{"id":1715,"date":"2024-12-15T07:59:00","date_gmt":"2024-12-14T23:59:00","guid":{"rendered":"https:\/\/blog.laoyulaoyu.top\/?p=1715"},"modified":"2024-11-21T16:23:54","modified_gmt":"2024-11-21T08:23:54","slug":"%e8%82%a1%e5%b8%82%e6%8a%95%e8%b5%84%e7%ad%96%e7%95%a5%e5%8d%87%e7%ba%a7%ef%bc%9a%e6%8e%8c%e6%8f%a1%e9%a9%ac%e5%b0%94%e5%8f%af%e5%a4%ab%e5%86%b3%e7%ad%96%e8%bf%87%e7%a8%8b%e4%b8%8e%e5%bc%ba%e5%8c%96","status":"publish","type":"post","link":"https:\/\/laoyulaoyu.com\/index.php\/2024\/12\/15\/%e8%82%a1%e5%b8%82%e6%8a%95%e8%b5%84%e7%ad%96%e7%95%a5%e5%8d%87%e7%ba%a7%ef%bc%9a%e6%8e%8c%e6%8f%a1%e9%a9%ac%e5%b0%94%e5%8f%af%e5%a4%ab%e5%86%b3%e7%ad%96%e8%bf%87%e7%a8%8b%e4%b8%8e%e5%bc%ba%e5%8c%96\/","title":{"rendered":"\u80a1\u5e02\u6295\u8d44\u7b56\u7565\u5347\u7ea7\uff1a\u638c\u63e1\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\u4e0e\u5f3a\u5316\u5b66\u4e60\uff0c\u63d0\u5347\u4ea4\u6613\u6280\u80fd"},"content":{"rendered":"\n<p>\u4f5c\u8005\uff1a<a href=\"https:\/\/www.laoyulaoyu.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u8001\u4f59\u635e\u9c7c<\/a><\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-cyan-bluish-gray-color\">\u539f\u521b\u4e0d\u6613\uff0c\u8f6c\u8f7d\u8bf7\u6807\u660e\u51fa\u5904\u53ca\u539f\u4f5c\u8005\u3002<\/mark><\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/www.laoyulaoyu.com\/wp-content\/uploads\/2024\/11\/102705.png\" alt=\"\" class=\"wp-image-3052\"\/><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<pre class=\"wp-block-verse\"><strong>\u5199\u5728\u524d\u9762\u7684\u8bdd\uff1a<\/strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">\u672c\u6587\u5c06\u6df1\u5165\u63a2\u8ba8\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\uff08MDP\uff09\u548c\u5f3a\u5316\u5b66\u4e60\u5728\u80a1\u7968\u4ea4\u6613\u4e2d\u7684\u8fd0\u7528\u3002<\/mark>\u901a\u8fc7\u9610\u8ff0MDP\u7684\u57fa\u672c\u539f\u7406\u548c\u5176\u5728\u4ea4\u6613\u7b56\u7565\u4e2d\u7684\u5b9e\u9645\u5e94\u7528\uff0c\u8bd5\u56fe\u5411\u60a8\u63ed\u793a\u8fd9\u4e9b\u5148\u8fdb\u6280\u672f\u5982\u4f55\u5e2e\u52a9\u6295\u8d44\u8005\u505a\u51fa\u66f4\u660e\u667a\u7684\u51b3\u7b56\u3002\u540c\u65f6\u6211\u8fd8\u63d0\u4f9b\u4e86\u6848\u4f8b\u548c\u4ee3\u7801\u793a\u4f8b\uff0c\u4f7f\u8bfb\u8005\u80fd\u591f\u66f4\u76f4\u89c2\u5730\u7406\u89e3\u8fd9\u4e9b\u6982\u5ff5\uff0c\u4ece\u800c\u5728\u80a1\u7968\u5e02\u573a\u4e2d\u83b7\u5f97\u4f18\u52bf\u3002<\/pre>\n<\/blockquote>\n\n\n\n<p>\u5bf9\u4e8e\u90a3\u4e9b\u6e34\u671b\u6301\u7eed\u76c8\u5229\u7684\u6295\u8d44\u8005\u6765\u8bf4\uff0c\u80a1\u7968\u4ea4\u6613\u65e0\u7591\u662f\u4e00\u9879\u65e2\u590d\u6742\u53c8\u5145\u6ee1\u6311\u6218\u7684\u4efb\u52a1\u3002\u51c6\u786e\u9884\u6d4b\u80a1\u7968\u4ef7\u683c\u53ef\u80fd\u88ab\u4e0a\u5347\u5230\u7384\u5b66\u7684\u9ad8\u5ea6\uff0c\u4f46\u5982\u679c\u6211\u4eec\u80fd\u6559\u4f1a\u8ba1\u7b97\u673a\u5982\u4f55\u505a\u51fa\u660e\u667a\u7684\u4ea4\u6613\u51b3\u7b56\u5462\uff1f\u8fd9\u5c31\u662f\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\uff08MDP\uff09\u548c\u5f3a\u5316\u5b66\u4e60\uff08RL\uff09\u7684\u7528\u6b66\u4e4b\u5730\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u4e00\u3001\u4ec0\u4e48\u662f\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b \uff1f<\/strong><\/h2>\n\n\n\n<p>\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\uff08Markov Decision