{"id":199098,"date":"2024-05-10T00:47:52","date_gmt":"2024-05-09T16:47:52","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/199098.html"},"modified":"2024-05-10T00:48:03","modified_gmt":"2024-05-09T16:48:03","slug":"l-bfgs%e7%ae%97%e6%b3%95%e4%b8%ba%e4%bb%80%e4%b9%88%e5%bf%ab","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/199098.html","title":{"rendered":"L-BFGS\u7b97\u6cd5\u4e3a\u4ec0\u4e48\u5feb"},"content":{"rendered":"

\"L-BFGS\u7b97\u6cd5\u4e3a\u4ec0\u4e48\u5feb\"<\/p>\n

L-BFGS\u7b97\u6cd5\u4e4b\u6240\u4ee5\u5feb\uff0c\u4e3b\u8981\u539f\u56e0\u5728\u4e8e\u5b83\u91c7\u7528\u4e86\u51c6\u725b\u987f\u6cd5\u7684\u6846\u67b6\u3001\u6709\u9650\u5185\u5b58\u7279\u6027\u3001\u6709\u6548\u7684\u66f2\u7387\u4f30\u8ba1\u4ee5\u53ca\u81ea\u9002\u5e94\u7279\u6027<\/strong>\u3002\u51c6\u725b\u987f\u6cd5\u660e\u663e\u52a0\u5feb\u4f18\u5316\u901f\u5ea6\uff0c\u56e0\u4e3a\u5b83\u4f7f\u7528\u66f2\u7387\u4fe1\u606f\u6765\u6539\u8fdb\u641c\u7d22\u65b9\u5411\uff0c\u8fd9\u901a\u5e38\u6bd4\u7b80\u5355\u7684\u68af\u5ea6\u4e0b\u964d\u6cd5\u66f4\u6709\u6548\u3002\u6709\u9650\u5185\u5b58\u7279\u6027\u4f7f\u5f97L-BFGS\u5728\u5904\u7406\u5927\u89c4\u6a21\u95ee\u9898\u65f6\u5185\u5b58\u9700\u6c42\u8f83\u4f4e\uff0c\u56e0\u4e3a\u5b83\u5e76\u4e0d\u9700\u8981\u5b58\u50a8\u6574\u4e2a\u8fd1\u4f3c\u7684Hessian\u77e9\u9635\uff0c\u800c\u53ea\u4fdd\u5b58\u51e0\u4e2a\u6700\u8fd1\u7684\u66f4\u65b0\u5411\u91cf\u3002\u6709\u6548\u7684\u66f2\u7387\u4f30\u8ba1\u5219\u662f\u901a\u8fc7\u4f7f\u7528\u8fd1\u671f\u7684\u8fed\u4ee3\u4fe1\u606f\u6765\u53cd\u6620\u76ee\u6807\u51fd\u6570\u7684\u5c40\u90e8\u66f2\u7387\u7279\u6027\uff0c\u8fd9\u6837\u53ef\u4ee5\u751f\u6210\u66f4\u5408\u7406\u7684\u641c\u7d22\u65b9\u5411\u3002\u81ea\u9002\u5e94\u7279\u6027\u662f\u6307\u7b97\u6cd5\u80fd\u591f\u6839\u636e\u95ee\u9898\u672c\u8eab\u7684\u7279\u70b9\u8c03\u6574\u5176\u53c2\u6570\uff0c\u4ece\u800c\u5728\u4e0d\u540c\u7684\u4f18\u5316\u9636\u6bb5\u4fdd\u6301\u9ad8\u6548\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u51c6\u725b\u987f\u6cd5\u7684\u6846\u67b6<\/h3>\n<\/p>\n

