{"id":9147,"date":"2024-05-11T09:01:01","date_gmt":"2024-05-11T01:01:01","guid":{"rendered":""},"modified":"2024-05-11T09:01:01","modified_gmt":"2024-05-11T01:01:01","slug":"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09","status":"publish","type":"post","link":"https:\/\/mushiming.com\/9147.html","title":{"rendered":"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09"},"content":{"rendered":"<p>\u539f\u6587\u51fa\u5904\uff1ahttps:\/\/zhuanlan.zhihu.com\/p\/22402784?utm_source=tuicool&amp;utm_medium=referral<\/p>\n<p><span style=\"color:rgb(51,51,51); font-size:16px; line-height:27.2px\">\u8fd9\u7bc7\u6587\u7ae0\u56de\u987e\u4e86\u57fa\u4e8e\u68af\u5ea6\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u5728\u8fd9\u51e0\u5e74\u7684\u91cd\u8981\u53d1\u5c55 -- SAG\u3001SVRG\u3002<\/span><\/p>\n<p style=\"margin-top:20px; margin-bottom:20px; color:rgb(51,51,51); font-size:16px; line-height:27.2px\"> \u5f88\u591a\u5e38\u89c1\u7684\u673a\u5668\u5b66\u4e60\u6a21\u578b\u7684\u76ee\u6807\uff08\u6bd4\u5982\u6700\u5c0f\u4e8c\u4e58\u505a\u7ebf\u6027\u56de\u5f52\u3001\u903b\u8f91\u56de\u5f52\uff09\u90fd\u53ef\u4ee5\u6982\u62ec\u6210\u4ee5\u4e0b\u8fd9\u79cd\u4e00\u822c\u5f62\u5f0f\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"\\min_{\\mathbf{w}} \\frac{1}{N} \\sum_{i=1}^N f(\\mathbf{x}_i, \\mathbf{w}) + \\lambda h(\\mathbf{w})\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c1\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c1\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<\/p>\n<div>\n  <\/p>\n<p>\u5176\u4e2d <img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"f(\\mathbf{x}_i, \\mathbf{w})\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c2\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c2\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > \u4ee3\u8868\u6837\u672c<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"\\mathbf{x}_i\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c3\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c3\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7684\u635f\u5931\u51fd\u6570\uff0c<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"\\mathbf{w}\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c4\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c4\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u662f\u6a21\u578b\u7684\u53c2\u6570\uff0c<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"h(\\mathbf{w})\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c5\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c5\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4ee3\u8868\u6b63\u5219\u5316\u9879\uff08\u7528\u4e8e\u63a7\u5236\u6a21\u578b\u590d\u6742\u5ea6\u6216\u8005\u6a21\u578b\u7a00\u758f\u5ea6\u7b49\u7b49\uff09\uff0c\u6709\u4e9b\u65f6\u5019\u8fd9\u4e2a\u6b63\u5219\u5316\u9879\u662f\u4e0d\u5e73\u6ed1\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\u5b83\u53ef\u80fd\u4e0d\u53ef\u5bfc\u3002<\/p>\n<p>\u6682\u65f6\u5148\u4e0d\u8003\u8651\u8fd9\u4e2a\u6b63\u5219\u5316\u9879\uff0c\u53ea\u8003\u8651\u6837\u672c\u4e0a\u7684\u635f\u5931\uff0c\u5e76\u4e14\u5bf9\u7b26\u53f7\u505a\u4e00\u70b9\u7b80\u5316\uff08<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"f(\\mathbf{x}_i,\\mathbf{w}) \\triangleq f_i(\\mathbf{w})\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c6\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c6\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff09\uff0c\u8003\u8651\u4e0b\u9762\u8fd9\u4e2a\u4f18\u5316\u76ee\u6807\uff1a <\/p>\n<p> <img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"\\min_{\\mathbf{w}}\\frac{1}{N}\\sum_{i=1}^N f_i( \\mathbf{w})\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c7\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c7\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/>\n  <\/p>\n<p>\u8fd9\u4e2a\u5f62\u5f0f\u975e\u5e38\u7b80\u5355\uff0c\u53ea\u8981\u6bcf\u4e2a<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"f_i(\\mathbf{w})\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u90fd\u53ef\u5bfc\uff0c\u5c31\u53ef\u4ee5\u7528\u68af\u5ea6\u4e0b\u964d\u6cd5\uff08Gradient Descent\uff09\u8fed\u4ee3\u6c42\u89e3:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"\\mathbf{w}_{t+1} = \\mathbf{w}_t - \\eta \\frac{1}{N}\\sum_{i=1}^N \\triangledown f_i(\\mathbf{w}_t)\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c9\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c9\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u5176\u4e2d<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"\\mathbf{w}_{t+1}\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c10\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c10\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > \u8868\u793a\u7b2c t+1 \u6b21\u66f4\u65b0\u540e\u7684\u53c2\u6570\u3002 <\/p>\n<p>\u68af\u5ea6\u4e0b\u964d\u5bf9\u4e8e\u6837\u672c\u6570\u76ee\u6bd4\u8f83\u591a\u7684\u65f6\u5019\u6709\u4e00\u4e2a\u5f88\u5927\u7684\u52a3\u52bf\uff0c\u90a3\u5c31\u662f\u6bcf\u6b21\u9700\u8981\u6c42\u89e3\u6240\u6709\u6837\u672c\u7684\u68af\u5ea6\uff0c\u6837\u672c\u6570\u591a\u7684\u65f6\u5019\uff0c\u5bfc\u81f4\u8ba1\u7b97\u91cf\u5927\u589e\uff0c\u6240\u4ee5\u5b9e\u9645\u751f\u4ea7\u73af\u5883\u4e2d\uff0c\u5f80\u5f80\u91c7\u7528\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\uff08Stochastic Gradient Descent\uff09\uff0c\u4e00\u822c\u7b80\u5199\u505aSGD\u3002<\/p>\n<p>SGD\u6bcf\u6b21\u8fed\u4ee3\u7684\u65f6\u5019\u5747\u5300\u968f\u673a\u5f97\u9009\u62e9\u4e00\u4e2a\u6837\u672c\u6216\u8005mini-batch\u505a\u66f4\u65b0\uff1a<\/p>\n<p> <img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"\\mathbf{w}_{t+1} = \\mathbf{w}_t - \\eta \\triangledown f_i(\\mathbf{w}_t)\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c11\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c11\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p><strong><span style=\"font-size:18px\">\u76f8\u5bf9\u4e8e\u68af\u5ea6\u4e0b\u964d\uff0cSGD\u7684\u597d\u5904\u975e\u5e38\u660e\u663e\uff0c\u5c31\u662f\u53ef\u4ee5\u51cf\u5c11\u6bcf\u6b21\u66f4\u65b0\u7684\u8ba1\u7b97\u4ee3\u4ef7\uff0c\u4f46\u662fSGD\u5e26\u6765\u7684\u95ee\u9898\u662f\u6536\u655b\u901f\u5ea6\u4e0d\u5982\u68af\u5ea6\u4e0b\u964d<\/span><\/strong>\uff08\u6536\u655b\u901f\u5ea6\u662f\u8861\u91cf\u4f18\u5316\u7b97\u6cd5\u8ba1\u7b97\u590d\u6742\u5ea6\u7684\u57fa\u672c\u5de5\u5177\uff0c\u5177\u4f53\u5b9a\u4e49\u53ef\u4ee5\u53c2\u8003https:\/\/en.wikipedia.org\/wiki\/Rate_of_convergence \u6216\u8005\u5176\u4ed6\u4f18\u5316\u76f8\u5173\u7684\u6559\u6750\uff09\uff0c<span style=\"font-size:18px\"><strong>\u4e5f\u5c31\u662f\u8bf4\u4e3a\u4e86\u8fbe\u5230\u540c\u6837\u7684\u7cbe\u5ea6\uff0cSGD\u9700\u8981\u7684\u603b\u8fed\u4ee3\u6b21\u6570\u8981\u5927\u4e8e\u68af\u5ea6\u4e0b\u964d\uff0c\u4f46\u662f\uff0c\u5355\u6b21\u8fed\u4ee3\u7684\u8ba1\u7b97\u91cf\u8981\u5c0f\u5f97\u591a\u3002<\/strong><\/span>\u4ece\u6536\u655b\u901f\u5ea6\u5206\u6790\u4e0a\u770b\uff0cSGD\u80fd\u591f\u5728\u76ee\u6807\u51fd\u6570\u5f3a\u51f8\u5e76\u4e14\u9012\u51cf\u6b65\u957f\u7684\u60c5\u51b5\u4e0b\u505a\u5230<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"O(1\/T)\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c12\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c12\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > \u7684\u6b21\u7ebf\u6027\u6536\u655b\uff08sublinear