Process, MDP\uff09\u662f\u4e00\u79cd\u7528\u4e8e\u5efa\u6a21\u51b3\u7b56\u95ee\u9898\u7684\u6570\u5b66\u6846\u67b6\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u4eba\u5de5\u667a\u80fd\u3001\u8fd0\u7b79\u5b66\u548c\u7ecf\u6d4e\u5b66\u7b49\u9886\u57df\u3002MDP\u63d0\u4f9b\u4e86\u4e00\u79cd\u7cfb\u7edf\u7684\u65b9\u6cd5\u6765\u63cf\u8ff0\u5728\u4e0d\u786e\u5b9a\u73af\u5883\u4e2d\u8fdb\u884c\u51b3\u7b56\u7684\u8fc7\u7a0b\uff0c\u7279\u522b\u662f\u5728\u72b6\u6001\u548c\u884c\u52a8\u4e4b\u95f4\u5b58\u5728\u968f\u673a\u6027\u7684\u60c5\u51b5\u4e0b\u3002<\/p>\n\n\n\n<p>\u5c3d\u7ba1\u5e02\u573a\u672a\u6765\u5145\u6ee1\u4e86\u4e0d\u786e\u5b9a\u6027\uff0c\u4f46MDP\u63d0\u4f9b\u4e86\u4e00\u79cd\u7b56\u7565\uff0c\u80fd\u5e2e\u52a9\u6211\u4eec\u5728\u6bcf\u4e00\u6b65\u505a\u51fa\u6700\u4f73\u9009\u62e9\uff0c\u4ee5\u5b9e\u73b0\u957f\u671f\u7684\u6295\u8d44\u76ee\u6807\u3002\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u6295\u8d44\u8005\u53ef\u4ee5\u66f4\u79d1\u5b66\u5730\u89c4\u5212\u4ed6\u4eec\u7684\u6295\u8d44\u8def\u5f84\uff0c\u5373\u4f7f\u9762\u5bf9\u4e0d\u786e\u5b9a\u7684\u5e02\u573a\u73af\u5883\uff0c\u4e5f\u80fd\u66f4\u52a0\u81ea\u4fe1\u5730\u505a\u51fa\u51b3\u7b56\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>1.1 MDP\u7684\u57fa\u672c\u7ec4\u6210\u90e8\u5206<\/strong><\/h3>\n\n\n\n<p>\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\u4e3b\u8981\u7531\u4ee5\u4e0b\u51e0\u4e2a\u8981\u7d20\u6784\u6210\uff1a<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/www.laoyulaoyu.com\/wp-content\/uploads\/2024\/11\/image-103.png\" alt=\"\" class=\"wp-image-3040\"\/><\/figure>\n<\/div>\n\n\n<ol id=\"bh-htJfkfZsjSVgGjzHulVYp\" class=\"wp-block-list\">\n<li><strong>\u72b6\u6001\u96c6\uff08S\uff09<\/strong>\uff1a\u8868\u793a\u7cfb\u7edf\u53ef\u80fd\u5904\u4e8e\u7684\u6240\u6709\u72b6\u6001\u7684\u96c6\u5408\uff0c\u4e5f\u53ef\u7406\u89e3\u4e3a\u5f53\u524d\u5f62\u52bf\u6216\u73af\u5883\uff08\u5982\u67d0\u4e00\u5929\u7684\u80a1\u7968\u4ef7\u683c\uff09\u3002<\/li>\n\n\n\n<li><strong>\u884c\u52a8\u96c6\uff08A\uff09<\/strong>\uff1a\u8868\u793a\u5728\u6bcf\u4e2a\u72b6\u6001\u4e0b\u53ef\u4ee5\u91c7\u53d6\u7684\u6240\u6709\u53ef\u80fd\u884c\u52a8\u7684\u96c6\u5408\uff08\u5982\u4e70\u5165\u3001\u5356\u51fa\u6216\u6301\u6709\uff09\u3002<\/li>\n\n\n\n<li><strong>\u8f6c\u79fb\u6982\u7387\uff08P\uff09<\/strong>\uff1a\u91c7\u53d6\u67d0\u79cd\u884c\u52a8\u540e\uff0c\u4e00\u79cd\u72b6\u6001\u8f6c\u53d8\u4e3a\u53e6\u4e00\u79cd\u72b6\u6001\u7684\u6982\u7387\uff08\u4f8b\u5982\uff0c\u4e70\u5165\u80a1\u7968\u540e\u80a1\u4ef7\u4e0a\u6da8\u7684\u6982\u7387\uff09\u3002\u901a\u5e38\u8868\u793a\u4e3a ( P(s&#8217;|s,a) )\uff0c\u5176\u4e2d ( s ) \u662f\u5f53\u524d\u72b6\u6001\uff0c( a ) \u662f\u91c7\u53d6\u7684\u884c\u52a8\uff0c( s&#8217; ) \u662f\u4e0b\u4e00\u4e2a\u72b6\u6001\u3002<\/li>\n\n\n\n<li><strong>\u5956\u52b1\u51fd\u6570\uff08R\uff09<\/strong>\uff1a\u884c\u52a8\u540e\u7684\u76f4\u63a5\u6536\u76ca\u6216\u635f\u5931\uff08\u5982\u51fa\u552e\u80a1\u7968\u7684\u5229\u6da6\u6216\u635f\u5931\uff09\u3002\u901a\u5e38\u8868\u793a\u4e3a ( R(s,a) )\uff0c\u8868\u793a\u5728\u72b6\u6001 ( s ) \u4e0b\u91c7\u53d6\u884c\u52a8 ( a ) \u6240\u83b7\u5f97\u7684\u5956\u52b1\u3002<\/li>\n\n\n\n<li><strong>\u6298\u6263\u56e0\u5b50\uff08\u03b3\uff09<\/strong>\uff1a\u5e73\u8861\u77ed\u671f\u4e0e\u957f\u671f\u56de\u62a5\u7684\u53c2\u6570\u3002\u6298\u6263\u7cfb\u6570\u8d8a\u4f4e\uff0c\u4ee3\u7406\u4eba\u5c31\u8d8a\u5728\u4e4e\u773c\u524d\u7684\u56de\u62a5\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>1.2 MDP\u7684\u51b3\u7b56\u8fc7\u7a0b<\/strong><\/h3>\n\n\n\n<p id=\"bh-wka-iAf2hGDVopi6AnpDe\">\u5728MDP\u4e2d\uff0c\u51b3\u7b56\u8005\u7684\u76ee\u6807\u662f\u9009\u62e9\u4e00\u4e2a\u7b56\u7565\uff08policy\uff09\uff0c\u5373\u5728\u6bcf\u4e2a\u72b6\u6001\u4e0b\u9009\u62e9\u884c\u52a8\u7684\u89c4\u5219\uff0c\u4ee5\u6700\u5927\u5316\u957f\u671f\u7d2f\u79ef\u5956\u52b1\u3002\u7b56\u7565\u53ef\u4ee5\u662f\u786e\u5b9a\u6027\u7684\uff08\u5728\u6bcf\u4e2a\u72b6\u6001\u4e0b\u9009\u62e9\u4e00\u4e2a\u7279\u5b9a\u7684\u884c\u52a8\uff09\u6216\u968f\u673a\u7684\uff08\u5728\u6bcf\u4e2a\u72b6\u6001\u4e0b\u4ee5\u4e00\u5b9a\u6982\u7387\u9009\u62e9\u4e0d\u540c\u7684\u884c\u52a8\uff09\u3002<\/p>\n\n\n\n<p