{"id":15938,"date":"2025-02-09T20:43:19","date_gmt":"2025-02-09T12:43:19","guid":{"rendered":"https:\/\/www.orczhou.com\/?p=15938"},"modified":"2025-12-24T19:06:47","modified_gmt":"2025-12-24T11:06:47","slug":"adam-stochastic-gradient-descent","status":"publish","type":"post","link":"https:\/\/www.orczhou.com\/index.php\/2025\/02\/adam-stochastic-gradient-descent\/","title":{"rendered":"Stochastic Gradient Descent\u7684\u68af\u5ea6\u6ce2\u52a8\u95ee\u9898\u548cAdam optimization"},"content":{"rendered":"


\n<\/p>\n\n\n\n

\u57282015\u5e74\uff0c\u7531 OpenAI \u7684 DP Kingma \u7b49\u53d1\u5e03\u4e86 \u300aADAM: A METHOD FOR STOCHASTIC OPTIMIZATION<\/a>\u300b\u7b97\u6cd5\u540e\uff0c\u7531\u4e8e\u5176\u8fed\u4ee3\u6548\u7387\u63d0\u5347\u975e\u5e38\u660e\u663e\uff0c\u6240\u4ee5 ADAM\uff08\u6216\u5176\u53d8\u79cd\uff09\u5c31\u88ab\u5e7f\u6cdb\u7684\u91c7\u7528\u3002\u672c\u6587\u5c06\u7ee7\u7eed\u5bf9\u4e0a\u4e00\u7bc7\u4ecb\u7ecd\u7684\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5<\/a>\u8fdb\u884c\u4f18\u5316\uff0c\u5e76\u4ecb\u7ecd ADAM \u7b97\u6cd5\uff08\u4e00\u79cd\u5bf9\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u7684\u4f18\u5316\u7b97\u6cd5\uff09\u7684\u5b9e\u73b0\u4ee5\u53ca\u6548\u679c\u3002<\/p>\n\n\n\n

Stochastic Gradient Descent<\/code> \u6216\u8005\u8bf4 mini-batch<\/code>\u89e3\u51b3\u4e86\u6837\u672c\u91cf\u5de8\u5927\u65f6\uff0c\u68af\u5ea6\u4e0b\u964d\u8fed\u4ee3\u7684\u95ee\u9898\u3002\u4f46\u662f\uff0c\u4e5f\u5e26\u4e86\u4e00\u4e9b\u65b0\u7684\u95ee\u9898\u3002\u6700\u4e3a\u4e3b\u8981\u7684\u662f\uff0c\u56e0\u4e3a\u6837\u672c\u6570\u636e\u7684\u6ce2\u52a8\uff0c\u800c\u5bfc\u81f4\u6bcf\u6b21\u68af\u5ea6\u4e0b\u964d\u8ba1\u7b97\u65f6\uff0c\u68af\u5ea6\u65b9\u5411\u7684\u6ce2\u52a8\uff0c\u4ece\u800c\u964d\u4f4e\u4e86\u68af\u5ea6\u4e0b\u964d\u8fed\u4ee3\u7684\u6548\u7387\u3002<\/p>\n\n\n\n

\u5728\u524d\u9762\u7684\u300aMini-batch Gradient Descent\u548c\u968f\u673a\u68af\u5ea6\u4e0b\u964d(SGD)<\/a>\u300b\u6587\u7ae0\u4e2d\uff0c\u6211\u4eec\u5bf9\u6bd4\u4e86 mini-batch \u548c batch gradient descent \u7684\u5728\u8fed\u4ee3\u65f6\uff0c\u76ee\u6807\u51fd\u6570\u4e0b\u964d\u7684\u901f\u5ea6\u3002<\/p>\n\n\n\n

\n
\n
\"\"<\/figure>\n<\/div>\n\n\n\n
\n
\"\"<\/figure>\n<\/div>\n<\/div>\n\n\n\n