\u51c6\u725b\u987f\u6cd5\u7684\u6838\u5fc3\u5728\u4e8e\u6784\u5efa\u4e00\u4e2a\u76ee\u6807\u51fd\u6570\u7684\u4e8c\u9636\u8fd1\u4f3c\u6a21\u578b<\/strong>\uff0c\u8be5\u6a21\u578b\u4f7f\u7528Hessian\u77e9\u9635\u6216\u5176\u8fd1\u4f3c\u6765\u52a0\u901f\u6c42\u89e3\u3002L-BFGS\u7b97\u6cd5\u4f5c\u4e3a\u4e00\u79cd\u51c6\u725b\u987f\u6cd5\uff0c\u5b83\u91c7\u7528\u4e86\u8fd9\u4e2a\u9ad8\u6548\u6c42\u89e3\u975e\u7ebf\u6027\u4f18\u5316\u95ee\u9898\u7684\u6846\u67b6\u3002<\/p>\n<\/p>\n

\u66f2\u9762\u8fd1\u4f3c\u548c\u641c\u7d22\u65b9\u5411<\/h4>\n<\/p>\n

L-BFGS\u7b97\u6cd5\u901a\u8fc7\u4f30\u8ba1\u76ee\u6807\u51fd\u6570\u7684\u4e8c\u9636Taylor\u5c55\u5f00\u4e2d\u7684Hessian\u77e9\u9635\uff0c\u6765\u6784\u5efa\u4e00\u9636\u548c\u4e8c\u9636\u7684\u8fd1\u4f3c\u66f2\u9762\u3002\u8fd9\u6709\u52a9\u4e8e\u627e\u5230\u4e00\u4e2a\u597d\u7684\u4e0b\u964d\u65b9\u5411\uff0c\u4ece\u800c\u52a0\u5feb\u6536\u655b\u901f\u5ea6\u3002<\/p>\n<\/p>\n

Hessian\u77e9\u9635\u66f4\u65b0<\/h4>\n<\/p>\n

\u5728\u6bcf\u6b21\u8fed\u4ee3\u4e2d\uff0c\u800c\u4e0d\u662f\u663e\u5f0f\u5730\u8ba1\u7b97Hessian\u77e9\u9635\uff0cL-BFGS\u4f7f\u7528\u4e00\u7ec4\u5411\u91cf\uff08\u66f2\u7387\u5bf9\uff09\u6765\u6784\u5efaHessian\u77e9\u9635\u7684\u8fd1\u4f3c\u9006\u3002\u8fd9\u51cf\u5c11\u4e86\u8ba1\u7b97\u590d\u6742\u5ea6\uff0c\u5e76\u4fdd\u6301\u4e86\u7b97\u6cd5\u7684\u6548\u7387\u3002<\/p>\n<\/p>\n

\u4e8c\u3001\u6709\u9650\u5185\u5b58\u7279\u6027<\/h3>\n<\/p>\n

L-BFGS\u7684\u6709\u9650\u5185\u5b58\u7279\u6027\u8ba9\u5b83\u6210\u4e3a\u5904\u7406\u5927\u578b\u95ee\u9898\u7684\u7406\u60f3\u9009\u62e9<\/strong>\uff0c\u56e0\u4e3a\u5b83\u964d\u4f4e\u4e86\u5b58\u50a8\u9700\u6c42\u5e76\u4f18\u5316\u4e86\u8ba1\u7b97\u6548\u7387\u3002<\/p>\n<\/p>\n

\u51cf\u5c11\u5b58\u50a8\u9700\u6c42<\/h4>\n<\/p>\n

\u4f20\u7edf\u7684BFGS\u7b97\u6cd5\u9700\u8981\u5b58\u50a8\u5b8c\u6574\u7684n\u00d7n\u7ef4Hessian\u8fd1\u4f3c\u77e9\u9635\uff0c\u5176\u4e2dn\u662f\u53d8\u91cf\u7684\u6570\u91cf\u3002\u5bf9\u4e8e\u5927\u89c4\u6a21\u95ee\u9898\uff0c\u8fd9\u662f\u4e0d\u5207\u5b9e\u9645\u7684\u3002L-BFGS\u7b97\u6cd5\u901a\u8fc7\u4ec5\u5b58\u50a8\u6700\u8fd1m\u6b21\u8fed\u4ee3\u7684\u4fe1\u606f\uff08\u901a\u5e38m\u8fdc\u5c0f\u4e8en\uff09\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u5927\u5927\u51cf\u5c11\u4e86\u5185\u5b58\u8981\u6c42\u3002<\/p>\n<\/p>\n

