{"id":11822,"date":"2018-10-10T01:00:00","date_gmt":"2018-10-09T17:00:00","guid":{"rendered":"http:\/\/swarma.org\/%e8%ae%ba%e6%96%87%e8%a7%a3%e8%af%bb%ef%bc%9a%e8%be%9b%e6%a2%af%e5%ba%a6%e4%bc%98%e5%8c%96-%e5%a4%9a%e4%ba%ba%e5%8d%9a%e5%bc%88%e7%ba%b3%e4%bb%80%e5%9d%87%e8%a1%a1%e7%9a%84%e5%85%a8\/"},"modified":"2018-12-05T13:43:51","modified_gmt":"2018-12-05T05:43:51","slug":"%e8%ae%ba%e6%96%87%e8%a7%a3%e8%af%bb%ef%bc%9a%e8%be%9b%e6%a2%af%e5%ba%a6%e4%bc%98%e5%8c%96-%e5%a4%9a%e4%ba%ba%e5%8d%9a%e5%bc%88%e7%ba%b3%e4%bb%80%e5%9d%87%e8%a1%a1%e7%9a%84%e5%85%a8","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=11822","title":{"rendered":"\u8bba\u6587\u89e3\u8bfb\uff1a\u8f9b\u68af\u5ea6\u4f18\u5316\u2014\u2014\u591a\u4eba\u535a\u5f08\u7eb3\u4ec0\u5747\u8861\u7684\u5168\u65b0\u89e3\u6cd5"},"content":{"rendered":"
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\"\u96c6\u667a\"<\/div>\n

\u00a9borealisai <\/span><\/strong><\/span><\/p>\n

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\u5bfc\u8bed<\/span><\/strong><\/span><\/section>\n
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\u8bba\u6587 “The Mechanics of n-Player Differentiable Games” \u8363\u83b7\u673a\u5668\u5b66\u4e60\u9876\u4f1a ICML 2018 \u6700\u4f73\u8bba\u6587\u63d0\u540d\u5956\uff0c\u5b83\u521b\u65b0\u6027\u5730\u63d0\u51fa\u4e00\u79cd\u53ef\u4ee5\u5728\u666e\u901a\u535a\u5f08\u4e2d\u5bfb\u627e\u7a33\u5b9a\u4e0d\u52a8\u70b9\u7684\u7b97\u6cd5\u2014\u2014\u8f9b\u68af\u5ea6\u8c03\u8282\u7b97\u6cd5\uff08SGA\uff09\uff0c\u8be5\u7b97\u6cd5\u4e0e\u8fd1\u671f\u63d0\u51fa\u7684\u5728GANs\u4e2d\u5bfb\u627e\u7a33\u5b9a\u4e0d\u52a8\u70b9\u7684\u7b97\u6cd5\u6709\u540c\u6837\u4f18\u79c0\u7684\u8868\u73b0\uff0c\u5e76\u4e14\u9002\u7528\u4e8e\u66f4\u666e\u904d\u7684\u535a\u5f08\u95ee\u9898\u5e76\u4fdd\u8bc1\u6536\u655b\u6027\u3002<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u4ece\u591a\u6a21\u578b<\/strong><\/span><\/p>\n

\u4f18\u5316\u95ee\u9898\u5230\u591a\u73a9\u5bb6\u535a\u5f08<\/span><\/strong><\/span><\/p>\n

<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n

\u8fd1\u5e74\u6765\uff0c\u673a\u5668\u5b66\u4e60\u7684\u8fdb\u5c55\u5f88\u5927\u7a0b\u5ea6\u4e0a\u4f9d\u8d56\u4e8e\u68af\u5ea6\u4e0b\u964d\u7684\u4f7f\u7528\uff0c\u68af\u5ea6\u4e0b\u964d\u4f7f\u5f97\u4e00\u4e2a\u76ee\u6807\u6700\u7ec8\u53ef\u4ee5\u6536\u655b\u5230\u67d0\u4e2a\u5c40\u90e8\u6700\u5c0f\u503c\uff0c\u4ece\u800c\u4f18\u5316\u6a21\u578b\u53c2\u6570\u3002\u7136\u800c\u8d8a\u6765\u8d8a\u591a\u7684\u6a21\u578b\u9700\u8981\u4f18\u5316\u591a\u4e2a\u76ee\u6807\uff0c\u5982\u751f\u6210\u5bf9\u6297\u7f51\u7edc\u3001\u5206\u5c42\u5f3a\u5316\u5b66\u4e60\u3001\u5408\u6210\u68af\u5ea6\u7b49\u3002<\/span><\/p>\n