\u53ef\u4ee5\u770b\u5230\uff0cbatch gradient descent \u7684\u76ee\u6807\u51fd\u6570\u4e0b\u964d\u975e\u5e38\u7a33\u5b9a\uff0c\u800c Mini-batch \u7684\u5b9e\u73b0\u5219\u4f1a\u6709\u660e\u663e\u7684\u6ce2\u52a8\u3002\u4e3a\u4e86\u5c1d\u8bd5\u4fee\u6b63\u8fd9\u4e2a\u95ee\u9898\uff0c\u4ece\u800c\u63d0\u9ad8\u8fed\u4ee3\u6548\u7387\uff0c\u5728\u795e\u7ecf\u7f51\u7edc\u7b97\u6cd5\u4e0a\uff0c\u9010\u6e10\u63a2\u7d22\u51fa\u4e86\u4e00\u4e9b\u8f83\u4e3a\u9ad8\u6548\u7684\u4f18\u5316\u7b97\u6cd5\uff1aAdam SGD\u3002\u8be5\u7b97\u6cd5\u5c06 RMSprop \u548c \u201cExponential smoothing\u201d\u7684\u60f3\u6cd5\u7ed3\u5408\u5728\u4e00\u8d77\uff0c\u5f62\u6210\u4e86\u4e00\u4e2a\u8f83\u4e3a\u9ad8\u6548\u7684\u7b97\u6cd5\uff0c\u5728\u5b9e\u8df5\u4e2d\u88ab\u5e7f\u4e3a\u4f7f\u7528\u3002<\/p>\n\n\n\n

Stochastic Gradient Descent \u4e0e Momentum<\/h4>\n\n\n\n

SGD<\/code> \u4f1a\u5728\u6bcf\u6b21\u8fed\u4ee3\u65f6\u6839\u636e\u6837\u672c\u7684\u504f\u5dee\uff0c\u5c55\u73b0\u51fa\u4e0d\u540c\u7684\u504f\u5dee\uff0c\u6240\u4ee5\uff0c\u5728\u4f7f\u7528SGD<\/code>\u8fdb\u884c\u8fed\u4ee3\u65f6\uff0c\u89c2\u5bdf\u5176 cost<\/code>\u51fd\u6570\u4e0b\u964d\uff0c\u5e94\u8be5\u4f1a\u6709\u66f4\u52a0\u660e\u663e\u7684\u6ce2\u52a8\uff08\u540e\u7eed\u5427\u81ea\u5df1\u5b9e\u73b0\u7684\u7a0b\u5e8f\u6539\u9020\u540e\uff0c\u5c1d\u8bd5\u89c2\u5bdf\u4e00\u4e0b\uff09\u3002<\/p>\n\n\n\n

\u4e3a\u4e86\u52a0\u5feb\u8fed\u4ee3\u7684\u901f\u5ea6\uff0c\u4e00\u4e2a\u6298\u4e2d\u7684\u601d\u8def\u662f\uff0c\u5f15\u5165\u4e00\u4e2a\u5747\u503c\u66ff\u6362\u5f53\u524d\u7684\u68af\u5ea6\u65b9\u5411\u3002\u8be5\u5982\u4f55\u5f15\u5165\u8fd9\u4e2a\u5747\u503c\u5462\uff1f\u68af\u5ea6\u662f\u4e00\u4e2a\u968f\u65f6\u8ba1\u7b97\u63a8\u8fdb\uff0c\u4e0d\u65ad\u63a8\u8fdb\u7684\u53d8\u91cf\uff0c\u5e38\u7528\u7684\u5747\u503c\u8ba1\u7b97\u53ef\u4ee5\u53c2\u8003\uff1aMoving average<\/a>\u3002\u6700\u4e3a\u5e38\u89c1\u7684\u5b9e\u73b0\u662f\u4f7f\u7528\u201cExponential moving average\u201d\uff0c\u8fd9\u79cd\u5e73\u5747\u503c\u7684\u8ba1\u7b97\uff0c\u5728\u8fed\u4ee3\u8ba1\u7b97\u65f6\u5b9e\u73b0\u975e\u5e38\u7b80\u5355\u3002<\/p>\n\n\n\n

