{"id":15847,"date":"2024-12-15T10:27:45","date_gmt":"2024-12-15T02:27:45","guid":{"rendered":"https:\/\/www.orczhou.com\/?p=15847"},"modified":"2025-12-17T12:22:33","modified_gmt":"2025-12-17T04:22:33","slug":"mini-batch-gradient-descent-stochastic","status":"publish","type":"post","link":"https:\/\/www.orczhou.com\/index.php\/2024\/12\/mini-batch-gradient-descent-stochastic\/","title":{"rendered":"\u968f\u673a\u68af\u5ea6\u4e0b\u964d(SGD)\u548cMini-batch\u68af\u5ea6\u4e0b\u964d"},"content":{"rendered":"\n\n\n\n<h4 class=\"wp-block-heading\">Mini-batch Gradient Descent\u7684\u4e3b\u8981\u60f3\u6cd5 <\/h4>\n\n\n\n\n\n\n<p>\u5728\u524d\u9762\u7684\u5b9e\u8df5\u4e2d\uff0c\u4f7f\u7528\u201cGradient Descent\u201d\u65f6\uff0c\u90fd\u662f\u4e00\u6b21\u6027\u628a\u6240\u6709\u7684\u6570\u636e\u96c6\u90fd\u8003\u8651\u8fdb\u53bb\uff0c\u4e00\u5207\u4f3c\u4e4e\u90fd\u6ca1\u6709\u4ec0\u4e48\u95ee\u9898\u3002<\/p>\n\n\n\n<p>\u4f46\u662f\uff0c\u5728\u73b0\u5b9e\u5b9e\u8df5\u4e2d\uff0c\u5982\u679c\u8bad\u7ec3\u6570\u636e\u91cf\u975e\u5e38\u5927\uff0c\u8fd9\u79cd\u65b9\u5f0f\u5c31\u4e0d\u9002\u7528\u4e86\u3002\u8bd5\u60f3\uff0c\u5728\u524d\u9762\u7684\u793a\u4f8b\u4e2d\uff0c\u8f93\u5165\u6837\u672c\u6570\u636e\uff0c\u5373\\( X \\)\uff08\u6216\u8005 \\( A^{[0]}\\)\uff09\uff0c\u5176\u7ef4\u5ea6\uff08\u6216\u8005\u8bf4shape\uff09\u5219\u53ef\u80fd\u662f\\( 300 \\times 10,000,000 \\)\u3002\u8fd9\u4f1a\u5bfc\u81f4\u6bcf\u4e00\u6b21\u7684\u68af\u5ea6\u8ba1\u7b97\u91cf\u90fd\u975e\u5e38\u5927\uff0c\u4e00\u6b21\u8fed\u4ee3\uff08<code>epoch<\/code>\uff09\u7684\u65f6\u95f4\u4f1a\u5f88\u957f\u3002<\/p>\n\n\n\n<p>\u4e00\u79cd\u975e\u5e38\u5e38\u89c1\u7684\u3001\u4e5f\u662f\u975e\u5e38\u7ecf\u5178\u7684\u68af\u5ea6\u4e0b\u964d\u6539\u8fdb\uff0c\u5c31\u662f mini-batch gradient descent\u3002\u9996\u5148\uff0c\u5c06\u6837\u672c\u5206\u5c42\u82e5\u5e72\u5c0f\u4efd\uff0c\u5e76\u5355\u72ec\u5bf9\u6bcf\u4e2a\u201c\u5c0f\u4efd\u201d\u8fdb\u884c\u201cGradient Descent\u201d\uff0c\u6700\u540e\u9010\u6b65\u5b8c\u6210\u6240\u6709\u6837\u672c\u7684\u8bad\u7ec3\u3002\u5b8c\u6210\u4e00\u6b21\u6240\u6709\u6837\u672c\u7684\u904d\u5386\uff0c\u79f0\u4e4b\u4e3a\u4e00\u6b21\u8fed\u4ee3<code>epoch<\/code>\u3002<\/p>\n\n\n\n<p>\u5728\u795e\u7ecf\u7f51\u7edc\u7684\u8bad\u7ec3\u4e2d\uff0c\u53ef\u4ee5\u7528\u4e0b\u9762\u6b65\u9aa4\u7406\u89e3\u8fd9\u4e2a\u8fc7\u7a0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"python\" class=\"language-python\">for \"a-small-batch-of-samples X^{t} \" in \"all-samples\"\n    forward  propagation on X^{t}\n    backward propagation on X^{t}\n    update W\/b\n        