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\u751f\u6210\u5bf9\u6297\u7f51\u7edc\uff1agenerative adversarial networks<\/span><\/p>\n

\u5206\u5c42\u5f3a\u5316\u5b66\u4e60\uff1ahierarchical reinforcement learning<\/span><\/p>\n

\u5408\u6210\u68af\u5ea6\uff1asynthetic gradients<\/span><\/p>\n<\/blockquote>\n

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\u601d\u8003\u8fd9\u7c7b\u95ee\u9898\u7684\u6b63\u786e\u65b9\u6cd5\u662f\u2014\u2014\u5c06\u5b83\u4eec\u89e3\u91ca\u4e3a\u535a\u5f08\u8bba\u95ee\u9898\uff0c\u89e3\u51b3\u8fd9\u4e9b\u95ee\u9898\u5c31\u662f\u8981\u627e\u5230\u6bcf\u4e2a\u76ee\u6807\u7684\u7eb3\u4ec0\u5747\u8861\u800c\u4e0d\u662f\u5c40\u90e8\u6700\u5c0f\u503c\u3002<\/strong><\/span><\/p>\n

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\u76ee\u524d\u5728\u535a\u5f08\u4e2d\u4f7f\u7528\u57fa\u4e8e\u68af\u5ea6\u7684\u65b9\u6cd5\u5e76\u6ca1\u6709\u5f97\u5230\u5f88\u597d\u7684\u7814\u7a76\u3002<\/span><\/p>\n

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\u68af\u5ea6\u4e0b\u964d\u7b49\u65e0\u6094\u7b97\u6cd5\u80fd\u4f7f\u535a\u5f08\u4e2d\u7684\u76ee\u6807\u6536\u655b\u5230\u4e00\u4e2a\u8fd1\u4f3c\u7684\u76f8\u5173\u5747\u8861\uff08coarse correlated equilibria\uff09,\u4f46\u662f\u5176\u52a8\u529b\u5b66\u8ba1\u7b97\u4e0d\u80fd\u6536\u655b\u5230\u7eb3\u4ec0\u5747\u8861\uff08Nash equilibria\uff09\uff0c\u751a\u81f3\u4e0d\u80fd\u7a33\u5b9a\u4e0b\u6765\u3002\u5df2\u6709\u7684\u7528\u4e8e\u627e\u5230\u7a33\u5b9a\u4e0d\u52a8\u70b9\u7684\u7b97\u6cd5\u4e5f\u5c40\u9650\u4e8e\u4e24\u4e2a\u73a9\u5bb6\u7684\u535a\u5f08\uff0c\u8fd8\u4e0d\u80fd\u5e94\u7528\u5230\u591a\u73a9\u5bb6\u7684\u666e\u901a\u535a\u5f08\u4e2d\u3002<\/span><\/p>\n

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\u968f\u7740\u5bf9\u6297\u6027\u4ee5\u53ca\u591a\u76ee\u6807\u7684\u6a21\u578b\u67b6\u6784\u7684\u53d1\u5c55\uff0c\u8fd9\u65b9\u9762\u7684\u7814\u7a76\u5c06\u53d8\u5f97\u8d8a\u6765\u8d8a\u91cd<\/span>\u8981\u3002<\/p>\n

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\u8d85\u8d8aGAN\u7684<\/strong><\/span><\/p>\n

\u8f9b\u68af\u5ea6\u6761\u4ef6\u7b97\u6cd5\uff08SGA\uff09<\/span><\/strong><\/span><\/p>\n