\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387<\/h4>\n<\/p>\n

\u5c11\u91cf\u7684\u5b58\u50a8\u9700\u6c42\u76f4\u63a5\u5f71\u54cd\u5230\u7b97\u6cd5\u7684\u8ba1\u7b97\u6548\u7387\u3002\u5728L-BFGS\u4e2d\uff0cHessian\u77e9\u9635\u7684\u8fd1\u4f3c\u4e0d\u662f\u76f4\u63a5\u8ba1\u7b97\uff0c\u800c\u662f\u9690\u5f0f\u5730\u901a\u8fc7\u51e0\u4e2a\u5411\u91cf\u7684\u8fed\u4ee3\u7ec4\u5408\u8ba1\u7b97\u5f97\u51fa\u3002\u8fd9\u4f7f\u5f97\u7b97\u6cd5\u80fd\u591f\u5feb\u901f\u8fdb\u884c\u641c\u7d22\u65b9\u5411\u7684\u786e\u5b9a\u548c\u53c2\u6570\u66f4\u65b0\u3002<\/p>\n<\/p>\n

\u4e09\u3001\u6709\u6548\u7684\u66f2\u7387\u4f30\u8ba1<\/h3>\n<\/p>\n

\u66f2\u7387\u4fe1\u606f\u7684\u6b63\u786e\u4f30\u8ba1\u5bf9\u4e8e\u51c6\u725b\u987f\u6cd5\u81f3\u5173\u91cd\u8981\uff0c\u800cL-BFGS\u7b97\u6cd5\u5728\u8fd9\u65b9\u9762\u505a\u5f97\u975e\u5e38\u51fa\u8272<\/strong>\u3002<\/p>\n<\/p>\n

\u5229\u7528\u5386\u53f2\u4fe1\u606f<\/h4>\n<\/p>\n

L-BFGS\u7b97\u6cd5\u4f7f\u7528\u5386\u53f2\u4e2d\u7684\u66f2\u7387\u5bf9\u6765\u4f30\u8ba1\u76ee\u6807\u51fd\u6570\u7684\u5c40\u90e8\u66f2\u7387\uff0c\u8fd9\u6bd4\u4f7f\u7528\u56fa\u5b9a\u516c\u5f0f\u4f30\u7b97<\/a>\u8981\u51c6\u786e\u5f97\u591a\u3002\u8fd9\u79cd\u52a8\u6001\u8c03\u6574\u4fdd\u8bc1\u4e86\u7b97\u6cd5\u80fd\u591f\u9002\u5e94\u76ee\u6807\u51fd\u6570\u7684\u53d8\u5316\uff0c\u4ece\u800c\u63d0\u9ad8\u641c\u7d22\u6548\u7387\u3002<\/p>\n<\/p>\n

\u66f4\u65b0\u641c\u7d22\u65b9\u5411<\/h4>\n<\/p>\n

\u6839\u636e\u76ee\u6807\u51fd\u6570\u5728\u65b0\u4f4d\u7f6e\u7684\u66f2\u7387\u4fe1\u606f\uff0cL-BFGS\u80fd\u591f\u8c03\u6574\u641c\u7d22\u65b9\u5411\uff0c\u4f7f\u5176\u4e0d\u4ec5\u6307\u5411\u68af\u5ea6\u4e0b\u964d\u6700\u5feb\u7684\u65b9\u5411\uff0c\u8fd8\u8003\u8651\u4e86\u79fb\u52a8\u8def\u5f84\u7684\u66f2\u7387\u3002\u8fd9\u79cd\u66f4\u7cbe\u7ec6\u7684\u641c\u7d22\u65b9\u5411\u901a\u5e38\u53ef\u4ee5\u4f7f\u7b97\u6cd5\u66f4\u5feb\u5730\u5230\u8fbe\u6781\u5c0f\u503c\u70b9\u3002<\/p>\n<\/p>\n

