\u7a0b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"567\" height=\"127\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-88.png\" alt=\"\" class=\"wp-image-2363\" style=\"width:433px;height:auto\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-88.png 567w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-88-300x67.png 300w\" sizes=\"auto, (max-width: 567px) 100vw, 567px\" \/><\/figure>\n\n\n\n<p>3. \u7ebf\u6027\u89c4\u5212\u6c42\u89e3\u6781\u5c0f\u6781\u5927\u65b9\u7a0b<\/p>\n\n\n\n<p>\u5728Q\u503c\u786e\u5b9a\u540e\uff0c\u7eb3\u4ec0\u5747\u8861\u7684\u7b56\u7565\u03c0*\u7531\u4e0b\u5f0f\u7ed9\u51fa\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"452\" height=\"62\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-89.png\" alt=\"\" class=\"wp-image-2364\" style=\"width:423px;height:auto\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-89.png 452w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-89-300x41.png 300w\" sizes=\"auto, (max-width: 452px) 100vw, 452px\" \/><\/figure>\n\n\n\n<p>\u5c06\u5176\u8f6c\u5316\u4e3a\u7ebf\u6027\u89c4\u5212\u6a21\u578b\uff0c\u6709\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"408\" height=\"149\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-90.png\" alt=\"\" class=\"wp-image-2365\" style=\"width:392px;height:auto\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-90.png 408w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-90-300x110.png 300w\" sizes=\"auto, (max-width: 408px) 100vw, 408px\" \/><\/figure>\n\n\n\n<p>4. \u52a8\u6001\u89c4\u5212\u6c42\u89e3\u8d1d\u5c14\u66fc\u4f60\u6781\u5c0f\u6781\u5927\u65b9\u7a0b\uff1a<\/p>\n\n\n\n<p>\u9884\u5148\u5b9a\u4e49\u4e24\u4e2a\u64cd\u4f5c\u7b26\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"666\" height=\"308\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-91.png\" alt=\"\" class=\"wp-image-2366\" style=\"width:400px;height:auto\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-91.png 666w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-91-300x139.png 300w\" sizes=\"auto, (max-width: 666px) 100vw, 666px\" \/><\/figure>\n\n\n\n<p>\u7b2c\u4e00\u4e2a\u5f0f\u5b50T\u901a\u8fc7\u6781\u5927\u6781\u5c0f\u8ba1\u7b97\u4e0b\u4e00\u6b65\u7684\u503c\u3002\u7b2c\u4e8c\u4e2aT\u03c0\u9075\u5faa\u7ed9\u5b9a\u7684\u81ea\u5df1\u7684\u7b56\u7565\u03c0\uff0c\u4f7f\u5bf9\u624b\u52a8\u4f5c\u96c6\u7684\u4e0b\u4e00\u6b65\u503c\u6700\u5c0f\u5316\uff0c\u56e0\u6b64\u53ef\u4ee5\u5c06\u5176\u770b\u4f5c\u5177\u6709\u4e8c\u4ebaQ\u503c\u7684\u6700\u5c0f\u5316Bellman\u6700\u4f18\u65b9\u7a0b\u3002\u4e24\u4e2a\u5f0f\u5b50\u5177\u6709\u76f8\u540c\u6027\u8d28\uff1a<\/p>\n\n\n\n<p>  \uff081\uff09\u5355\u8c03\u548c\u03b3-\u6536\u7f29\u7b97\u5b50<\/p>\n\n\n\n<p>  \uff082\uff09\u5177\u6709\u552f\u4e00\u7684\u56fa\u5b9a\u70b9<\/p>\n\n\n\n<p>5.\u4ef7\u503c\u8fed\u4ee3\u4e0e\u7b56\u7565\u8fed\u4ee3<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"159\" height=\"43\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-92.png\" alt=\"\" class=\"wp-image-2376\" style=\"width:129px;height:auto\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"203\" height=\"58\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-93.png\" alt=\"\" class=\"wp-image-2377\" style=\"width:191px;height:auto\"\/><\/figure>\n\n\n\n<p>6. \u6781\u5927\u6781\u5c0fQ\u7f51\u7edc\u5b66\u4e60<\/p>\n\n\n\n<p>\u6536\u5230DQN\u7684\u542f\u53d1\uff0c\u4f5c\u8005\u5f15\u5165\u795e\u7ecf\u7f51\u7edc\u6765\u8fd1\u4f3cTZMG\u4e2d\u7684\u590d\u6742Q\u51fd\u6570<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"609\" height=\"865\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-94.png\" alt=\"\" class=\"wp-image-2378\" style=\"width:492px;height:auto\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-94.png 