<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n

\u5728\u8fd9\u7bc7\u8bba\u6587\u4e2d\uff0c\u4f5c\u8005\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u65b9\u6cd5\u6765\u7406\u89e3\u4e0e\u63a7\u5236\u666e\u901a\u535a\u5f08\u4e2d\u7684\u52a8\u529b\u5b66\uff0c\u5176\u5173\u952e\u6210\u679c\u662f\u628a\u4e8c\u9636\u52a8\u529b\u5b66\u5206\u89e3\u4e3a\u4e24\u4e2a\u90e8\u5206\u3002<\/span><\/p>\n

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\u7b2c\u4e00\u90e8\u5206\u4e0e\u6f5c\u535a\u5f08\uff08potential games\uff09\u6709\u5173\uff0c\u5b83\u968f\u7740\u9690\u5f0f\u51fd\u6570\u68af\u5ea6\u4e0b\u964d\u800c\u51cf\u5c0f\uff1b\u7b2c\u4e8c\u90e8\u5206\u4e0e\u54c8\u5bc6\u5c14\u987f\u535a\u5f08\uff08Hamiltonian games\uff09\u6709\u5173\uff0c\u8fd9\u662f\u4e00\u7c7b\u65b0\u7684\u9075\u5faa\u5b88\u6052\u5b9a\u5f8b\u7684\u535a\u5f08\uff0c\u548c\u7ecf\u5178\u673a\u68b0\u7cfb\u7edf\u4e2d\u7684\u5b88\u6052\u5b9a\u5f8b\u7c7b\u4f3c\u3002<\/span><\/p>\n

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\u8fd9\u79cd\u5206\u89e3\u542f\u53d1\u4f5c\u8005\u63d0\u51fa\u4e86\u8f9b\u68af\u5ea6\u8c03\u8282\u7b97\u6cd5\uff08Symplectic Gradient Adjustment\uff0c SGA\uff09\uff0c\u8fd9\u662f\u4e00\u79cd\u53ef\u4ee5\u5728\u666e\u901a\u535a\u5f08\u4e2d\u5bfb\u627e\u7a33\u5b9a\u4e0d\u52a8\u70b9\u7684\u65b0\u7b97\u6cd5\u3002\u5927\u91cf\u57fa\u7840\u6027\u5b9e\u9a8c\u8868\u660e\uff0cSGA\u4e0e\u8fd1\u671f\u63d0\u51fa\u7684\u5728GANs\u4e2d\u5bfb\u627e\u7a33\u5b9a\u4e0d\u52a8\u70b9\u7684\u7b97\u6cd5\u6709\u540c\u6837\u4f18\u79c0\u7684\u8868\u73b0\uff0c\u5e76\u4e14\u9002\u7528\u4e8e\u66f4\u666e\u904d\u7684\u535a\u5f08\u95ee\u9898\u5e76\u4fdd\u8bc1\u6536\u655b\u6027\u3002<\/span><\/p>\n

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\u5728GANs\u4e2d\u5bfb\u627e\u7a33\u5b9a\u4e0d\u52a8\u70b9\u7684\u7b97\u6cd5\u5305\u62ec\u68af\u5ea6\u4e0b\u964d\uff08gradient descent\uff09\u3001\u4e50\u89c2\u955c\u50cf\u4e0b\u964d\uff08optimistic mirror descent, OMD\uff09\u3001\u540c\u65f6\u68af\u5ea6\u4e0b\u964d\uff08simultaneous gradient descent\uff09\u7b49\u7b49\uff0c\u76f8\u6bd4\u4e4b\u4e0b\uff0cSGA \u66f4\u5177\u7ade\u4e89\u529b\uff0c\u4e0d\u4ec5\u80fd\u591f\u5feb\u901f\u627e\u5230\u7a33\u5b9a\u4e0d\u52a8\u70b9\uff0c\u8fd8\u80fd\u591f\u5e94\u7528\u5230\u591a\u73a9\u5bb6\u535a\u5f08\u95ee\u9898\u3002<\/strong><\/strong><\/span><\/p>\n<\/p>\n