\u56db\u3001\u81ea\u9002\u5e94\u7279\u6027<\/h3>\n<\/p>\n

L-BFGS\u7b97\u6cd5\u80fd\u591f\u81ea\u6211\u8c03\u6574\uff0c\u4f7f\u5176\u5728\u4e0d\u540c\u7c7b\u578b\u7684\u95ee\u9898\u4e0a\u90fd\u80fd\u4fdd\u6301\u826f\u597d\u7684\u6027\u80fd\u3002<\/p>\n<\/p>\n

\u53c2\u6570\u81ea\u6211\u8c03\u6574<\/h4>\n<\/p>\n

L-BFGS\u7b97\u6cd5\u80fd\u591f\u57fa\u4e8e\u5f53\u524d\u4f18\u5316\u8fc7\u7a0b\u7684\u7279\u70b9\u81ea\u52a8\u8c03\u6574\u53c2\u6570\uff0c\u5982\u6b65\u957f\uff08learning rate\uff09\u4ee5\u53ca\u5386\u53f2\u4fe1\u606f\u7684\u5b58\u50a8\u6570\u91cfm\u3002\u8fd9\u79cd\u81ea\u9002\u5e94\u6027\u80fd\u591f\u63d0\u5347\u7b97\u6cd5\u9762\u5bf9\u590d\u6742\u95ee\u9898\u65f6\u7684\u9c81\u68d2\u6027\u3002<\/p>\n<\/p>\n

\u53cd\u9988\u673a\u5236<\/h4>\n<\/p>\n

\u901a\u8fc7\u8bc4\u4ef7\u6bcf\u4e00\u6b65\u7684\u4f18\u5316\u6548\u679c\uff0cL-BFGS\u80fd\u591f\u8c03\u6574\u5176\u5185\u90e8\u7b56\u7565\u6765\u5e94\u5bf9\u76ee\u6807\u51fd\u6570\u7684\u7279\u6027\u3002\u5982\u679c\u53d1\u73b0\u4e00\u6b21\u8fed\u4ee3\u540e\u6027\u80fd\u6ca1\u6709\u663e\u8457\u6539\u8fdb\uff0c\u7b97\u6cd5\u53ef\u4ee5\u9009\u62e9\u66f4\u4e3a\u4fdd\u5b88\u7684\u66f4\u65b0\u7b56\u7565\uff0c\u907f\u514d\u8fc7\u5927\u6b65\u957f\u5e26\u6765\u7684\u4e0d\u7a33\u5b9a\u6027\u3002<\/p>\n<\/p>\n

\u603b\u7ed3\u800c\u8a00\uff0cL-BFGS\u7b97\u6cd5\u5feb\u901f\u7684\u4e3b\u8981\u539f\u56e0\u662f\u5b83\u7ed3\u5408\u4e86\u51c6\u725b\u987f\u6cd5\u7684\u9ad8\u6548\u6846\u67b6\u3001\u6709\u9650\u5185\u5b58\u7684\u8282\u7701\u7279\u5f81\u3001\u6709\u6548\u7684\u66f2\u7387\u4f30\u8ba1\u4ee5\u53ca\u81ea\u6211\u8c03\u6574\u7684\u9002\u5e94\u6027<\/strong>\u3002\u8fd9\u4e9b\u7279\u70b9\u4f7f\u5f97L-BFGS\u7b97\u6cd5\u5728\u5927\u89c4\u6a21\u4f18\u5316\u95ee\u9898\u4e2d\u8868\u73b0\u4f18\u5f02\uff0c\u627e\u5230\u89e3\u51b3\u65b9\u6848\u65e2\u5feb\u901f\u53c8\u51c6\u786e\u3002<\/p>\n<\/p>\n