id=\"bh-wPAmTm5lbeqxUEWpLCmlO\">MDP\u7684\u6838\u5fc3\u662f\u9a6c\u5c14\u53ef\u592b\u6027\u8d28\uff0c\u5373\u672a\u6765\u72b6\u6001\u4ec5\u4f9d\u8d56\u4e8e\u5f53\u524d\u72b6\u6001\u548c\u6240\u91c7\u53d6\u7684\u884c\u52a8\uff0c\u800c\u4e0e\u8fc7\u53bb\u7684\u72b6\u6001\u65e0\u5173\u3002\u8fd9\u4e00\u7279\u6027\u4f7f\u5f97MDP\u80fd\u591f\u6709\u6548\u5730\u5efa\u6a21\u8bb8\u591a\u5b9e\u9645\u95ee\u9898\u3002<\/p>\n\n\n\n<p><strong>\u5728\u80a1\u7968\u4ea4\u6613\u4e2d\uff0cMDP \u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u6a21\u62df\u4ea4\u6613\u8005\u5982\u4f55\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\u4e0e\u5e02\u573a\u4ef7\u683c\u4e92\u52a8\uff0c\u5e76\u505a\u51fa\u8fde\u7eed\u51b3\u7b56\uff0c\u4ee5\u6700\u5927\u5316\u5176\u6295\u8d44\u7ec4\u5408\u7684\u4ef7\u503c\u3002<\/strong>\u6bcf\u5929\u90fd\u88ab\u89c6\u4e3a\u4e00\u4e2a\u72b6\u6001\uff0c\u76ee\u6807\u662f\u91c7\u53d6\u6b63\u786e\u7684\u884c\u52a8\uff0c\u4f7f\u6295\u8d44\u7ec4\u5408\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\u4e0d\u65ad\u589e\u957f\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/www.laoyulaoyu.com\/wp-content\/uploads\/2024\/11\/image-104.png\" alt=\"\" class=\"wp-image-3041\"\/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\"><strong>1.3 MDP\u7684\u5e94\u7528<\/strong><\/h3>\n\n\n\n<p>\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\u5728\u591a\u4e2a\u9886\u57df\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\uff0c\u91d1\u878d\u51b3\u7b56\u662f\u5176\u6700\u6700\u91cd\u8981\u7684\u4e00\u4e2a\u9886\u57df\uff0c\u5176\u4ed6\u5305\u62ec\u4f46\u4e0d\u9650\u4e8e\uff1a<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/www.laoyulaoyu.com\/wp-content\/uploads\/2024\/11\/image-105.png\" alt=\"\" class=\"wp-image-3042\"\/><\/figure>\n<\/div>\n\n\n<ul id=\"bh-aIlTMKjAP-9OCM0EQukVC\" class=\"wp-block-list\">\n<li><strong>\u91d1\u878d\u51b3\u7b56<\/strong>\uff1a\u7528\u4e8e\u6295\u8d44\u7ec4\u5408\u4f18\u5316\u548c\u98ce\u9669\u7ba1\u7406\u3002<\/li>\n\n\n\n<li><strong>\u533b\u7597\u51b3\u7b56<\/strong>\uff1a\u8f85\u52a9\u533b\u751f\u5728\u6cbb\u7597\u65b9\u6848\u4e2d\u505a\u51fa\u6700\u4f73\u9009\u62e9\u3002<\/li>\n\n\n\n<li><strong>\u6e38\u620fAI<\/strong>\uff1a\u7528\u4e8e\u8bbe\u8ba1\u667a\u80fd\u4f53\u5728\u6e38\u620f\u4e2d\u505a\u51fa\u51b3\u7b56\u3002<\/li>\n\n\n\n<li><strong>\u673a\u5668\u4eba\u5bfc\u822a<\/strong>\uff1a\u5e2e\u52a9\u673a\u5668\u4eba\u5728\u672a\u77e5\u73af\u5883\u4e2d\u505a\u51fa\u6700\u4f73\u8def\u5f84\u9009\u62e9\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u4e8c\u3001\u4ec0\u4e48\u662f\u5f3a\u5316\u5b66\u4e60\uff08RL\uff09\uff1f<\/strong><\/h2>\n\n\n\n<p>\u5f3a\u5316\u5b66\u4e60\uff08RL\uff09\u662f\u673a\u5668\u5b66\u4e60\u7684\u4e00\u4e2a\u5206\u652f\uff0c\u5176\u4e2d\u4e00\u4e2a\u4ee3\u7406\u901a\u8fc7\u4e0e\u73af\u5883\u7684\u4ea4\u4e92\uff0c\u5728\u8bd5\u9519\u4e2d\u5b66\u4f1a\u505a\u51b3\u5b9a\u3002\u4ee3\u7406\u6839\u636e\u81ea\u5df1\u7684\u884c\u4e3a\u63a5\u53d7\u5956\u52b1\u6216\u60e9\u7f5a\uff0c\u5e76\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\u5229\u7528\u8fd9\u4e9b\u5956\u52b1\u6216\u60e9\u7f5a\u6539\u8fdb\u81ea\u5df1\u7684\u884c\u4e3a\u3002RL \u76f8\u5173\u6d41\u7a0b\u5305\u62ec\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u4ee3\u7406\uff1a<\/strong>\u51b3\u7b56\u8005\uff08\u5982\u6211\u4eec\u7684\u4ea4\u6613\u7b97\u6cd5\uff09\u3002<\/li>\n\n\n\n<li><strong>\u73af\u5883\uff1a<\/strong>\u80a1\u7968\u5e02\u573a\u63d0\u4f9b\u4ef7\u683c\u548c\u56de\u62a5\u3002<\/li>\n\n\n\n<li><strong>\u884c\u52a8\uff1a<\/strong>\u4ee3\u7406\u4eba\u505a\u51fa\u7684\u9009\u62e9\uff08\u5982\u8d2d\u4e70\u3001\u51fa\u552e\u3001\u6301\u6709\uff09\u3002<\/li>\n\n\n\n<li><strong>\u7b56\u7565\uff1a<\/strong>\u4ee3\u7406\u9075\u5faa\u7684\u7b56\u7565\uff0c\u5c06\u72b6\u6001\u6620\u5c04\u4e3a\u884c\u52a8\u3002<\/li>\n\n\n\n<li><strong>\u5956\u52b1\u4fe1\u53f7\uff1a<\/strong>\u6bcf\u6b21\u884c\u52a8\u540e\u7ed9\u4ee3\u7406\u7684\u53cd\u9988\uff08\u5982\u4ea4\u6613\u7684\u76c8\u4e8f\uff09\u3002<\/li>\n\n\n\n<li><strong>\u4ef7\u503c\u51fd\u6570\uff1a<\/strong>\u8861\u91cf\u5904\u4e8e\u7279\u5b9a\u72b6\u6001\u6216\u9075\u5faa\u7279\u5b9a\u653f\u7b56\u7684\u957f\u671f\u56de\u62a5\u3002<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u4e09\u3001MDP \u548c RL \u5982\u4f55\u878d\u5165\u80a1\u7968\u4ea4\u6613 \uff1f<\/strong><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><br><strong>3.1 \u7406\u5ff5\u4ecb\u7ecd<\/strong><\/h3>\n\n\n\n<p>\u5728\u80a1\u7968\u4ea4\u6613\u4e2d\uff0c\u4ea4\u6613\u8005\u9700\u8981\u53cd\u590d\u505a\u51fa\u51b3\u7b56\uff0c\u800c\u4e14\u5f80\u5f80\u9700\u8981\u638c\u63e1\u4e0d\u5b8c\u6574\u7684\u672a\u6765\u4fe1\u606f\u3002\u8fd9\u4f7f\u5f97 MDP \u548c RL \u975e\u5e38\u9002\u5408\u5f00\u53d1\u81ea\u52a8\u4ea4\u6613\u7cfb\u7edf\u3002\u4e0b\u9762\u5c31\u6765\u770b\u770b\u5b83\u4eec\u662f\u5982\u4f55\u5951\u5408\u7684\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u72b6\u6001\uff1a<\/strong>\u6bcf\u5929\u7684\u5e02\u573a\u72b6\u51b5\uff0c\u5305\u62ec\u80a1\u7968\u4ef7\u683c\u548c\u8d8b\u52bf\uff08\u5982\u4ef7\u683c\u6da8\u8dcc\uff09\u3002<\/li>\n\n\n\n<li><strong>\u884c\u52a8\uff1a<\/strong>\u4ea4\u6613\u8005\u5fc5\u987b\u51b3\u5b9a\u4e70\u5165\u3001\u5356\u51fa\u6216\u6301\u6709\u3002<\/li>\n\n\n\n<li><strong>\u5956\u52b1\uff1a<\/strong>\u5956\u52b1\u662f\u6307\u6bcf\u6b21\u4ea4\u6613\u8d5a\u53d6\u7684\u5229\u6da6\u6216\u635f\u5931\u3002<\/li>\n\n\n\n<li><strong>\u8fc7\u6e21\u6982\u7387\uff1a<\/strong>\u80a1\u7968\u4ef7\u683c\u9075\u5faa\u4e0d\u786e\u5b9a\u7684\u6a21\u5f0f&#8211;\u6ca1\u6709\u4eba\u786e\u5207\u77e5\u9053\u4e0b\u4e00\u6b65\u4f1a\u53d1\u751f\u4ec0\u4e48\uff0c\u4f46 MDP \u53ef\u4ee5\u6839\u636e\u73b0\u6709\u4fe1\u606f\u4f18\u5316\u51b3\u7b56\uff0c\u4ece\u800c\u5e2e\u52a9\u7ba1\u7406\u8fd9\u79cd\u4e0d\u786e\u5b9a\u6027\u3002<\/li>\n\n\n\n<li><strong>\u884c\u52a8\u4e2d\u7684 RL\uff1a<\/strong>RL \u4ee3\u7406\u901a\u8fc7\u53cd\u590d\u4ea4\u6613\u4ece\u8fc7\u53bb\u7684\u6570\u636e\u4e2d\u5b66\u4e60\uff0c\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\u4e0d\u65ad\u66f4\u65b0\u7b56\u7565\uff0c\u505a\u51fa\u66f4\u660e\u667a\u7684\u51b3\u7b56\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5728\u80a1\u7968\u4ea4\u6613\u4e2d\uff0c\u4ee3\u7406\u901a\u8fc7\u4e0e\u5386\u53f2\u5e02\u573a\u6570\u636e\u4e92\u52a8\u6765\u5b66\u4e60\u5982\u4f55\u4ea4\u6613\u3002\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\uff0c\u5b83\u5c06\u5b66\u4f1a\u5728\u5404\u79cd\u5e02\u573a\u6761\u4ef6\u4e0b\u54ea\u4e9b\u64cd\u4f5c\u6700\u6709\u5229\u53ef\u56fe\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>3.2 \u57fa\u7840\u73af\u5883\u642d\u5efa<\/strong><\/h3>\n\n\n\n<p><strong>\u52a0\u8f7d\u6240\u9700\u7684\u5e93<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>#required libraries \nimport numpy as np\nimport matplotlib.pyplot as plt\nimport yfinance as yf\nimport pandas as pd\nfrom pykalman import KalmanFilter  # Using pykalman for the Kalman filter<\/code><\/pre>\n\n\n\n<p><strong>\u83b7\u53d6\u6570\u636e<\/strong>\uff1a\u6211\u4eec\u83b7\u53d6\u4e86\u82f9\u679c\u516c\u53f8\u4e24\u5e74\u7684\u5386\u53f2\u6570\u636e\u3002\u6211\u4eec\u8ba1\u7b97\u6bcf\u65e5\u56de\u62a5\uff0c\u5e76\u5220\u9664\u6240\u6709\u7f3a\u5931\u503c\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># Fetch stock data (Apple)\nstock = yf.Ticker(\"AAPL\")  \ndata = stock.history(period=\"2y\")\nreturns = data&#91;'Close'].pct_change().dropna().to_numpy()  # Daily returns\n\n# Save