\"\u96c6\u667a\"<\/div>\n

\u56fe1<\/span><\/strong><\/span><\/p>\n

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\u7531\u56fe1\u53ef\u77e5\uff0c\u68af\u5ea6\u4e0b\u964d\u5bf9\u5b66\u4e60\u7387\u7684\u9009\u62e9\u5f88\u654f\u611f\uff0c\u5b66\u4e60\u7387\u4e3a0.01\u65f6\u7f13\u6162\u6536\u655b\uff0c\u5b66\u4e60\u7387\u4e3a0.032\u65f6\u7f13\u6162\u53d1\u6563\uff0c\u5b66\u4e60\u7387\u4e3a0.1\u65f6\u5feb\u901f\u53d1\u6563\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0cSGA\u80fd\u591f\u66f4\u5feb\u3001\u66f4\u9c81\u68d2\u5730\u6536\u655b\uff0c\u53ea\u6709\u5728\u5b66\u4e60\u7387\u4e3a0.1\u65f6\uff0c\u8d77\u59cb\u9636\u6bb5\u7a0d\u5fae\u504f\u79bb\u7a33\u5b9a\u4e0d\u52a8\u70b9\uff0c\u4f46\u5f88\u5feb\u5c31\u8c03\u6574\u8fc7\u6765\uff0c\u8d8b\u5411\u7a33\u5b9a\u4e0d\u52a8\u70b9\u6536\u655b\u3002<\/span><\/p>\n

\"\u96c6\u667a\"<\/div>\n

\u56fe2<\/span><\/strong><\/p>\n<\/p>\n

\u7531\u56fe2\u53ef\u77e5\uff0c\u867d\u7136OMD\u7684\u5cf0\u503c\u8868\u73b0\u6bd4SGA\u597d\uff0c\u4f46\u662f\u5728\u5927\u90e8\u5206\u5b66\u4e60\u7387\u4e0b\uff0cSGA\u66f4\u5feb\u6536\u655b\u3002\u800cOMD\u5728\u5b66\u4e60\u7387\u4e3a[0.3, 1.2]\u4e4b\u5916\u4e0d\u6536\u655b\u3002SGA\u5141\u8bb8\u6211\u4eec\u8bbe\u7f6e\u66f4\u9ad8\u7684\u5b66\u4e60\u7387\uff0c\u4ece\u800c\u4f7f\u76ee\u6807\u66f4\u5feb\u6536\u655b\u3002<\/p>\n<\/p>\n

\"\u96c6\u667a\"<\/div>\n

\u56fe3<\/span><\/strong><\/p>\n<\/p>\n

\u56fe3\u5c55\u793a\u4e86\u7ecf\u8fc72000\u30014000\u30016000\u30018000\u6b21\u8fed\u4ee3\u540e\u7684\u7ed3\u679c\uff0c\u53ef\u4ee5\u770b\u5230\uff0c\u540c\u65f6\u68af\u5ea6\u4e0b\u964d\u4f1a\u51fa\u73b0\u6a21\u5f0f\u5d29\u6e83\u548c\u6a21\u5f0f\u8df3\u8dc3\uff0c\u800c\u6ca1\u6709\u8fdb\u884c\u5bf9\u9f50\u7684SGA\u5e73\u6ed1\u6536\u655b\uff0c\u6709\u8fdb\u884c\u5bf9\u9f50\u7684SGA\u66f4\u5feb\u6536\u655b\u3002\u53ef\u89c1\uff0cSGA\u5728\u6027\u80fd\u4e0a\u4f18\u4e8e\u540c\u65f6\u68af\u5ea6\u4e0b\u964d\uff0c\u5e76\u4e14\u5bf9\u9f50\u8c03\u8282\u7b97\u6cd5\u80fd\u4f7f\u76ee\u6807\u66f4\u5feb\u6536\u655b\u3002<\/span><\/p>\n

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\u5982\u4f55\u5728<\/strong><\/span><\/p>\n

\u666e\u901a\u535a\u5f08\u4e2d\u627e\u5230\u7a33\u5b9a\u4e0d\u52a8\u70b9\uff1f<\/span><\/strong><\/span><\/p>\n