W^{[l]} = W^{[l]} - lr * dW^{[l]}\n        b^{[l]} = b^{[l]} - lr * db^{[l]}<\/code><\/pre>\n\n\n\n<p>\u76f8\u5bf9\u4e8e mini-batch gradient descent \uff0c\u524d\u9762\u4ecb\u7ecd\u7684\u4e00\u6b21\u628a\u6240\u6709\u6837\u672c\u90fd\u7528\u4e8e\u8bad\u7ec3\u7684\u65b9\u6cd5\uff0c\u4e5f\u88ab\u79f0\u4e3a\u201cbatch gradient descent\u201d\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Stochastic Gradient Descent<\/h4>\n\n\n\n<p>\u5728 mini-batch \u4e2d\uff0c\u5982\u679c\u6bcf\u6b21\u6279\u91cf\u7684\u6837\u672c\u5927\u5c0f\u662f <code>1<\/code> \u7684\u8bdd\uff0c\u90a3\u4e48\uff0c\u4e5f\u79f0\u4e3a<code>Stochastic Gradient Descent<\/code>\uff08\u7b80\u79f0 <code>SGD<\/code>,\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff09\u3002\u4e8b\u5b9e\u4e0a\uff0c\u81ea\u5f00\u59cb\u4f7f\u7528 Backpropagation \u7b97\u6cd5\u4ee5\u6765\uff0c<code>SGD<\/code>\u5c31\u88ab\u7528\u4e8e\u63d0\u5347\u795e\u7ecf\u7f51\u7edc\u7684\u8bad\u7ec3\u7684\u6548\u7387\u3002\u5e76\u4e14\u5f88\u5feb\u7684\uff0cmini-batch gradient descent \u5c31\u4f5c\u4e3a\u4e00\u79cd\u4f18\u5316\u88ab\u4f7f\u7528\u3002\u76ee\u524d\uff0cmini-batch gradient descent \u4f9d\u65e7\u662f\u4e00\u79cd\u5e38\u7528\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u65b9\u6cd5<sup><a href=\"https:\/\/en.wikipedia.org\/wiki\/Stochastic_gradient_descent#History\">[1]<\/a><a href=\"https:\/\/ieeexplore.ieee.org\/document\/8945166\">[2]<\/a><\/sup>\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u6536\u655b\u7a33\u5b9a\u6027\u9884\u4f30<\/h4>\n\n\n\n<p>\u4e0d\u96be\u60f3\u8c61\uff0c\u5728\u201cbatch gradient descent\u201d\u4e2d\uff0c\u4e00\u6b21\u6027\u628a\u6240\u6709\u6570\u636e\u90fd\u7528\u4e8e\u68af\u5ea6\u4e0b\u964d\u7684\u7b97\u6cd5\uff0c\u901a\u5e38\u90fd\u80fd\u591f\u83b7\u5f97\u66f4\u597d\u7684\u6536\u655b\u901f\u5ea6\u3002\u800c\u5728\u4f7f\u7528 mini-batch \u7684\u65f6\u5019\uff0c\u7531\u4e8e\u4e0d\u540c\u7684\u6279\u6b21\u7684\u6837\u672c\u5728\u8ba1\u7b97\u65f6\uff0c\u201c\u8ba1\u7b97\u68af\u5ea6\u201d\u90fd\u4e0e\u201c\u5168\u5c40\u68af\u5ea6\u201d\u6709\u4e00\u5b9a\u7684\u504f\u5dee\uff0c\u5e76\u4e14\u6709\u65f6\u5019\u504f\u5dee\u8f83\u5927\uff0c\u6709\u65f6\u5019\u8f83\u5c0f\uff0c\u6240\u4ee5\uff0c\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u6536\u655b\u901f\u5ea6\u8981\u6162\u4e00\u4e9b\u3002\u800c\uff0cStochastic Gradient Descent \u5219\u53ef\u80fd\u4f1a\u66f4\u6162\u4e00\u4e9b\u3002<\/p>\n\n\n\n<p>\u53ef\u4ee5\u8fd9\u4e48\u7406\u89e3\uff0c mini-batch \u548c Stochastic Gradient Descent \u90fd\u603b\u662f\u4f7f\u7528\u4e00\u4e2a\u5c40\u90e8\u7684\u68af\u5ea6\uff08\u90e8\u5206\u6837\u672c\u7684\u68af\u5ea6\uff09\u6765\u9884\u4f30\u6574\u4f53\u7684\u68af\u5ea6\u65b9\u5411\uff0c\u81ea\u7136\u6548\u679c\u4f1a\u5dee\u4e00\u4e9b\u3002<\/p>\n\n\n\n<p>\u8fd9\u91cc\u6211\u4eec\u6539\u8fdb\u4e86\u539f\u6765\u7684\u795e\u7ecf\u7f51\u7edc\u5b9e\u73b0 ssnn_bear.py\uff0c\u5c06\u5176\u66f4\u65b0\u4e3a\u4f7f\u7528 mini-batch \u7684 ssnn_cat.py\u3002\u8be6\u7ec6\u4ee3\u7801\u53ef\u4ee5\u53c2\u8003GitHub\u4ed3\u5e93\uff1a<a href=\"https:\/\/github.com\/orczhou\/ssnn\" target=\"_blank\" rel=\"noreferrer noopener\">super simple neural network<\/a> \u3002<\/p>\n\n\n\n<p>\u8fd0\u884c ssnn_cat.py \u5e76\u89c2\u5bdf mini-batch \u7684 cost \u4e0b\u964d\u901f\u5ea6\u5982\u4e0b\uff1a<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center\"><strong>mini-batch \u8fed\u4ee3\u4e0bcost\u603b\u662f\u5728\u4e0a\u4e0b\u6ce2\u52a8<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"604\" src=\"https:\/\/www.orczhou.com\/wp-content\/uploads\/2024\/11\/image-35-1024x604.png\" alt=\"\" class=\"wp-image-16123\" srcset=\"https:\/\/www.orczhou.com\/wp-content\/uploads\/2024\/11\/image-35-1024x604.png 1024w, https:\/\/www.orczhou.com\/wp-content\/uploads\/2024\/11\/image-35-300x177.png 300w, https:\/\/www.orczhou.com\/wp-content\/uploads\/2024\/11\/image-35-768x453.png 768w, https:\/\/www.orczhou.com\/wp-content\/uploads\/2024\/11\/image-35.png 1478w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center\"><strong>batch gd\u7b97\u6cd5\u4e0bcost\u4e0b\u964d\u975e\u5e38\u7a33\u5b9a<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"605\" src=\"https:\/\/www.orczhou.com\/wp-content\/uploads\/2024\/11\/image-36-1024x605.png\" alt=\"\" class=\"wp-image-16124\" srcset=\"https:\/\/www.orczhou.com\/wp-content\/uploads\/2024\/11\/image-36-1024x605.png 1024w, https:\/\/www.orczhou.com\/wp-content\/uploads\/2024\/11\/image-36-300x177.png 300w, https:\/\/www.orczhou.com\/wp-content\/uploads\/2024\/11\/image-36-768x454.png 768w, https:\/\/www.orczhou.com\/wp-content\/uploads\/2024\/11\/image-36.png 1480w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<h4 class=\"wp-block-heading\">batch_size \u5927\u5c0f\u7684\u914d\u7f6e<\/h4>\n\n\n\n<p>\u4e00\u4e9b\u7ecf\u9a8c\u6570\u503c\u53ef\u80fd\u662f64\u3001128\u3001256\u3001512\u7b49\u3002Mini-batch \u9700\u8981\u5728\u5927\u6570\u636e\u91cf\u548c\u5411\u91cf\u5316\u8ba1\u7b97\u4e4b\u95f4\u53d6\u5f97\u4e00\u4e2a\u5e73\u8861\uff0c\u6240\u4ee5\u901a\u5e38\u9700\u8981\u66f4\u5177\u8bad\u7ec3\u7684\u8bbe\u5907\u9009\u62e9\u5408\u9002\u7684 batch \u5927\u5c0f\uff0c\u4f7f\u5f97\u6bcf\u6b21\u8fed\u4ee3\u90fd\u5145\u5206\u5229\u7528\u786c\u4ef6\u7684\u8d44\u6e90\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u4ee3\u7801\u5b9e\u73b0<\/h4>\n\n\n\n<p>\u5728\u524d\u8ff0\u7684\u795e\u7ecf\u7f51\u7edc\u4e0a\uff08<a href=\"https:\/\/www.orczhou.com\/index.php\/2024\/11\/build-a-image-classification-neural-network-from-scratch\/\">\u53c2\u8003<\/a>\uff09\uff0c\u518d\u505a\u4e86\u4e00\u4e9b\u4fee\u6539\uff0c\u5b9e\u73b0\u4e86 Mini-Batch \u6216\u8005\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u65b0\u589e batch \u5927\u5c0f\u53c2\u6570<\/h5>\n\n\n\n<p>\u9996\u5148\uff0c\u65b0\u589e\u4e86 batch_size \u53c2\u6570\u8868\u793a\uff0c\u540c\u65f6\u589e\u52a0\u5bf9\u5e94\u53c2\u6570 batch_iteration \u8868\u793a\uff0c\u5728\u4e00\u6b21\u6837\u672c\u8fed\u4ee3\u4e2d\uff0c\u603b\u8ba1\u9700\u8981\u5faa\u73af\u591a\u5c11\u6b21\u3002\u6240\u4ee5\uff0c\u8fd9\u4e24\u4e2a\u53c2\u6570\u6709\u5982\u4e0b\u5173\u7cfb\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"python\" class=\"language-python\">batch_iteration = math.ceil(m\/batch_size)<\/code><\/pre>\n\n\n\n<h5 class=\"wp-block-heading\">\u5bf9\u6bcf\u6279\u6b21\u6837\u672c\u505a\u8fed\u4ee3<\/h5>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"python\" class=\"language-python\">batch_iteration = math.ceil(m\/batch_size)\n...\nfor i in range(iteration_count):\n    for i_batch in range(batch_iteration):\n        ...\n        # sample from i_batch*batch_size\n        batch_from  = i_batch*batch_size\n        batch_to    = min((i_batch+1)*batch_size,m)\n        batch_count = batch_to - batch_from\n        A0  = X[:,batch_from:batch_to] # column  [batch_from,batch_to)\n        Y_L = Y[:,batch_from:batch_to] # Y_label [batch_from,batch_to)\n        ...<\/code><\/pre>\n\n\n\n<p>\u4ee3\u7801\u7684\u5176\u4ed6\u5730\u65b9\uff0c\u51e0\u4e4e\u4e0d\u9700\u8981\u592a\u5927\u7684\u6539\u52a8\u3002\u5b8c\u6574\u7684\u4ee3\u7801\u53c2\u8003\uff1a<a href=\"https:\/\/github.com\/orczhou\/ssnn\/blob\/main\/ssnn_cat.py\">ssnn_cat.py<\/a><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u53c2\u8003<\/h4>\n\n\n\n<ul class=\"wp-block-list is-style-no-disc\">\n<li>[1] <a href=\"https:\/\/en.wikipedia.org\/wiki\/Stochastic_gradient_descent#History\">Stochastic gradient