the data to a CSV file for later use\ndata.to_csv('AAPL_stock_data.csv')  # Save the historical data<\/code><\/pre>\n\n\n\n<p><strong>\u53c2\u6570\u521d\u59cb\u5316<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>N = 504<\/code>: \u5171\u6709 504 \u4e2a\u4ea4\u6613\u65e5\uff0c\u4ee3\u8868\u7cfb\u7edf\u7684\u72b6\u6001\u3002<\/li>\n\n\n\n<li><code>A = 3<\/code>:\u53ef\u7528\u7684\u4e09\u4e2a\u64cd\u4f5c<\/li>\n\n\n\n<li>\u4fdd\u6301\uff1a\u4ec0\u4e48\u4e5f\u4e0d\u505a\u3002<\/li>\n\n\n\n<li>\u5356\u51fa\uff1a\u5356\u51fa\u8be5\u80a1\u7968\u3002<\/li>\n\n\n\n<li>\u4e70\u5165\uff1a\u4e70\u5165\u8be5\u80a1\u7968\u3002<\/li>\n\n\n\n<li><code>GAMMA = 0.99<\/code>: \u6298\u6263\u7cfb\u6570\uff0c\u786e\u4fdd\u672a\u6765\u56de\u62a5\u7684\u91cd\u8981\u6027\u7565\u4f4e\u4e8e\u773c\u524d\u56de\u62a5\u3002<\/li>\n\n\n\n<li><code>TRADING_COST = 0.005<\/code>:\u6bcf\u7b14\u4ea4\u6613\u7684\u6210\u672c\u4e3a 0.5%\uff08\u6a21\u62df\u4ea4\u6613\u8d39\u7528\uff09\u3002<\/li>\n\n\n\n<li><code>TEMP = 1.0<\/code>: \u6709\u52a9\u4e8e\u63a7\u5236\u51b3\u7b56\u968f\u673a\u6027\u7684\u53c2\u6570\uff08\u5bf9\u63a5\u4e0b\u6765\u7684\u63a2\u7d22\u5f88\u91cd\u8981\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>\u751f\u6210\u6a21\u62df\u80a1\u7968\u6536\u76ca<\/strong><\/p>\n\n\n\n<p>\u5728\u73b0\u5b9e\u4e2d\uff0c\u6536\u76ca\u662f\u6709\u566a\u58f0\u7684\uff0c\u56e0\u6b64\u6211\u4eec\u5728\u771f\u5b9e\u6536\u76ca\u4e2d\u52a0\u5165\u4e00\u4e9b\u968f\u673a\u566a\u58f0\uff0c\u4ee5\u521b\u5efa\u4ee3\u7406\u6240\u770b\u5230\u7684\u6536\u76ca\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>true_returns = np.random.normal(0, 1, N)\nobserved_returns = true_returns + np.random.normal(0, 0.5, N)<\/code><\/pre>\n\n\n\n<p><strong>\u4f7f\u7528\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\uff08Kalman Filter\uff09\u5e73\u6ed1\u6536\u76ca\u7387<\/strong><\/p>\n\n\n\n<p>\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u5e2e\u52a9\u6211\u4eec\u8fc7\u6ee4\u6389\u89c2\u5bdf\u5230\u7684\u56de\u62a5\u7387\u4e2d\u7684\u566a\u97f3\uff0c\u5e76\u4f30\u7b97\u51fa\u57fa\u672c\u8d8b\u52bf\uff08\u5e73\u6ed1\u72b6\u6001\uff09\u3002\u5e73\u6ed1\u72b6\u6001\u6709\u52a9\u4e8e\u6211\u4eec\u505a\u51fa\u66f4\u597d\u7684\u51b3\u7b56\u3002\u5982\u679c\u89c2\u5bdf\u5230\u7684\u56de\u62a5\u7387\u6709\u566a\u58f0\uff0c\u5e73\u6ed1\u503c\u5c31\u4f1a\u544a\u8bc9\u6211\u4eec\u56de\u62a5\u7387\u53ef\u80fd\u5e94\u8be5\u662f\u591a\u5c11\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>kf = KalmanFilter( ... )\nfiltered_state_means, filtered_state_covariances = kf.filter(observed_returns)\nsmoothed_state_means, smoothed_state_covariances = kf.smooth(observed_returns)<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>3.3 \u521d\u59cb\u5316\u4ef7\u503c\u51fd\u6570\u548c\u653f\u7b56\u6982\u7387\u8bf4\u660e<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Value\uff08\u4ef7\u503c\uff09<\/strong>\uff1a\u8fd9\u662f\u6211\u4eec\u5b58\u50a8\u6bcf\u4e2a\u72b6\u6001\uff08\u65e5\uff09\u9884\u671f\u4ef7\u503c\u7684\u5730\u65b9\u3002\u53ef\u4ee5\u628a\u5b83\u60f3\u8c61\u6210\u6839\u636e\u4ee5\u67d0\u79cd\u65b9\u5f0f\u884c\u52a8\u7684\u4ef7\u503c\u4e3a\u6bcf\u4e00\u5929\u6253\u5206\u3002<\/li>\n\n\n\n<li><code><strong>policy_probs<\/strong><\/code>\uff1a\u8be5\u6570\u7ec4\u5b58\u50a8\u6bcf\u4e2a\u72b6\u6001\uff08\u65e5\uff09\u4e0b\u6bcf\u4e2a\u64cd\u4f5c\uff08\u4e70\u5165\u3001\u5356\u51fa\u3001\u6301\u6709\uff09\u7684\u6982\u7387\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>\u503c\u51fd\u6570\u8fed\u4ee3<\/strong><\/p>\n\n\n\n<p>\u8fd9\u662f\u4e00\u4e2a\u6838\u5fc3\u5faa\u73af\uff0c\u5728\u8fd9\u4e2a\u5faa\u73af\u4e2d\uff0c\u4ee3\u7406\u901a\u8fc7\u53cd\u590d\u66f4\u65b0\u6bcf\u4e2a\u72b6\u6001\uff08\u65e5\uff09\u7684\u503c\uff0c\u76f4\u5230\u6536\u655b\uff08\u5373\u53d8\u5316\u53d8\u5f97\u975e\u5e38\u5c0f\uff09\u4e3a\u6b62\uff0c\u8bd5\u56fe\u627e\u5230\u6700\u4f73\u7b56\u7565\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>for