<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n

\u8fd9\u7bc7\u8bba\u6587\u63d0\u51fa\u7684\u65b9\u6cd5\u662f\u5c06\u535a\u5f08\u52a8\u529b\u5b66\u7684\u4e8c\u9636\u7ed3\u6784\u5206\u89e3\u4e3a\u6f5c\u535a\u5f08\u548c\u54c8\u5bc6\u5c14\u987f\u535a\u5f08\uff0c\u7136\u540e\u4f7f\u7528\u8f9b\u68af\u5ea6\u8c03\u8282\u6765\u627e\u5230\u7a33\u5b9a\u4e0d\u52a8\u70b9\u3002<\/span><\/p>\n

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\u5728\u8bba\u6587\u4e2d\uff0c\u4f5c\u8005\u9996\u5148\u5bf9\u535a\u5f08\u95ee\u9898\u8fdb\u884c\u6570\u5b66\u5b9a\u4e49\uff0c\u58f0\u660e\u4e0d\u9650\u5236\u53c2\u6570\u96c6\uff08\u4f8b\u5982\uff0c\u6982\u7387\u5355\u7eaf\u5f62\uff09\uff0c\u4e0d\u8981\u6c42\u635f\u5931\u662f\u51f8\u7684\uff0c\u73a9\u5bb6\u751a\u81f3\u53ef\u4ee5\u901a\u8fc7\u795e\u7ecf\u7f51\u7edc\u8fdb\u884c\u4ea4\u4e92\uff0c\u4f8b\u5982GANs\u3002\u7136\u540e\u4f5c\u8005\u6307\u51fa\u591a\u73a9\u5bb6\u535a\u5f08\u7684\u635f\u5931\u4e0d\u662f\u5355\u4e00\u51fd\u6570\uff0c\u82e5\u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\uff0c\u5176\u52a8\u529b\u5b66\u8ba1\u7b97\u4e0d\u80fd\u6536\u655b\u5230\u4e00\u4e2a\u4e0d\u52a8\u70b9\u3002<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u96f6\u548c\u535a\u5f08\u00a9gnHHbB<\/span><\/strong><\/p>\n<\/p>\n

\u4f5c\u8005\u63a5\u7740\u8ba8\u8bba\u4e86\u8457\u540d\u7684\u96f6\u548c\u53cc\u77e9\u9635\u535a\u5f08\uff08zero-sum bimatrix game\uff09\u95ee\u9898\uff0c\u6307\u660e\u540c\u65f6\u8fdb\u884c\u591a\u4e2a\u76ee\u6807\u68af\u5ea6\u4e0b\u964d\u7684\u52a8\u529b\u5b66\u53ef\u4ee5\u4f7f\u7528\u54c8\u5bc6\u5c14\u987f\u7b49\u5f0f\u91cd\u65b0\u5b9a\u4e49\u3002\u8fd9\u6837\u505a\u7684\u597d\u5904\u662f\uff0c\u54c8\u5bc6\u5c14\u987f\u51fd\u6570\u4e0a\u7684\u68af\u5ea6\u4e0b\u964d\u53ef\u4ee5\u6536\u655b\u5230\u7eb3\u4ec0\u5747\u8861\u3002<\/span><\/p>\n

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\u53cc\u77e9\u9635\u535a\u5f08\uff1a\u5728\u535a\u5f08\u8bba\u4e2d\uff0c\u53cc\u77e9\u9635\u535a\u5f08\u662f\u4e24\u4e2a\u73a9\u5bb6\u540c\u6b65\u8fdb\u884c\u7684\u535a\u5f08\uff0c\u6bcf\u4e2a\u73a9\u5bb6\u6301\u6709\u6709\u9650\u4e2a\u53ef\u80fd\u52a8\u4f5c\u3002\u8fd9\u6837\u535a\u5f08\u80fd\u591f\u7528\u4e24\u4e2a\u77e9\u9635\uff081\u53f7\u73a9\u5bb6\u7684\u6536\u76ca\u77e9\u9635\u548c2\u53f7\u73a9\u5bb6\u7684\u6536\u76ca\u77e9\u9635\uff09\u6765\u63cf\u8ff0\uff0c\u56e0\u6b64\u88ab\u79f0\u4e3a\u53cc\u77e9\u9635\u535a\u5f08\u3002<\/span><\/p>\n<\/blockquote>\n