Momentum \u5c31\u662f \u201cExponential moving average<\/a>\u201d\u5b9e\u73b0\u65f6\u7684\u53c2\u6570\u201csmoothing factor\u201d\uff0c\u5728\u795e\u7ecf\u7f51\u7edc\u4e2d\uff0c\u7ecf\u5e38\u4f7f\u7528 \\( \\beta \\)\u8868\u793a\uff08\u539f\u56e0\u662f \\( \\alpha \\) \u5df2\u7ecf\u8868\u793a\u5b66\u4e60\u7387\u4e86 \uff09\u3002<\/p>\n\n\n\n

\u800c\u8fd9\u91cc\u7684 Momentum \uff0c\u4e5f\u662f TensorFlow \u5728\u6784\u9020 SGD \u7b97\u6cd5\u65f6\u9700\u8981\u7684\u53e6\u4e00\u4e2a\u53c2\u6570\u3002<\/p>\n\n\n\n

\u5173\u4e8eExponential moving average <\/h4>\n\n\n\n

\u6216\u8005\u53eb\u201cExponential smoothing\u201d\u3002\u6211\u4eec\u770b\u770b\u8fd9\u4e2a\u7b97\u6cd5\u7684\u5177\u4f53\u5b9e\u73b0\u662f\u600e\u6837\u7684\uff1f<\/p>\n\n\n\n

\u539f\u59cb\u7684\u8fed\u4ee3\uff1a\\( w = w – \\alpha \\frac{\\partial J}{\\partial w} \\)<\/p>\n\n\n\n

\u4f7f\u7528 \u201cExponential smoothing\u201d \u540e\u7684\u8fed\u4ee3\uff1a <\/p>\n\n\n

$$
\n\\begin{align}
\nv_0 & = 0 \\quad \\partial{w}_t = \\frac{\\partial J}{\\partial w}|_{(for \\, sample \\, t)} \\\\
\nv_{t} & = \\beta*v_{t-1} + (1-\\beta)\\partial{w}_{t} \\\\
\nw & := w – \\alpha v_t
\n\\end{align}
\n$$<\/p>\n\n\n\n

\u8003\u8651 \\( \\beta = 0.9 \\)\uff0c\u5982\u679c\u6570\u5b66\u76f4\u89c9\u6bd4\u8f83\u597d\u7684\u8bdd\uff0c\u53ef\u4ee5\u770b\u51fa\uff0c\u539f\u672c\u4f7f\u7528\u68af\u5ea6\\( \\partial{w} \\)\u8fdb\u884c\u8fed\u4ee3\u7684\uff0c\u8fd9\u91cc\u4f7f\u7528\u4e86\u4e00\u4e2a\u68af\u5ea6\u7684\u201cExponential smoothing\u201d \\( v_t \\)\u53bb\u66ff\u4ee3\u3002\u4e0a\u9762\u7684\u5f0f\u5b50\u4e2d\uff0c\\( v_t \\) \u5982\u679c\u5c55\u5f00\u6709\u5982\u4e0b\u8868\u8fbe\u5f0f\uff1a<\/p>\n\n\n

$$
\n\\begin{align}
\nv_t & = (1-\\beta)\\partial{w}_{t} + \\beta(1-\\beta)\\partial{w}_{t-1} + \\beta^2(1-\\beta)\\partial{w}_{t-2} … \\\\
\n& = \\sum\\limits_{i=0}^{t} \\beta^{i}(1-\\beta)\\partial{w}_{i}
\n\\end{align}
\n$$<\/p>\n\n\n\n

\u4f7f\u7528\u201cExponential smoothing\u201d \u4e4b\u540e\uff0c\u65b0\u7684\u8fed\u4ee3\u65b9\u5411 \\( v_t \\)\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u4e00\u4e2a\u524d\u9762\u6240\u6709\u68af\u5ea6\u65b9\u5411\u7684\u52a0\u6743\u5e73\u5747\u3002<\/em>\u79bb\u5f97\u8d8a\u8fd1\u7684\u68af\u5ea6\uff0c\u6743\u91cd\u8d8a\u9ad8\uff0c\u4f8b\u5982\uff0c\\( \\partial{w}_{t} \\)\u7684\u6743\u91cd\u662f\\( (1-\\beta) \\)\uff1b\u800c\u4e4b\u524d\u7684\u68af\u5ea6\uff0c\u5219\u6bcf\u6b21\u4e58\u4ee5\u4e00\u4e2a \\( \\beta \\)\u8870\u51cf\u3002<\/p>\n\n\n\n