ite in range(ITEMAX):\n    value_old = value.copy()  # Store old value\n    value = np.zeros(N)  # Reset value for this iteration<\/code><\/pre>\n\n\n\n<p>\u76ee\u6807\u662f\u51b3\u5b9a\u54ea\u79cd\u64cd\u4f5c\uff08\u4e70\u5165\u3001\u5356\u51fa\u6216\u6301\u6709\uff09\u80fd\u5728 504 \u5929\u5185\u83b7\u5f97\u6700\u5927\u56de\u62a5\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Hold action (Action 0)<\/strong>  \u4fdd\u6301\u884c\u52a8\uff08\u884c\u52a8 0\uff09<\/li>\n\n\n\n<li><strong>\u56de\u62a5\uff08Reward\uff09<\/strong> = \u4eca\u65e5\u4ef7\u683c + \u672a\u6765\u4ef7\u503c\uff08\u8d34\u73b0\uff09<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>hold_reward = smoothed_price + GAMMA * value_old&#91;ss]<\/code><\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Sell action (Action 1)<\/strong>  \u5356\u51fa\u884c\u52a8\uff08\u884c\u52a8 1\uff09<\/li>\n\n\n\n<li><strong>\u5956\u52b1\uff08Reward\uff09<\/strong>= \u5356\u51fa\u80a1\u7968\uff08\u51cf\u53bb\u6210\u672c\uff09+ \u672a\u6765\u4ef7\u503c<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>sell_reward = smoothed_price * (1 - TRADING_COST) + GAMMA * value_old&#91;ss]<\/code><\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Buy action (Action 2)<\/strong>  \u8d2d\u4e70\u884c\u52a8\uff08\u884c\u52a8 2\uff09<\/li>\n\n\n\n<li><strong>\u56de\u62a5\uff08Reward\uff09<\/strong> = \u8d2d\u4e70\u80a1\u7968\u7684\u6210\u672c + \u672a\u6765\u4ef7\u503c<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>buy_reward = -smoothed_price * (1 + TRADING_COST) + GAMMA * value_old&#91;ss]<\/code><\/pre>\n\n\n\n<p>\u6bcf\u4e00\u5929\u4ee3\u7406\u90fd\u4f1a\u9009\u62e9\u4ef7\u503c\u6700\u9ad8\u7684\u884c\u52a8<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>value&#91;ss] = np.max(val)<\/code><\/pre>\n\n\n\n<p><strong>Softmax \u7b56\u7565\u9009\u62e9<\/strong><\/p>\n\n\n\n<p>\u8fd9\u786e\u4fdd\u4e86\u4ee3\u7406\u5076\u5c14\u4f1a\u8fdb\u884c\u63a2\u7d22\uff0c\u800c\u4e0d\u662f\u603b\u662f\u9009\u62e9\u6700\u719f\u6089\u7684\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>exp_vals = np.exp(val - np.max(val))\npolicy_probs&#91;ss] = exp_vals \/ np.sum(exp_vals)<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>3.4 \u4ee3\u7801\u7ec4\u5408<\/strong><\/h3>\n\n\n\n<p>\u4e0a\u8ff0\u6b65\u9aa4\u7684\u7ec4\u5408\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># PARAMETERS\nN = 504  # Number of trading days (states)\nA = 3  # Number of actions (buy, sell, hold)\nGAMMA = 0.99  # Discount factor\nTRADING_COST = 0.005  # 0.5% trading cost\nTEMP = 1.0  # Temperature parameter for softmax (controls exploration)\n\n# Generate synthetic stock returns as an example\nnp.random.seed(42)\ntrue_returns = np.random.normal(0, 1, N)  # True returns\nobserved_returns = true_returns + np.random.normal(0, 0.5, N)  # Noisy observations\n\n# Define the state-space model for Kalman Filter\nkf = KalmanFilter(\n    transition_matrices=&#91;1],  # State transition\n    observation_matrices=&#91;1],  # Observation matrix\n    initial_state_mean=0,  # Initial state mean\n    initial_state_covariance=1,  # Initial state covariance\n    observation_covariance=0.5,  # Observation noise\n    transition_covariance=0.1  # Process noise\n)\n\n# Use Kalman Filter to estimate the hidden states\nfiltered_state_means, filtered_state_covariances = kf.filter(observed_returns)\nsmoothed_state_means, smoothed_state_covariances = kf.smooth(observed_returns)\n\n# Initialize value and policy arrays\nvalue = np.zeros(N)\npolicy_probs = np.zeros((N, A))  # Store probabilities