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\u7eb3\u4ec0\u5747\u8861\uff1a\u4efb\u4f55\u4e00\u65b9\u91c7\u53d6\u7684\u7b56\u7565\u90fd\u662f\u5bf9\u5176\u4f59\u6240\u6709\u65b9\u91c7\u53d6\u7b56\u7565\u7ec4\u5408\u4e0b\u7684\u6700\u4f73\u5bf9\u7b56\uff1b\u5f53\u6240\u6709\u5176\u4ed6\u4eba\u90fd\u4e0d\u6539\u53d8\u7b56\u7565\u65f6\uff0c\u4e3a\u4e86\u8ba9\u81ea\u5df1\u7684\u6536\u76ca\u6700\u5927\uff0c\u4efb\u4f55\u4e00\u65b9\u90fd\u4e0d\u4f1a\uff08\u6216\u8005\u65e0\u6cd5\uff09\u6539\u53d8\u81ea\u5df1\u7684\u7b56\u7565\uff0c\u8fd9\u4e2a\u65f6\u5019\u7684\u7b56\u7565\u7ec4\u5408\u5c31\u662f\u4e00\u4e2a\u7eb3\u4ec0\u5747\u8861\u3002\u5728\u6570\u5b66\u9886\u57df\u4e2d\uff0c\u7eb3\u4ec0\u5747\u8861\u5728\u535a\u5f08\u51fd\u6570\u4e2d\u5c31\u662f\u978d\u70b9\u3002<\/span><\/p>\n<\/blockquote>\n

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\"\u96c6\u667a\"<\/p>\n

\u7eb3\u4ec0\u5747\u8861\u00a9wikipedia<\/span><\/strong><\/p>\n<\/p>\n

\u7136\u540e\u4f5c\u8005\u5bf9Helmholtz\u5206\u89e3\u5b9a\u7406\u8fdb\u884c\u63a8\u5e7f\uff0c\u63a8\u5bfc\u51fa\u4efb\u4f55\u535a\u5f08\u7684Hessian\u77e9\u9635\u90fd\u53ef\u4ee5\u5206\u89e3\u4e3a\u5bf9\u79f0\u77e9\u9635\u548c\u53cd\u5bf9\u79f0\u77e9\u9635\u3002<\/span><\/p>\n

\n

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\n

\u5bf9\u4e8e\u53cc\u77e9\u9635\u95ee\u9898\uff0c\u54c8\u5bc6\u5c14\u987f\u535a\u5f08\u7b49\u4ef7\u4e8e\u96f6\u548c\u535a\u5f08\uff1b\u5bf9\u4e8e\u975e\u7ebf\u6027\u7684\u635f\u5931\u6216\u8005\u591a\u73a9\u5bb6\u53c2\u4e0e\u7684\u95ee\u9898\uff0c\u54c8\u5bc6\u5c14\u987f\u535a\u5f08\u4e0e\u96f6\u548c\u535a\u5f08\u6709\u6240\u533a\u522b\u3002\u4f5c\u8005\u540c\u65f6\u8bc1\u660e\u4e86\u54c8\u5bc6\u5c14\u987f\u535a\u5f08\u9075\u5faa\u5b88\u6052\u5b9a\u5f8b\uff0c\u8fd9\u4f7f\u6211\u4eec\u80fd\u591f\u901a\u8fc7\u5bf9\u5b88\u6052\u91cf\u8fdb\u884c\u68af\u5ea6\u4e0b\u964d\u6765\u89e3\u51b3\u54c8\u5bc6\u5c14\u987f\u535a\u5f08\u3002<\/span><\/p>\n

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Helmholtz\u5206\u89e3\u5b9a\u7406\uff1a\u7a7a\u95f4\u533a\u57df\u4e0a\u7684\u4efb\u610f\u77e2\u91cf\u573a\uff0c\u5982\u679c\u5b83\u7684\u6563\u5ea6\u3001\u65cb\u5ea6\u548c\u8fb9\u754c\u6761\u4ef6\u5df2\u77e5\uff0c\u5219\u8be5\u77e2\u91cf\u573a\u53ef\u4ee5\u8868\u793a\u4e3a\u4e00\u4e2a\u65e0\u6563\u77e2\u91cf\u573a\u548c\u4e00\u4e2a\u65e0\u65cb\u77e2\u91cf\u573a\u7684\u53e0\u52a0\u3002<\/span><\/p>\n<\/blockquote>\n