Exponential moving average\u7684\u201c\u51b7\u542f\u52a8\u95ee\u9898\u201d\u4e0e\u4fee\u6b63<\/h4>\n\n\n\n

\u4ed4\u7ec6\u89c2\u6d4b\u4e0a\u8bc9\u7684 \u201cExponential moving average\u201d \u516c\u5f0f\uff0c\u53ef\u4ee5\u6ce8\u610f\u5230\u4e00\u4e2a\u95ee\u9898\uff0c\u5c31\u662f\u5176\u6700\u521d\u7684\u51e0\u4e2a\u70b9\u603b\u662f\u4f1a\u504f\u5c0f\u3002\u5176\u539f\u56e0\u662f\uff0c\u5f53\u524d\u503c\u7684\u6743\u91cd\u603b\u662f\u4e3a \\( 1- \\beta \\)\uff0c\u800c\u56e0\u4e3a\u662f\u521d\u59cb\u7684\u51e0\u4e2a\u503c\uff0c\u5e76\u6ca1\u6709\u66f4\u524d\u9762\u7684\u6570\u636e\u53bb\u201c\u5e73\u5747\u201d\u5f53\u524d\u503c\uff0c\u4e5f\u5c31\u4f1a\u51fa\u73b0\uff0c\u521d\u59cb\u503c\u603b\u662f\u4f1a\u504f\u5c0f\u7684\u95ee\u9898\u3002<\/p>\n\n\n\n

\u901a\u5e38\uff0c\u5982\u679c\u6837\u672c\u91cf\u5f88\u5927\u7684\u4e8b\u65f6\u5019\uff0c\u5219\u53ef\u4ee5\u5ffd\u7565\u8fd9\u4e2a\u95ee\u9898\uff0c\u56e0\u4e3a\u521d\u59cb\u503c\u504f\u5c0f\u7684\u70b9\u5360\u6bd4\u4f1a\u975e\u5e38\u5c11\uff0c\u53ef\u4ee5\u5ffd\u7565\u3002\u5982\u679c\u8981\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u4e5f\u6709\u7ee7\u7eed\u5bf9\u4e0a\u8ff0\u7684 \u201cExponential moving average\u201d\u505a\u4e86\u4e00\u4e9b\u4fee\u6b63\uff0c\u53ef\u4ee5\u8003\u8651\u5bf9 \\( v_t \\)\u7684\u7ed3\u679c\u503c\u505a\u4e00\u4e2a\u4fee\u6b63\uff1a\\( v_t := \\frac{vt}{1-\\beta^t} \\)\u3002<\/p>\n\n\n\n

\u4e00\u822c\u7684\uff0c\u56e0\u4e3a\u6837\u672c\u7684\u6570\u91cf\u603b\u662f\u6bd4\u8f83\u5927\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u5ffd\u7565\u8fd9\u4e2a\u95ee\u9898\uff0c\u800c\u65e0\u9700\u505a\u4efb\u4f55\u4fee\u6b63\u3002<\/p>\n\n\n\n

RMSprop<\/h4>\n\n\n\n

\u5728\u524d\u9762\u7684\u201cGradient Descent with Momentum\u201d\u4e2d\uff0c\u6211\u4eec\u770b\u5230\u4e3a\u4e86\u89e3\u51b3\u68af\u5ea6\u6ce2\u52a8\u8f83\u5927\u7684\u95ee\u9898\uff0c\u4f7f\u7528\u4e86 \u201cExponential moving average\u201d \u53bb\u5c1d\u8bd5\u5c06\u4e00\u4e9b\u6bd4\u8f83\u504f\u7684\u68af\u5ea6\uff0c\u62c9\u5012\u4e00\u4e2a\u8f83\u4e3a\u5e73\u5747\u7684\u65b9\u5411\u4e0a\u6765\u3002RMSprop<\/code>\u7684\u60f3\u6cd5\u4e5f\u662f\u7c7b\u4f3c\u7684\uff0c\u8fd9\u91cc\u901a\u8fc7\u4e86root mean square<\/code>\u7684\u60f3\u6cd5\u8fdb\u884c\u5e73\u5747\u503c\u7684\u8ba1\u7b97\u3002\u5177\u4f53\u7684\uff0c\u5728\u8fdb\u884c SGD \u65f6\uff0c\u6bcf\u6b21\u66f4\u65b0\u68af\u5ea6\uff0c\u6309\u7167\u5982\u4e0b\u7684\u65b9\u6cd5\u8fdb\u884c\u66f4\u65b0\uff1a<\/p>\n\n\n