609w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-94-211x300.png 211w\" sizes=\"auto, (max-width: 609px) 100vw, 609px\" \/><\/figure>\n\n\n\n<p><strong>\u56db\u3001\u5b9e\u9a8c<\/strong><\/p>\n\n\n\n<p>\u6587\u7ae0\u4e2d\u5171\u6709\u4e09\u79cd\u5b9e\u9a8c\u573a\u666f\uff0c\u8fd9\u91cc\u5217\u4e3e\u5176\u4e2d\u4e00\u79cd\uff1a<\/p>\n\n\n\n<p>\u975e\u5bf9\u79f0TZMG\u4e0a\u57fa\u4e8enn\u7684M2QN:\u4fdd\u536b\u9886\u571f<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"975\" height=\"551\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-96.png\" alt=\"\" class=\"wp-image-2380\" style=\"width:460px;height:auto\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-96.png 975w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-96-300x170.png 300w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-96-768x434.png 768w\" sizes=\"auto, (max-width: 975px) 100vw, 975px\" \/><\/figure>\n\n\n\n<p>\u7f51\u683c\u4e2d\u6709\u4e00\u4e2a\u5165\u4fb5\u8005\u548c\u4e00\u4e2a\u5b88\u536b\uff0c\u5728\u6bcf\u4e00\u6b65\u4e2d\uff0c\u4ed6\u4eec\u9009\u62e9\u505a\u51fa\u4e00\u4e2a\u52a8\u4f5c\uff1a\u5de6\u3001\u4e0a\u3001\u53f3\u3001\u4e0b\u548c\u505c\u7559\u3002\u5165\u4fb5\u8005\u7684\u76ee\u6807\u662f\u4e00\u4e2a\u6807\u8bb0\u4e3a\u9886\u571f\u7684\u7f51\u683c\u3002\u5982\u679c\u5165\u4fb5\u8005\u5728\u88ab\u6355\u83b7\u4e4b\u524d\u5230\u8fbe\u9886\u571f\uff0c\u6216\u8005\u6355\u83b7\u521a\u597d\u53d1\u751f\u5728\u9886\u571f\u4e0a\uff0c\u5219\u5165\u4fb5\u6210\u529f\u3002\u8b66\u536b\u7684\u76ee\u6807\u662f\u5728\u5c3d\u53ef\u80fd\u8fdc\u7684\u5730\u65b9\u62e6\u622a\u5165\u4fb5\u8005\u3002\u4ee5\u8b66\u536b\u4e3a\u4e2d\u5fc3\u7684\u4e5d\u4e2a\u7262\u623f\u6784\u6210\u4e86\u5176\u6293\u6355\u533a\u57df\u3002\u5f53\u6210\u529f\u5165\u4fb5\u6216\u6355\u83b7\u53d1\u751f\u65f6\uff0c\u6e38\u620f\u7ed3\u675f\u3002\u7136\u540e\uff0c\u5728\u4e0b\u4e00\u8f6e\u4e2d\uff0c\u8b66\u536b\u548c\u5165\u4fb5\u8005\u7684\u4f4d\u7f6e\u88ab\u968f\u673a\u91cd\u7f6e\u3002\u8fd9\u573a\u6bd4\u8d5b\u662f\u4e0d\u5bf9\u79f0\u7684\uff0c\u56e0\u4e3a\u53cc\u65b9\u7403\u5458\u9700\u8981\u5b8c\u5168\u4e0d\u540c\u7684\u7b56\u7565\u3002<\/p>\n\n\n\n<p>\u5b88\u536b\u7684\u5956\u52b1\u51fd\u6570\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"700\" height=\"122\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-98.png\" alt=\"\" class=\"wp-image-2382\" style=\"width:470px;height:auto\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-98.png 700w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-98-300x52.png 300w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/figure>\n\n\n\n<p>\u5176\u4e2d\u7b2c\u4e00\u4e2a\u6761\u4ef6\u9009\u62e9\u8d1f\u503c\u4f5c\u4e3a\u5165\u4fb5\u5956\u52b1\uff0c\u7b2c\u4e8c\u4e2a\u6761\u4ef6\u4f7f\u7528\u5165\u4fb5\u8005\u548c\u9886\u571f\u4e4b\u95f4\u7684\u66fc\u54c8\u987f\u8ddd\u79bb\u4f5c\u4e3a\u6355\u83b7\u5956\u52b1\uff0c\u5373\u5f53\u6355\u83b7\u65f6\uff0c\u5165\u4fb5\u8005\u8ddd\u79bb\u9886\u571f\u8d8a\u8fdc\u5956\u52b1\u8d8a\u5927\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"605\" height=\"610\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-99.png\" alt=\"\" class=\"wp-image-2383\" style=\"width:401px;height:auto\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-99.png 605w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-99-298x300.png 298w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-99-150x150.png 150w\" sizes=\"auto, (max-width: 605px) 100vw, 605px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"601\" height=\"506\" src=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-100.png\" alt=\"\" class=\"wp-image-2384\" style=\"width:418px;height:auto\" srcset=\"https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-100.png 