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\u6f5c\u535a\u5f08\uff1a\u5728\u535a\u5f08\u8bba\u4e2d\uff0c\u5982\u679c\u6240\u6709\u53c2\u4e0e\u8005\u6539\u53d8\u7b56\u7565\u7684\u6fc0\u52b1\u53ef\u4ee5\u4f7f\u7528\u5355\u4e2a\u5168\u5c40\u51fd\u6570\u6765\u8868\u8fbe\uff0c\u5219\u8fd9\u79cd\u535a\u5f08\u88ab\u79f0\u4e3a\u6f5c\u535a\u5f08\uff0c\u8fd9\u4e2a\u5168\u5c40\u51fd\u6570\u88ab\u79f0\u4e3a\u6f5c\u51fd\u6570\u3002\u8fd9\u4e2a\u6982\u5ff5\u8d77\u6e90\u4e8eDov Monderer\u548cLloyd Shapley\u57281996\u5e74\u7684\u4e00\u7bc7\u8bba\u6587\u4e2d\uff08Monderer, Dov; Shapley, Lloyd (1996). “Potential Games”. Games and Economic Behavior. 14: 124\u2013143. doi:10.1006\/game.1996.0044\uff09\u3002<\/span><\/p>\n<\/blockquote>\n

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\u54c8\u5bc6\u5c14\u987f\u535a\u5f08\uff1a\u672c\u6587\u4f5c\u8005\u9996\u6b21\u7ed9\u51fa\u5b9a\u4e49\uff0c\u5e76\u547d\u540d\uff0c\u5176\u6982\u5ff5\u4e0e1992 Lu\u7b49\u4eba\u63d0\u51fa\u7684\u54c8\u5bc6\u5c14\u987f\u6e38\u620f\u4e0d\u540c\u3002\u54c8\u5bc6\u5c14\u987f\u77e9\u9635\u662f\u53cd\u5bf9\u79f0\u77e9\u9635\uff0c\u73a9\u5bb6\u4e4b\u95f4\u7684\u6240\u6709\u6210\u5bf9\u76f8\u4e92\u4f5c\u7528\u90fd\u662f\u96f6\u548c\u7684\u3002<\/span><\/p>\n<\/blockquote>\n

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\"\u96c6\u667a\"SGA\u7b97\u6cd5<\/span><\/strong><\/p>\n<\/p>\n

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\u5e94\u7528\uff1a<\/strong><\/span><\/p>\n

\u89e3\u51b3\u591a\u73a9\u5bb6\u535a\u5f08\u95ee\u9898<\/span><\/strong><\/span><\/p>\n

<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\n

\u5e7f\u4e49Helmholtz\u5206\u89e3\u4e3a\u535a\u5f08\u52a8\u529b\u5b66\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u65b0\u89c6\u89d2\uff0c\u8fd9\u79cd\u5206\u6790\u65b9\u5f0f\u4e0e\u73a9\u5bb6\u6570\u91cf\u65e0\u5173\uff0c\u5b83\u662f\u635f\u5931\u7684\u540c\u65f6\u68af\u5ea6\u4e0e\u4e8c\u9636\u9879\u7684\u5bf9\u79f0\u548c\u53cd\u5bf9\u79f0\u77e9\u9635\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u80fd\u6307\u5bfc\u7b97\u6cd5\u8bbe\u8ba1\u5e76\u63a7\u5236\u68af\u5ea6\u8c03\u6574\u7684\u52a8\u529b\u5b66\u3002<\/span><\/p>\n