$$
\n\\begin{align}
\ns_0 & = 0 \\quad \\partial{w}_t = \\frac{\\partial J}{\\partial w}|_{(for \\, sample \\, t)} \\\\
\ns_{t} & = \\beta*s_{t-1} + (1-\\beta)(\\partial{w}_{t})^2 \\\\
\nw & := w – \\alpha \\frac{\\partial w}{\\sqrt{s_{t}}}
\n\\end{align}
\n$$<\/p>\n\n\n\n

\u8bf4\u660e\uff1a\u8fd9\u91cc\u5bf9\u68af\u5ea6\u8fdb\u884c\u5e73\u65b9\u65f6\uff0c\u5982\u679c\u5728\u7a0b\u5e8f\u4e2d\u662f\u4e00\u4e2a\u68af\u5ea6\u5411\u91cf\uff0c\u90a3\u4e48\u8fd9\u91cc\u201c\u5e73\u65b9\u201d\u4e5f\u5c31\u662f\u5bf9\u68af\u5ea6\u7684\u6bcf\u4e00\u4e2a\u5206\u91cf\u8fdb\u884c\u4e00\u6b21\u5e73\u65b9\u3002<\/p>\n\n\n\n

\u5728\u201cExponential smoothing\u201d\u7684\u5b9e\u73b0\u4e2d\uff0c\u662f\u5c06\u5f53\u524d\u503c\uff0c\u4f7f\u7528\u4e00\u4e2a\u52a0\u6743\u5e73\u5747\u66ff\u4ee3\u3002\u4e0e\u201cExponential smoothing\u201d\u7c7b\u4f3c\u7684\uff0c\u539f\u672c\u7684\u68af\u5ea6\u65b9\u5411\uff0c\u73b0\u5728\u4f7f\u7528\u5982\u4e0b\u7684\u65b9\u5411\u53bb\u66ff\u4ee3\u4e86\uff1a<\/p>\n\n\n

$$
\n\\begin{align}
\ns_t & = \\frac{\\partial{w}_{t}}{\\sqrt{(1-\\beta)(\\partial{w}_{t})^2 + \\beta(1-\\beta)(\\partial{w}_{t-1})^2 + \\beta^2(1-\\beta)(\\partial{w}_{t-2})^2 + \\cdots }} \\\\
\n & = \\frac{\\partial{w}_{t}}{\\sqrt{\\sum\\limits_{i=1}^{t}\\beta^i(1-\\beta)(\\partial{w}_{i})^2}} \\\\
\n\\end{align}
\n$$<\/p>\n\n\n\n

<\/p>\n\n\n\n

Adam Gradient Descent<\/h4>\n\n\n\n

\u8fd9\u53ef\u80fd\u662f\u5b9e\u9645\u4f7f\u7528\u6700\u591a\u7684\u7b97\u6cd5\uff0c\u5168\u79f0\u662f Adaptive Moment Estimation \u3002\u8be5\u5b9e\u73b0\uff0c\u5c06 \u201cMomentum\u201d \u548c \u201cRMSprop\u201d \u505a\u4e86\u4e00\u5b9a\u7684\u878d\u5408\uff0c\u5f62\u6210\u4e86\u65b0\u7684\u201c\u6700\u4f73\u5b9e\u8df5\u201d Adam\u3002\u5728\u878d\u5408\u4e0a\uff0c\u5177\u4f53\u7684\u5b9e\u73b0\u4e0e\u4e24\u4e2a\u7ec6\u8282\u70b9\uff1a<\/p>\n\n\n\n