convergence\uff09\uff0c\u800c\u68af\u5ea6\u4e0b\u964d\u5219\u53ef\u4ee5\u5728\u76ee\u6807\u51fd\u6570\u5f3a\u51f8\u7684\u60c5\u51b5\u4e0b\u505a\u5230<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"O(\\rho^T)\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c13\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c13\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > (<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"\\rho < 1\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c14\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c14\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >) \u7684\u7ebf\u6027\u6536\u655b\uff08linear convergence\uff09\u3002\u603b\u7ed3\u8d77\u6765\u5c31\u662f\uff0c<strong><span style=\"font-size:18px\">\u5982\u679c\u60f3\u5feb\u901f\u5f97\u5230\u4e00\u4e2a\u53ef\u4ee5\u52c9\u5f3a\u63a5\u53d7\u7684\u89e3\uff0cSGD\u6bd4\u68af\u5ea6\u4e0b\u964d\u66f4\u52a0\u5408\u9002\uff0c\u4f46\u662f\u5982\u679c\u60f3\u5f97\u5230\u4e00\u4e2a\u7cbe\u786e\u5ea6\u9ad8\u7684\u89e3\uff0c\u5e94\u5f53\u9009\u62e9\u68af\u5ea6\u4e0b\u964d\u3002<\/span><\/strong><\/p>\n<p>SGD\u540e\u6765\u540e\u6765\u4e5f\u884d\u751f\u51fa\u4e86\u975e\u5e38\u591a\u7684\u53d8\u79cd\uff0c\u5c24\u5176\u662f\u4e00\u7c7b\u5206\u6790regret\u7684online\u7b97\u6cd5\uff0c\u5305\u62ecAdagrad\u3001Dual Averaging\u3001FTRL\u7b49\u3002\u4f46\u662f\uff0c\u59cb\u7ec8\u5b66\u672f\u754c\u5bf9\u4e8eSGD\u8fd8\u6709\u4e00\u79cd\u671f\u5f85\uff0c\u5c31\u662f\uff1a\u662f\u5426\u53ef\u4ee5\u628aSGD\u505a\u5230\u548c\u68af\u5ea6\u4e0b\u964d\u4e00\u6837\u7684\u7ebf\u6027\u6536\u655b\u3002\u76f4\u52302012\u548c2013\u5e74\uff0cSAG[1]\u4e0eSVRG[2]\u7b97\u6cd5\u53d1\u8868\u5728NIPS\u4e0a\uff0c<strong>\u6210\u4e3a\u8fd1\u51e0\u5e74SGD\u7c7b\u7b97\u6cd5\u7684\u6700\u5927\u7a81\u7834<\/strong>\u3002<\/p>\n<p><strong>SAG\u7b97\u6cd5<\/strong>\uff08\u7b97\u6cd5\u6846\u56fe\u6458\u81ea[4]\uff0c\u8fd9\u91cc\u7684<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"f_i'(.)\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c15\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c15\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u662f\u6307\u68af\u5ea6\u51fd\u6570<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"\\triangledown f_i(.)\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c16\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c16\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u800c<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"x\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c17\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c17\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u662f\u6307\u4e0a\u6587\u4e2d\u7684\u4f18\u5316\u53c2\u6570<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"\\mathbf{w}\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c4\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c4\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff09<\/p>\n<p> <img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/b25a6ff63f754df6a9558c9db15c5b48.png\" =\"\" =\"\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c19\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c19\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\n<\/div>\n<div>\n<div>\n   \u4f5c\u8005\uff1ali Eta<br \/>\n  <br \/> \u94fe\u63a5\uff1ahttps:\/\/zhuanlan.zhihu.com\/p\/22402784<br \/>\n  <br \/> \u6765\u6e90\uff1a\u77e5\u4e4e<br \/>\n  <br \/> \u8457\u4f5c\u6743\u5f52\u4f5c\u8005\u6240\u6709\u3002\u5546\u4e1a\u8f6c\u8f7d\u8bf7\u8054\u7cfb\u4f5c\u8005\u83b7\u5f97\u6388\u6743\uff0c\u975e\u5546\u4e1a\u8f6c\u8f7d\u8bf7\u6ce8\u660e\u51fa\u5904\u3002 <\/p>\n<p>SAG\u7b97\u6cd5\u5728\u5185\u5b58\u4e2d\u4e3a\u6bcf\u4e2a\u6837\u672c\u90fd\u7ef4\u62a4\u4e00\u4e2a\u65e7\u7684\u68af\u5ea6<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"y_i\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c20\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c20\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u968f\u673a\u9009\u62e9\u4e00\u4e2a\u6837\u672c<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"i\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c21\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c21\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u6765\u66f4\u65b0<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"d\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c22\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c22\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u5e76\u7528<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"d\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c22\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c22\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u6765\u66f4\u65b0\u53c2\u6570<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"x\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c17\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c17\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u3002\u5177\u4f53\u5f97\u8bf4\uff0c\u66f4\u65b0\u7684\u9879<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"d\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c22\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c22\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u6765\u81ea\u4e8e\u7528\u65b0\u7684\u68af\u5ea6<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"f_i'(x)\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c26\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c26\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u66ff\u6362\u6389<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"d\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c22\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c22\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4e2d\u7684\u65e7\u68af\u5ea6<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"y_i\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c20\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c20\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u8fd9\u4e5f\u5c31\u662f<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"d = d - y_i + f_i'(x)\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c29\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c29\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u8868\u8fbe\u7684\u610f\u601d\u3002\u5982\u6b64\uff0c\u6bcf\u6b21\u66f4\u65b0\u7684\u65f6\u5019\u4ec5\u4ec5\u9700\u8981\u8ba1\u7b97\u4e00\u4e2a\u6837\u672c\u7684\u68af\u5ea6\uff0c\u800c\u4e0d\u662f\u6240\u6709\u6837\u672c\u7684\u68af\u5ea6\u3002\u8ba1\u7b97\u5f00\u9500\u4e0eSGD\u65e0\u5f02\uff0c\u4f46\u662f\u5185\u5b58\u5f00\u9500\u8981\u5927\u5f97\u591a\u3002[1]\u4e2d\u5df2\u7ecf\u8bc1\u660eSAG\u662f\u4e00\u79cd\u7ebf\u6027\u6536\u655b\u7b97\u6cd5\uff0c\u8fd9\u4e2a\u901f\u5ea6\u8fdc\u6bd4SGD\u5feb\u3002<\/p>\n<p><strong>SAG\u5b9e\u9a8c\u7ed3\u679c<\/strong>\uff08\u7ed3\u679c\u6458\u81ea[1]\u7684arxiv\u957f\u6587\u7248\uff09<\/p>\n<p>  <img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/9ef7fa263ec0498ea38aae862b3f064e.png\" =\"\" =\"\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c30\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c30\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u5b9e\u9a8c\u76ee\u6807\u51fd\u6570\u662fl2-regularized logistic regression\uff0c\u5de6\u4e00\u662f\u8bad\u7ec3\u8bef\u5dee\uff0c\u5de6\u4e8c\u548c\u5de6\u4e09\u5206\u522b\u662f\u4e24\u79cd\u6d4b\u8bd5\u76ee\u6807\u51fd\u6570\u4e0e\u6d4b\u8bd5\u8bef\u5dee\u3002\u6ce8\u610f\u5de6\u4e00\u7684\u7eb5\u5750\u6807\u662f\u5bf9\u6570\u5750\u6807\uff0c\u4e00\u822c\u8861\u91cf\u4f18\u5316\u7b97\u6cd5\u7684\u901f\u5ea6\u90fd\u4f1a\u91c7\u7528\u5bf9\u6570\u5750\u6807\uff0c\u56e0\u4e3a\u5728\u5bf9\u6570\u5750\u6807\u4e2d\u53ef\u4ee5\u660e\u663e\u770b\u51fa\u4e00\u4e2a\u7b97\u6cd5\u662f\u7ebf\u6027\u6536\u655b\uff08\u8fd1\u4e4e\u76f4\u7ebf\u4e0b\u964d\uff09\u8fd8\u662f\u6b21\u7ebf\u6027\u6536\u655b\uff08\u5927\u4f53\u662f\u4e00\u6761\u5411\u4e0b\u51f8\u7684\u66f2\u7ebf\uff09\u3002\u53ef\u4ee5\u770b\u51faSAG\u662f\u4e00\u79cd\u7ebf\u6027\u6536\u655b\u7b97\u6cd5\uff0c\u4e14\u76f8\u5bf9\u4e8e\u5176\u4ed6\u53c2\u4e0e\u6bd4\u8f83\u7684\u7b97\u6cd5\u6709\u5f88\u5927\u7684\u4f18\u52bf\u3002\u5177\u4f53\u5b9e\u9a8c\u914d\u7f6e\u6570\u636e\u96c6\u7b49\u53ef\u4ee5\u53c2\u8003\u539f\u6587\u3002<\/p>\n<p><strong>SVRG\u7b97\u6cd5<\/strong>\uff08\u7b97\u6cd5\u6458\u81ea[2]\uff0c\u8fd9\u91cc\u7684<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"\\psi\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c31\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c31\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5c31\u662f\u4e0a\u6587\u4e2d\u7684\u635f\u5931\u51fd\u6570<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"f\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c32\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c32\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff09<\/p>\n<p>  <img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/008a3f6574904f4c88b175b4e29fa8ac.png\" =\"\" =\"\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c33\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c33\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>SVRG\u7684\u7b97\u6cd5\u601d\u8def\u662f\uff0c\u6bcf\u8fc7\u4e00\u6bb5\u65f6\u95f4\u8ba1\u7b97\u4e00\u6b21\u6240\u6709\u6837\u672c\u7684\u68af\u5ea6<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"\\tilde{\\mu}\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c34\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c34\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u6bcf\u4e2a\u9636\u6bb5\u5185\u90e8\u7684\u5355\u6b21\u66f4\u65b0\u91c7\u7528<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"\\triangledown \\psi_{i_t} (w_{t-1}) - \\triangledown \\psi_{i_t} (\\tilde{w}) + \\tilde{\\mu}\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c35\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c35\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u6765\u66f4\u65b0\u5f53\u524d\u53c2\u6570\uff0c\u6bcf\u6b21\u66f4\u65b0\u6700\u591a\u8ba1\u7b97\u4e24\u6b21\u68af\u5ea6\u3002\u76f8\u5bf9\u4e8eSAG\u6765\u8bf4\uff0c\u4e0d\u9700\u8981\u5728\u5185\u5b58\u4e2d\u4e3a\u6bcf\u4e2a\u6837\u672c\u90fd\u7ef4\u62a4\u4e00\u4e2a\u68af\u5ea6\uff0c\u4e5f\u5c31\u662f\u8bf4\u8282\u7701\u4e86\u5185\u5b58\u8d44\u6e90\u3002\u6b64\u5916\uff0cSVRG\u4e2d\u63d0\u51fa\u4e86\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u6982\u5ff5\u53eb\u505avariance