\n

\u8f9b\u68af\u5ea6\u8c03\u8282\u7b97\u6cd5\u662fHelmholtz\u5206\u89e3\u7684\u76f4\u63a5\u5e94\u7528\uff0c\u8fd9\u4e0d\u662f\u627e\u5230\u7a33\u5b9a\u4e0d\u52a8\u70b9\u7684\u552f\u4e00\u6216\u6700\u4f73\u65b9\u6cd5\u3002\u6df1\u5165\u7406\u89e3\u6f5c\u5206\u91cf\u548c\u54c8\u5bc6\u5c14\u987f\u5206\u91cf\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u6709\u52a9\u4e8e\u627e\u5230\u66f4\u6709\u6548\u7684\u7b97\u6cd5\uff0c\u7279\u522b\u662f\u4e0d\u4f7f\u7528Hessian\u77e2\u91cf\u79ef\u7684\u7eaf\u4e00\u9636\u65b9\u6cd5\u3002<\/span><\/p>\n

\n

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\u4f5c\u8005\uff1a\u738b\u4f73\u7eaf<\/span><\/p>\n

\u7f16\u8f91\uff1a\u738b\u6021\u853a<\/span><\/p>\n

\u8bba\u6587\u4e0b\u8f7d\uff1a<\/span><\/p>\n

http:\/\/proceedings.mlr.press\/v80\/balduzzi18a\/balduzzi18a.pdf<\/span><\/p>\n

\u8865\u5145\u6750\u6599\uff1a<\/span><\/p>\n

http:\/\/proceedings.mlr.press\/v80\/balduzzi18a\/balduzzi18a-supp.pdf<\/span><\/p>\n<\/blockquote>\n

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\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/span><\/p>\n

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\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/a><\/p>\n<\/p>\n

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\u63a8\u8350\u8bfe\u7a0b<\/span><\/strong><\/span><\/p>\n

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\"\u96c6\u667a\"<\/p>\n

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PC\u7aef\uff1a<\/span><\/p>\n

http:\/\/campus.swarma.org\/gpac=8<\/span><\/p>\n

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\u96c6\u667a\u4ff1\u4e50\u90e8QQ\u7fa4\uff5c877391004<\/span><\/strong><\/p>\n

\u5546\u52a1\u5408\u4f5c\u53ca\u6295\u7a3f\u8f6c\u8f7d\uff5cswarma@swarma.org<\/span><\/strong><\/p>\n

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\u25c6<\/span>\u25c6<\/span>\u25c6<\/span><\/span><\/strong><\/strong><\/h1>\n<\/section>\n

\u641c\u7d22\u516c\u4f17\u53f7\uff1a\u96c6\u667a\u4ff1\u4e50\u90e8<\/span><\/strong><\/span><\/p>\n<\/p>\n

\u52a0\u5165\u201c\u6ca1\u6709\u56f4\u5899\u7684\u7814\u7a76\u6240\u201d<\/span><\/strong><\/span><\/p>\n

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\u8ba9\u82f9\u679c\u7838\u5f97\u66f4\u731b\u70c8\u4e9b\u5427\uff01<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u539f\u6587\u59cb\u53d1\u4e8e\u5fae\u4fe1\u516c\u4f17\u53f7\uff08 \u96c6\u667a\u4ff1\u4e50\u90e8 \uff09\uff1a\u96c6\u667a<\/a><\/p>\n<\/blockquote>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u00a9borealisai \u5bfc\u8bed \u8bba\u6587 “The Mechanics of n-Player Differentiable Games” \u8363\u83b7\u673a\u5668\u5b66\u4e60\u9876\u4f1a ICML 2018 \u6700\u4f73\u8bba\u6587\u63d0\u540d\u5956\uff0c\u5b83\u521b\u65b0\u6027\u5730\u63d0\u51fa\u4e00\u79cd\u53ef\u4ee5\u5728\u666e\u901a\u535a\u5f08\u4e2d\u5bfb\u627e\u7a33\u5b9a\u4e0d\u52a8\u70b9\u7684\u7b97\u6cd5\u2014\u2014\u8f9b\u68af\u5ea6\u8c03\u8282\u7b97\u6cd5\uff08SGA\uff09\uff0c\u8be5\u7b97…<\/p>\n","protected":false},"author":1,"featured_media":11824,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[19,18],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/11822"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11822"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/11822\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/11824"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11822"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11822"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11822"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=11822"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}