601w, https:\/\/www.15zhi.net\/blog\/wp-content\/uploads\/2025\/01\/image-100-300x253.png 300w\" sizes=\"auto, (max-width: 601px) 100vw, 601px\" \/><\/figure>\n\n\n\n<p><strong>\u4e94\u3001\u7ed3\u8bba\u4e0e\u542f\u53d1<\/strong><\/p>\n\n\n\n<p>\u6587\u7ae0\u4e2d\uff0c\u4f5c\u8005\u5c06\u535a\u5f08\u8bba\u4e0e\u6700\u65b0\u7684DQN\u6280\u672f\u76f8\u7ed3\u5408\uff0c\u6765\u5904\u7406\u9700\u8981\u53cc\u65b9\u540c\u65f6\u51b3\u7b56\u7684TZMG\u3002\u6240\u63d0\u51fa\u7684M2QN\u7b97\u6cd5\u4eceGPI\u53d1\u5c55\u800c\u6765\uff0c\u4e0e\u795e\u7ecf\u7f51\u7edc\u76f8\u7ed3\u5408\uff0c\u7528\u4e8e\u5927\u89c4\u6a21\u95ee\u9898\u3002\u5b83\u57fa\u4e8e\u65e0\u6a21\u578b\u7684\u65b9\u5f0f\u4ee5\u535a\u5f08\u6570\u636e\u5b66\u4e60\u7eb3\u4ec0\u5747\u8861\uff0c\u9002\u7528\u4e8e\u5bf9\u79f0\u548c\u975e\u5bf9\u79f0\u535a\u5f08\u3002\u5b9e\u9a8c\u793a\u4f8b\u9a8c\u8bc1\u4e86M2QN\u9002\u7528\u4e8e\u5404\u79cdTZMG\u95ee\u9898\u3002<\/p>\n\n\n\n<p>\u5f53\u524d\u7b97\u6cd5\u7684\u4e00\u4e2a\u5c40\u9650\u6027\u662f\u5b83\u53ea\u8003\u8651\u5177\u6709\u6709\u9650\u52a8\u4f5c\u96c6\u7684\u6e38\u620f\u3002MDP\u7684\u4e00\u4e9bDRL\u7b97\u6cd5\uff0c\u5982DDPG\u3001PPO\u548cTRPO\uff0c\u4e3a\u5927\u89c4\u6a21\u52a8\u4f5c\u96c6\u6216\u8fde\u7eed\u52a8\u4f5c\u7a7a\u95f4\u5b9a\u4e49\u4e86\u4e00\u4e2a\u7b56\u7565\u7f51\u7edc\u3002\u5b83\u4eec\u7684\u7b56\u7565\u53c2\u6570\u6839\u636e\u8fd4\u56de\u503c\u6216\u8bc4\u4f30\u503c\u6cbf\u7b56\u7565\u68af\u5ea6\u8fdb\u884c\u8c03\u6574\u3002\u7136\u800c\uff0c\u5f53\u5c06\u8fd9\u4e9b\u7b97\u6cd5\u6269\u5c55\u5230TZMG\u65f6\uff0c\u6700\u5927\u7684\u56f0\u96be\u662f\u4f30\u8ba1\u51c6\u786e\u7684\u7b56\u7565\u68af\u5ea6\u3002\u5728MG\u4e2d\uff0c\u4e00\u4e2a\u73a9\u5bb6\u7b56\u7565\u7684\u503c\u6216\u56de\u62a5\u53d6\u51b3\u4e8e\u5176\u4ed6\u884c\u4e3a\uff0c\u4f7f\u5f97\u7b56\u7565\u68af\u5ea6\u5608\u6742\u4e14\u4e0d\u4e00\u81f4\u3002<\/p>\n\n\n\n<p>\u542f\u53d1\uff1a\u8be5\u7b97\u6cd5\u5bf9\u4f20\u7edf\u7684Minimax Q\u7b97\u6cd5\u8fdb\u884c\u4e86\u6539\u8fdb\uff0c\u5bf9\u4e8e\u975e\u5bf9\u79f0\u6027\u535a\u5f08\u5177\u6709\u9002\u7528\u6027\uff0c\u5728\u5bf9\u6297\u53cc\u65b9\u5177\u6709\u4e0d\u540c\u7684\u52a8\u4f5c\u96c6\u65f6\uff0c\u5177\u6709\u53c2\u8003\u610f\u4e49\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6765\u6e90\uff1aIEEE Transactions on Neural Networks and Learning Sy [&hellip;]<\/p>\n","protected":false},"author":64,"featured_media":0,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2337","post","type-post","status-publish","format-standard","hentry","category-events"],"_links":{"self":[{"href":"https:\/\/www.15zhi.net\/blog\/wp-json\/wp\/v2\/posts\/2337","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.15zhi.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.15zhi.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.15zhi.net\/blog\/wp-json\/wp\/v2\/users\/64"}],"replies":[{"embeddable":true,"href":"https:\/\/www.15zhi.net\/blog\/wp-json\/wp\/v2\/comments?post=2337"}],"version-history":[{"count":6,"href":"https:\/\/www.15zhi.net\/blog\/wp-json\/wp\/v2\/posts\/2337\/revisions"}],"predecessor-version":[{"id":2387,"href":"https:\/\/www.15zhi.net\/blog\/wp-json\/wp\/v2\/posts\/2337\/revisions\/2387"}],"wp:attachment":[{"href":"https:\/\/www.15zhi.net\/blog\/wp-json\/wp\/v2\/media?parent=2337"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.15zhi.net\/blog\/wp-json\/wp\/v2\/categories?post=2337"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.15zhi.net\/blog\/wp-json\/wp\/v2\/tags?post=2337"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}