\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n

\u4e3a\u4ec0\u4e48L-BFGS\u7b97\u6cd5\u5728\u4f18\u5316\u95ee\u9898\u4e2d\u5feb\u901f\u6536\u655b\uff1f<\/strong><\/p>\n

L-BFGS\uff08Limited memory Broyden-Fletcher-Goldfarb-Shanno\uff09\u662f\u4e00\u79cd\u5e38\u7528\u7684\u65e0\u7ea6\u675f\u4f18\u5316\u7b97\u6cd5\uff0c\u5177\u6709\u5feb\u901f\u6536\u655b\u7684\u7279\u70b9\u3002\u5176\u5feb\u901f\u6536\u655b\u7684\u539f\u56e0\u5982\u4e0b\uff1a<\/p>\n

    \n
  1. \n

    \u5229\u7528\u6709\u9650\u5185\u5b58\u5b58\u50a8<\/strong>\uff1aL-BFGS\u7b97\u6cd5\u901a\u8fc7\u5229\u7528\u6709\u9650\u7684\u5185\u5b58\u5b58\u50a8\u6765\u8fd1\u4f3c\u8ba1\u7b97Hessian\u77e9\u9635\u7684\u9006\uff0c\u907f\u514d\u4e86\u76f4\u63a5\u8ba1\u7b97\u548c\u5b58\u50a8Hessian\u77e9\u9635\u5bf9\u5185\u5b58\u5f00\u9500\u7684\u5f71\u54cd\uff0c\u4ece\u800c\u51cf\u5c11\u4e86\u7b97\u6cd5\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u3002<\/p>\n<\/li>\n

  2. \n

    \u6709\u6548\u7684\u68af\u5ea6\u4f30\u8ba1<\/strong>\uff1aL-BFGS\u7b97\u6cd5\u901a\u8fc7\u5229\u7528\u5386\u53f2\u8fed\u4ee3\u6b65\u957f\u548c\u68af\u5ea6\u5dee\u7684\u4fe1\u606f\u6765\u4f30\u8ba1Hessian\u77e9\u9635\u7684\u9006\uff0c\u901a\u8fc7\u5bf9\u5f53\u524d\u8fed\u4ee3\u70b9\u7684\u8fd1\u4f3cHessian\u77e9\u9635\u8fdb\u884c\u4f30\u8ba1\uff0c\u80fd\u591f\u66f4\u6709\u6548\u5730\u6307\u5bfc\u4e0b\u4e00\u4e2a\u8fed\u4ee3\u70b9\u7684\u641c\u7d22\u65b9\u5411\uff0c\u4ece\u800c\u52a0\u901f\u7b97\u6cd5\u7684\u6536\u655b\u901f\u5ea6\u3002<\/p>\n<\/li>\n

  3. \n

    \u7ebf\u6027\u65f6\u95f4\u548c\u7a7a\u95f4\u590d\u6742\u5ea6<\/strong>\uff1aL-BFGS\u7b97\u6cd5\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u662f\u7ebf\u6027\u7684\uff0c\u968f\u7740\u95ee\u9898\u53d8\u91cf\u7684\u589e\u52a0\u800c\u7ebf\u6027\u589e\u957f\u3002\u8fd9\u4f7f\u5f97\u8be5\u7b97\u6cd5\u9002\u7528\u4e8e\u5927\u89c4\u6a21\u4f18\u5316\u95ee\u9898\uff0c\u5e76\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u663e\u793a\u51fa\u4e86\u8f83\u9ad8\u7684\u6548\u7387\u3002<\/p>\n<\/li>\n<\/ol>\n

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