reduction\uff08\u65b9\u5dee\u7f29\u51cf\uff09\uff0c\u8fd9\u4e2a\u6982\u5ff5\u9700\u8981\u8054\u7cfbSGD\u7684\u6536\u655b\u6027\u5206\u6790\u6765\u7406\u89e3\uff0c\u5728SGD\u7684\u6536\u655b\u6027\u5206\u6790\u4e2d\u9700\u8981\u5047\u8bbe\u6837\u672c\u68af\u5ea6\u7684\u7684\u65b9\u5dee\u662f\u6709\u5e38\u6570\u4e0a\u754c\u7684\uff0c\u7136\u800c\u6b63\u662f\u56e0\u4e3a\u8fd9\u4e2a\u5e38\u6570\u4e0a\u754c\u5bfc\u81f4\u4e86SGD\u65e0\u6cd5\u7ebf\u6027\u6536\u655b\uff0c\u56e0\u6b64SVRG\u7684\u6536\u655b\u6027\u5206\u6790\u4e2d\u5229\u7528<img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/228bc6b7ad4b4164a4b49d24c12083a9.jpg\" =\"\" =\"\\triangledown \\psi_{i_t} (w_{t-1}) - \\triangledown \\psi_{i_t} (\\tilde{w}) + \\tilde{\\mu}\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c35\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c35\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u8fd9\u79cd\u7279\u6b8a\u7684\u66f4\u65b0\u9879\u6765\u8ba9\u65b9\u5dee\u6709\u4e00\u4e2a\u53ef\u4ee5\u4e0d\u65ad\u51cf\u5c11\u7684\u4e0a\u754c\uff0c\u56e0\u6b64\u4e5f\u5c31\u505a\u5230\u4e86\u7ebf\u6027\u6536\u655b\uff0c\u8fd9\u4e00\u70b9\u5c31\u662fSVRG\u7684\u6838\u5fc3\uff0cSAG\u7684\u7b56\u7565\u5176\u5b9e\u4e5f\u4e0e\u6b64\u7c7b\u4f3c\uff08\u867d\u7136\u8bc1\u660e\u8fc7\u7a0b\u4e0d\u540c\uff09\u3002<\/p>\n<p> <\/p>\n<p><strong>SVRG\u5b9e\u9a8c\u7ed3\u679c<\/strong>\uff08\u7ed3\u679c\u6458\u81ea[2]\uff09<\/p>\n<p>  <img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/dcb22e23d247475cbfc004aa69d1aaf2.png\" =\"\" =\"\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c37\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c37\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u4e0a\u56fe\u4e3aSVRG\u5728\u51f8\u7684logistic regression\u4e0a\u7684\u8868\u73b0\uff0c\u6ce8\u610f\u5de6\u4e00\u7eb5\u5750\u6807\u662f\u8bad\u7ec3\u8bef\u5dee\uff0c\u5de6\u4e8c\u5de6\u4e09\u7eb5\u5750\u6807\u662f\u5bf9\u6570\u5750\u6807\uff0c\u5b9e\u9a8c\u4e2d\u53ef\u4ee5\u770b\u51faSVRG\u663e\u7136\u662f\u7ebf\u6027\u6536\u655b\u7b97\u6cd5\uff0c\u76f8\u5bf9\u4e8eSGD\u6709\u975e\u5e38\u5927\u7684\u4f18\u52bf\uff0c\u548cSDCA\u5177\u5907\u540c\u9636\u7684\u901f\u5ea6\u3002<\/p>\n<p>  <img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/6a5ac6cc39614561a860f13ffa62aeb3.png\" =\"\" =\"\" alt=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09 (https:\/\/mushiming.com\/)  \u7b2c38\u5f20\" title=\"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09  \u7b2c38\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u4e0a\u56fe\u4e3aSVRG\u5728\u975e\u51f8\u7684\u795e\u7ecf\u7f51\u7edc\uff08Neural Network\u6216\u79f0\u4f5cDeep Learning\uff09\u4e0a\u7684\u8868\u73b0\uff08\u539f\u6587\u4e2d\u662f\u5728\u5355\u9690\u5c42\u795e\u7ecf\u7f51\u7edc\u4e0a\u505a\u7684\u5b9e\u9a8c\uff09\u3002\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u8bf4\u660e\uff0cSVRG\u5728NN\u4e0a\u4e5f\u53ef\u4ee5\u53d1\u6325\u5f88\u597d\u7684\u4f5c\u7528\u3002<\/p>\n<p>\u540e\u6765\u8fd9\u7c7b\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u9646\u7eed\u51fa\u73b0\u4e86\u5f88\u591a\u53d8\u79cd\uff0c\u6bd4\u5982SAGA\u7b97\u6cd5[3]\u3002<\/p>\n<p> <\/p>\n<p><strong>\u53c2\u8003\u6587\u732e\uff1a<\/strong><\/p>\n<ol>\n<li>Roux, Nicolas L., Mark Schmidt, and Francis R. Bach. \"A stochastic gradient method with an exponential convergence rate for finite training sets.\"<em>Advances in Neural Information Processing Systems<\/em>. 2012.  <\/li>\n<li>Johnson, Rie, and Tong Zhang. \"Accelerating stochastic gradient descent using predictive variance reduction.