(1) \u5728 Adam \u4e2d\u5747\u4f7f\u7528\u4e86\u201c\u4fee\u6b63\u201d\u8ba1\u7b97\uff0c\u5373 \\( \\hat{v_t} = \\frac{v_t}{1-(\\beta_1)^t} \\quad \\hat{s_t} = \\frac{s_t}{1-(\\beta_1)^t} \\)<\/p>\n\n\n\n

(2) \u53c2\u6570\u66f4\u65b0\u516c\u5f0f\uff0c\u4f7f\u7528\u4e86\u4e24\u4e2a\u7b97\u6cd5\u7684\u878d\u5408\uff1a \\( w := w – \\alpha \\frac{\\hat{v_t}}{\\sqrt{\\hat{s_t}}} \\)<\/p>\n\n\n\n

Adam optimization\u7684\u6548\u679c\u5bf9\u6bd4<\/h4>\n\n\n\n

\u5728 Adam \u7684\u8bba\u6587\u4e2d\u5bf9\u4e8e\u6548\u679c\u505a\u4e86\u975e\u5e38\u591a\u7684\u8bc4\u4f30\uff0c\u611f\u5174\u8da3\u7684\u53ef\u4ee5\u53c2\u8003\u76f8\u5173\u8bba\u6587\u3002<\/p>\n\n\n\n

\u8fd9\u91cc\u6839\u636e\u4e4b\u524d\u5b8c\u6210\u7684\u8bad\u7ec3\u7a0b\u5e8f\uff0c\u4e5f\u8fdb\u884c\u4e86\u4f18\u5316\uff0c\u5b9e\u73b0\u4e86Adam\u7b97\u6cd5\u3002\u5728 MNIST \u6570\u636e\u96c6\u7684\u8bad\u7ec3\u4e0a\uff0c\u6211\u4eec\u6765\u770b\u770b Adam \u7684\u6548\u679c\uff1a<\/p>\n\n\n\n

\n
\n
\"\"<\/figure>\n<\/div>\n\n\n\n
\n

\u4ece\u53f3\u56fe\u53ef\u4ee5\u770b\u5230\uff0cAdam\uff08\u84dd\u8272\uff09\u660e\u663e\u7684\u63d0\u5347\u4e86\u8fed\u4ee3\u6548\u7387\u3002\u4f9d\u65e7\u4e00\u5b9a\u7a0b\u5ea6\u5b58\u5728 mini-batch\uff08\u7eff\u8272\uff09 \u7684\u68af\u5ea6\u6ce2\u52a8\u7684\u95ee\u9898\u3002\u76f8\u6bd4\u4e8e\uff0cbatch gradient descent \uff08\u7ea2\u8272\uff09\u7b97\u6cd5\uff0c\u8fed\u4ee3\u6548\u7387\u5927\u5927\u589e\u52a0\uff0c\u7ea6\u5728\u7b2c10\u6b21\u8fed\u4ee3\uff0c\u5373\u5728\u7b2c\u4e00\u4e2aepoch \u7684\u7b2c\u5341\u6279\u6837\u672c\u8fdb\u884c\u8bad\u7ec3\u65f6\uff0ccost \u5c31\u4e0b\u964d\u5230\u4e86\u6bd4\u8f83\u4f4e\u7684\u7a0b\u5ea6\u3002<\/p>\n<\/div>\n<\/div>\n\n\n\n

\u5173\u4e8e root mean square<\/code><\/h4>\n\n\n\n

root mean square<\/code>\u4e5f\u53eb\u4e8c\u6b21\u5e73\u5747\u503c\uff0c\u8003\u8651\u4e00\u7ec4\u6570\u636e\uff1a\\( {x_1,x_2, \\cdots , x_n } \\)\uff0c\u5176RMS<\/code>\u5219\u4e3a\uff1a <\/p>\n\n\n\n

$$ x_{rms} = \\sqrt{\\frac{1}{n} \\sum_{i=1}^n x_i^2} = \\sqrt{\\frac{1}{n} (x_1^2 + x_2^2 + \\cdots + x_n^2)} $$<\/p>\n\n\n\n