descent<\/a><\/li>\n\n\n\n<li>[2] https:\/\/github.com\/orczhou\/ssnn\/blob\/main\/ssnn_cat.py<\/li>\n\n\n\n<li>[3] https:\/\/github.com\/orczhou\/ssnn\/blob\/main\/ssnn_bear.py<\/li>\n\n\n\n<li>[4] https:\/\/github.com\/orczhou\/ssnn<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u662f\u4e00\u4e2a\u7cfb\u5217\u6587\u7ae0\u5305\u542b\u4e86\uff0c\u5b8c\u6574\u7684\u6587\u7ae0\u8fd8\u5305\u62ec\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.orczhou.com\/index.php\/2024\/10\/directional-derivative-partial-derivative\/\">\u4e8c\u5143\u51fd\u6570\u7684\u504f\u5bfc\u6570\u3001\u65b9\u5411\u5bfc\u6570\u3001\u68af\u5ea6<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.orczhou.com\/index.php\/2024\/11\/implement-a-super-simple-neural-network-in-99-line-codes\/\">99\u884c\u4ee3\u7801\u6784\u5efa\u6781\u7b80\u7684\u795e\u7ecf\u7f51\u7edc<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.orczhou.com\/index.php\/2024\/11\/build-a-image-classification-neural-network-from-scratch\/\">\u4ece\u96f6\u6784\u5efa\u56fe\u7247\u8bc6\u522b\u7684\u795e\u7ecf\u7f51\u7edc<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.orczhou.com\/index.php\/2024\/12\/shallow-neural-network-hyper-parameter-analysis\/\">\u6d45\u5c42\u795e\u7ecf\u7f51\u7edc\u7684\u8d85\u53c2\u6570\u5206\u6790<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u524d\u9762\u7684\u5b9e\u8df5\u4e2d\uff0c\u4f7f\u7528\u201cGradient Descent\u201d\u65f6\uff0c\u90fd\u662f\u4e00\u6b21\u6027\u628a\u6240\u6709\u7684\u6570\u636e\u96c6\u90fd\u8003\u8651\u8fdb\u53bb\uff0c\u4e00\u5207\u4f3c\u4e4e\u90fd\u6ca1\u6709\u4ec0\u4e48\u95ee\u9898\u3002\u4f46\u662f\uff0c\u5728\u73b0\u5b9e\u5b9e\u8df5\u4e2d\uff0c\u5982\u679c\u8bad\u7ec3\u6570\u636e\u91cf\u975e\u5e38\u5927\uff0c\u8fd9\u79cd\u65b9\u5f0f\u5c31\u4e0d\u9002\u7528\u4e86\u3002<\/p>\n","protected":false},"author":1,"featured_media":21481,"comment_status":"open","ping_status":"closed","sticky":false,"template":"wp-custom-template-a-1440-px-width-template","format":"standard","meta":{"_eb_attr":"","inline_featured_image":false,"_tocer_settings":[],"footnotes":""},"categories":[1],"tags":[],"class_list":["post-15847","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-simplelife"],"_links":{"self":[{"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/posts\/15847","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/comments?post=15847"}],"version-history":[{"count":75,"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/posts\/15847\/revisions"}],"predecessor-version":[{"id":21411,"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/posts\/15847\/revisions\/21411"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/media\/21481"}],"wp:attachment":[{"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/media?parent=15847"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/categories?post=15847"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/tags?post=15847"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}