\"<em>Advances in Neural Information Processing Systems<\/em>. 2013. <\/li>\n<li>Defazio, Aaron, Francis Bach, and Simon Lacoste-Julien. \"Saga: A fast incremental gradient method with support for non-strongly convex composite objectives.\"<em>Advances in Neural Information Processing Systems<\/em>. 2014.<\/li>\n<li>Schmidt, Mark, Nicolas Le Roux, and Francis Bach. \"Minimizing finite sums with the stochastic average gradient.\"<em>arXiv preprint arXiv:1309.2388<\/em> (2013).<\/li>\n<\/ol>\n<div>\n   <br \/> \n  <\/div>\n<\/p><\/div>\n<div>\n  <span style=\"font-size:18px\"><strong>\u8865\u5145\uff1a<\/strong><\/span>\n <\/div>\n<div>\n<h2 style=\"margin:10px 0px; padding:0px; font-size:28px; line-height:1.5; font-family:Verdana,Arial,Helvetica,sans-serif\"> \u68af\u5ea6\u4e0b\u964d\u6cd5\u5927\u5bb6\u65cf\uff08BGD\uff0cSGD\uff0cMBGD\uff09<\/h2>\n<h3 style=\"margin:10px 0px; padding:0px; font-size:21px; line-height:1.5; font-family:Verdana,Arial,Helvetica,sans-serif\"> \u6279\u91cf\u68af\u5ea6\u4e0b\u964d\u6cd5\uff08Batch Gradient Descent\uff09<\/h3>\n<p style=\"margin:10px auto; padding-top:0px; padding-bottom:0px; font-family:Verdana,Arial,Helvetica,sans-serif; line-height:21.6px\"> \u3000\u3000\u3000\u3000\u6279\u91cf\u68af\u5ea6\u4e0b\u964d\u6cd5\uff0c\u662f\u68af\u5ea6\u4e0b\u964d\u6cd5\u6700\u5e38\u7528\u7684\u5f62\u5f0f\uff0c\u5177\u4f53\u505a\u6cd5\u4e5f\u5c31\u662f\u5728\u66f4\u65b0\u53c2\u6570\u65f6\u4f7f\u7528\u6240\u6709\u7684\u6837\u672c\u6765\u8fdb\u884c\u66f4\u65b0<\/p>\n<h3 style=\"margin:10px 0px; padding:0px; font-size:21px; line-height:1.5; font-family:Verdana,Arial,Helvetica,sans-serif\"> \u968f\u673a\u68af\u5ea6\u4e0b\u964d\u6cd5\uff08Stochastic Gradient Descent\uff09<\/h3>\n<p style=\"margin:10px auto; 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padding-top:0px; padding-bottom:0px; font-family:Verdana,Arial,Helvetica,sans-serif; line-height:21.6px\"> \u3000\u3000\u3000\u3000\u68af\u5ea6\u4e0b\u964d\u6cd5\u548c\u725b\u987f\u6cd5\/\u62df\u725b\u987f\u6cd5\u76f8\u6bd4\uff0c\u4e24\u8005\u90fd\u662f\u8fed\u4ee3\u6c42\u89e3\uff0c\u4e0d\u8fc7\u68af\u5ea6\u4e0b\u964d\u6cd5\u662f\u68af\u5ea6\u6c42\u89e3\uff0c\u800c\u725b\u987f\u6cd5\/\u62df\u725b\u987f\u6cd5\u662f\u7528\u4e8c\u9636\u7684\u6d77\u68ee\u77e9\u9635\u7684\u9006\u77e9\u9635\u6216\u4f2a\u9006\u77e9\u9635\u6c42\u89e3\u3002\u76f8\u5bf9\u800c\u8a00\uff0c\u4f7f\u7528\u725b\u987f\u6cd5\/\u62df\u725b\u987f\u6cd5\u6536\u655b\u66f4\u5feb\u3002\u4f46\u662f\u6bcf\u6b21\u8fed\u4ee3\u7684\u65f6\u95f4\u6bd4\u68af\u5ea6\u4e0b\u964d\u6cd5\u957f\u3002<\/p>\n<p> \n <\/div>\n<p> \n<\/div>\n<p> <\/p>\n","protected":false},"excerpt":{"rendered":"\u7ebf\u6027\u6536\u655b\u7684\u968f\u673a\u4f18\u5316\u7b97\u6cd5\u4e4b SAG\u3001SVRG\uff08\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09\u539f\u6587\u51fa\u5904\uff1ahttps:\/\/zhuanlan.zhihu.com\/p\/22402784?utm_source=tuicool&...","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"_links":{"self":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/9147"}],"collection":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/comments?post=9147"}],"version-history":[{"count":0,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/9147\/revisions"}],"wp:attachment":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/media?parent=9147"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/categories?post=9147"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/tags?post=9147"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}