<\/p>\n\n\n\n

\u8865\u5145\u8bf4\u660e<\/h4>\n\n\n\n

\u53ef\u4ee5\u770b\u5230\uff0c\u6240\u6709\u7684\u8fd9\u4e9b\u4f18\u5316\u90fd\u662f\u9762\u5411\u201c\u6700\u4f18\u5316\u201d\u95ee\u9898\u7684\u3002\u68af\u5ea6\u4e0b\u964d\u662f\u4e00\u4e2a\u4e00\u9636\u4f18\u5316\uff08First-order Optimization\uff09\u7684\u65b9\u6cd5\uff0c\u5176\u6838\u5fc3\u5c31\u5728\u4e0e\u6bcf\u6b21\u8fed\u4ee3\u65f6\uff0c\u5e94\u8be5\u5982\u4f55\u53bb\u66f4\u65b0\u54cd\u5e94\u7684\u53c2\u6570\u503c\uff0c\u5728\u68af\u5ea6\u4e0b\u964d\u4e2d\u4e5f\u5c31\u662f\u5982\u4f55\u53bb\u9009\u62e9\u5408\u9002\u7684\u5b66\u4e60\u7387\u3002<\/p>\n\n\n\n

\u725b\u987f\u6cd5\u662f\u5178\u578b\u7684\u4e8c\u9636\u4f18\u5316\uff08Second-order Optimization\uff09\uff0c\u5728\u8fed\u4ee3\u65f6\u4f7f\u7528\u4e86\u4e8c\u9636\u5bfc\u6570\uff0c\u6240\u4ee5\uff0c\u901a\u5e38\u53ef\u4ee5\u83b7\u5f97\u66f4\u597d\u7684\u8fed\u4ee3\u6548\u7387\u3002\u4f46\u662f\u56e0\u4e3a\u4e8c\u9636\u5bfc\u6570\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u4f1a\u4e0a\u5347\u975e\u5e38\u591a\uff08\u5bf9\u5e94\u7684\u77e9\u9635\u53ef\u80fd\u662f\u6240\u6709\u53c2\u6570\u7684\u5e73\u65b9\uff0c\u5e94\u8be5\u4e5f\u6709\u4eba\u5c1d\u8bd5\u53bb\u7b97\u8fc7\u4e86…\uff09\u3002\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48\u5728\u8fd9\u4e2a\u573a\u666f\u4e0b\uff0c\u4f9d\u65e7\u662f\u4f7f\u7528\u4e00\u9636\u4f18\u5316\u65b9\u6cd5\u7684\u539f\u56e0\u3002<\/p>\n\n\n\n

\u5982\u679c\u60f3\u6bd4\u8f83\u597d\u7684\u7406\u89e3\u5b66\u4e60\u7387\u3001Momentum\u3001RMSprop\u3001Adam\u7b49\u5185\u5bb9\uff0c\u5efa\u8bae\u5148\u4e86\u89e3\u68af\u5ea6\u3001\u6570\u503c\u65b9\u6cd5\u3001\u6700\u4f18\u5316\u95ee\u9898\u7b49\u6570\u5b66\u65b9\u6cd5\u3002<\/p>\n\n\n\n

\u5230\u8fd9\u91cc\u8fd9\u4e2a\u7cfb\u5217\u7b97\u662f\u4e00\u4e2a\u5c0f\u9636\u6bb5\u4e86\uff0c\u8fd9\u662f\u4e00\u4e2a\u4e2a\u4eba\u5b66\u4e60\u7684\u7b14\u8bb0\uff0c\u4ece\u6570\u5b66\u7684\u68af\u5ea6\u6982\u5ff5\u5f00\u59cb\uff0c\u9010\u6b65\u5230\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u7684Adam\u4f18\u5316\u7b97\u6cd5\uff0c\u4e5f\u5305\u542b\u90e8\u5206\u52a8\u624b\u5b9e\u8df5\u7684\u795e\u7ecf\u7f51\u7edc\u7b97\u6cd5\u5b9e\u73b0\u3002\u5b8c\u6210\u7684\u7cfb\u5217\u5305\u62ec\u4e86\uff1a<\/p>\n\n\n\n