for each action\n\n# VALUE FUNCTION ITERATION\nITEMAX = 10000  # Maximum iterations\nITETOL = 1e-6  # Tolerance for convergence\n\nfor ite in range(ITEMAX):\n    value_old = value.copy()  # Keep the previous value for comparison\n    value = np.zeros(N)  # Reset the value function\n\n    # Adjust value for actions\n    for ss in range(N):\n        val = np.zeros(A)  # Value for each action\n\n        # Use smoothed states instead of observed returns\n        smoothed_price = smoothed_state_means&#91;ss]\n\n        # Action 0: Hold\n        hold_reward = smoothed_price + GAMMA * value_old&#91;ss]\n        val&#91;0] = hold_reward\n\n        # Action 1: Sell\n        sell_reward = smoothed_price * (1 - trading_cost) + GAMMA * value_old&#91;ss]  # Include potential future value\n        val&#91;1] = sell_reward\n\n        # Action 2: Buy\n        buy_reward = -smoothed_price * (1 + trading_cost) + GAMMA * value_old&#91;ss]  # Cost + potential future value\n        val&#91;2] = buy_reward\n\n        # Update value for the current state\n        value&#91;ss] = np.max(val)\n\n        # Softmax policy selection\n        max_val = np.max(val)\n        exp_vals = np.exp(val - max_val)  # Subtract max_val before applying exp\n        policy_probs&#91;ss] = exp_vals \/ np.sum(exp_vals) if np.sum(exp_vals) &gt; 0 else np.zeros(A)\n\n\n# PLOT THE SMOOTHED RETURNS, VALUE FUNCTION, AND OPTIMAL POLICY PROBABILITIES\nplt.figure(figsize=(16, 6))\n\nplt.subplot(1, 3, 1)\nplt.plot(smoothed_state_means, label=\"Smoothed Returns\")\nplt.title(\"Smoothed Returns\", fontsize=\"x-large\")\nplt.xlabel(\"Days\", fontsize=\"x-large\")\nplt.legend()\n\nplt.subplot(1, 3, 2)\nplt.plot(value, label=\"Optimized Value Function\")\nplt.title(\"Value Function\", fontsize=\"x-large\")\nplt.xlabel(\"Days\", fontsize=\"x-large\")\nplt.legend()\n\nplt.subplot(1, 3, 3)\nfor action in range(A):\n    plt.plot(policy_probs&#91;:, action], marker='o', label=f\"Action {action} Probabilities\")\nplt.title(\"Optimal Policy Probabilities\", fontsize=\"x-large\")\nplt.xlabel(\"Days\", fontsize=\"x-large\")\nplt.legend()\n\nplt.tight_layout()\nplt.show()<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>3.5 \u7ed3\u679c\u5206\u6790<\/strong><\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/www.laoyulaoyu.com\/wp-content\/uploads\/2024\/11\/image-106.png\" alt=\"\" class=\"wp-image-3045\"\/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/www.laoyulaoyu.com\/wp-content\/uploads\/2024\/11\/image-107.png\" alt=\"\" class=\"wp-image-3046\"\/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/www.laoyulaoyu.com\/wp-content\/uploads\/2024\/11\/image-108.png\" alt=\"\" class=\"wp-image-3047\"\/><\/figure>\n<\/div>\n\n\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5c06\u4ece 10000 \u7f8e\u5143\u7684\u6295\u8d44\u7ec4\u5408\u5f00\u59cb\uff0c\u5bf9\u6240\u91c7\u53d6\u7684\u884c\u52a8\u548c\u6295\u8d44\u7ec4\u5408\u4ef7\u503c\u8fdb\u884c\u53ef\u89c6\u5316\u3002\u6839\u636e\u7ed3\u679c\uff0c\u6295\u8d44\u7ec4\u5408\u7684\u8d44\u91d1\u589e\u957f\u5230 10450 \u7f8e\u5143\u3002\u5982\u4e0b\u56fe\uff1a<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/www.laoyulaoyu.com\/wp-content\/uploads\/2024\/11\/image-109.png\" alt=\"\" class=\"wp-image-3048\"\/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/www.laoyulaoyu.com\/wp-content\/uploads\/2024\/11\/image-110.png\" alt=\"\" class=\"wp-image-3049\"\/><\/figure>\n<\/div>\n\n\n<p>\u8bf7\u6ce8\u610f\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u901a\u8fc7 Q-learning \u6765\u5f3a\u5316\u8fd9\u4e9b\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>\u6211\u4eec\u7684\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u7ed3\u5408MDP\u548cRL\u7684\u65b9\u6cd5\u786e\u5b9e\u53ef\u4ee5\u5e94\u7528\u4e8e\u80a1\u7968\u4ea4\u6613\uff0c\u5e2e\u52a9\u6295\u8d44\u8005\u505a\u51fa\u66f4\u4e3a\u660e\u667a\u7684\u51b3\u7b56\uff0c\u4ece\u800c\u5b9e\u73b0\u6536\u76ca\u7684\u6700\u5927\u5316\u3002\u8fd9\u79cd\u65b9\u6cd5\u4e0d\u4ec5\u8003\u8651\u4e86\u5e02\u573a\u7684\u52a8\u6001\u53d8\u5316\uff0c\u8fd8\u80fd\u591f\u6839\u636e\u5386\u53f2\u6570\u636e\u548c\u5f53\u524d\u5e02\u573a\u72b6\u51b5\uff0c\u4e3a\u6295\u8d44\u8005\u63d0\u4f9b\u4e2a\u6027\u5316\u7684\u4ea4\u6613\u5efa\u8bae\u3002\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u6295\u8d44\u8005\u53ef\u4ee5\u66f4\u52a0\u79d1\u5b66\u5730\u7ba1\u7406\u4ed6\u4eec\u7684\u6295\u8d44\u7ec4\u5408\uff0c\u63d0\u9ad8\u6295\u8d44\u56de\u62a5\u7387\uff0c\u5e76\u5728\u5145\u6ee1\u53d8\u6570\u7684\u80a1\u7968\u5e02\u573a\u4e2d\u4fdd\u6301\u7ade\u4e89\u529b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u56db\u3001\u89c2\u70b9\u603b\u7ed3<\/strong><\/h2>\n\n\n\n<p>\u5728\u63a2\u7d22\u5982\u4f55\u5229\u7528\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\uff08MDP\uff09\u548c\u5f3a\u5316\u5b66\u4e60\uff08RL\uff09\u6765\u8f85\u52a9\u80a1\u7968\u4ea4\u6613\u51b3\u7b56\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u91c7\u53d6\u4e86\u4e00\u7cfb\u5217\u63aa\u65bd\u6765\u63d0\u9ad8\u51b3\u7b56\u7684\u51c6\u786e\u6027\u548c\u6548\u7387\u3002\u9996\u5148\uff0c\u6211\u4eec\u5229\u7528\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u5bf9\u80a1\u7968\u6570\u636e\u8fdb\u884c\u5904\u7406\uff0c\u8fd9\u79cd\u65b9\u6cd5\u80fd\u591f\u8fc7\u6ee4\u6389\u6570\u636e\u4e2d\u7684\u566a\u58f0\uff0c\u4ece\u800c\u66f4\u6e05\u6670\u5730\u63ed\u793a\u51fa\u771f\u5b9e\u7684\u8d8b\u52bf\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u901a\u8fc7\u6a21\u62df\u4e0d\u540c\u7684\u64cd\u4f5c\uff08\u5982\u4e70\u5165\u3001\u5356\u51fa\u3001\u6301\u6709\uff09\u6765\u8bad\u7ec3\u667a\u80fd\u4ee3\u7406\uff0c\u540c\u65f6\u8003\u8651\u5230\u4ea4\u6613\u6210\u672c\u548c\u9884\u671f\u7684\u672a\u6765\u56de\u62a5\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u80a1\u7968\u4ea4\u6613\u662f\u4e00\u4e2a\u590d\u6742\u7684\u51b3\u7b56\u8fc7\u7a0b<\/strong>\uff0c\u6d89\u53ca\u5230\u4e0d\u786e\u5b9a\u6027\u548c\u968f\u673a\u6027\uff0cMDP\u548cRL\u63d0\u4f9b\u4e86\u4e00\u79cd\u5904\u7406\u8fd9\u79cd\u590d\u6742\u6027\u7684\u65b9\u6cd5\u3002<\/li>\n\n\n\n<li><strong>MDP\u80fd\u591f\u5e2e\u52a9\u4ea4\u6613\u8005\u5728\u4e0d\u786e\u5b9a\u7684\u5e02\u573a\u73af\u5883\u4e2d\u505a\u51fa\u8fde\u7eed\u7684\u51b3\u7b56<\/strong>\uff0c\u4ee5\u5b9e\u73b0\u957f\u671f\u7684\u6295\u8d44\u76ee\u6807\u3002<\/li>\n\n\n\n<li><strong>\u5f3a\u5316\u5b66\u4e60\u7684\u6838\u5fc3\u5728\u4e8e\u4ee3\u7406\u901a\u8fc7\u4e0e\u73af\u5883\u7684\u4ea4\u4e92\u6765\u5b66\u4e60<\/strong>\uff0c\u5b83\u901a\u8fc7\u5956\u52b1\u548c\u60e9\u7f5a\u6765\u4f18\u5316\u5176\u884c\u4e3a\uff0c\u4ee5\u8fbe\u5230\u6700\u5927\u5316\u7d2f\u79ef\u5956\u52b1\u7684\u76ee\u6807\u3002<\/li>\n\n\n\n<li><strong>\u5361\u5c14\u66fc\u6ee4\u6ce2\u5668\u5728\u5904\u7406\u566a\u58f0\u6570\u636e\u65f6\u975e\u5e38\u6709\u7528<\/strong>\uff0c\u80fd\u591f\u5e2e\u52a9\u4ea4\u6613\u8005\u8bc6\u522b\u51fa\u57fa\u672c\u7684\u5e02\u573a\u8d8b\u52bf\u3002<\/li>\n\n\n\n<li><strong>\u4ef7\u503c\u51fd\u6570\u548c\u7b56\u7565\u6982\u7387\u662fRL\u4e2d\u7684\u5173\u952e\u7ec4\u6210\u90e8\u5206<\/strong>\uff0c\u5b83\u4eec\u5e2e\u52a9\u4ee3\u7406\u8bc4\u4f30\u6bcf\u4e2a\u72b6\u6001\u7684\u957f\u671f\u4ef7\u503c\uff0c\u5e76\u6839\u636e\u8fd9\u4e9b\u8bc4\u4f30\u6765\u9009\u62e9\u6700\u4f18\u7684\u52a8\u4f5c\u3002<\/li>\n\n\n\n<li><strong>\u901a\u8fc7\u6a21\u62df\u4ea4\u6613\u548c\u4ef7\u503c\u51fd\u6570\u8fed\u4ee3\uff0c\u53ef\u4ee5\u8bad\u7ec3\u51fa\u4e00\u4e2a\u80fd\u591f\u5728\u5404\u79cd\u5e02\u573a\u6761\u4ef6\u4e0b\u505a\u51fa\u660e\u667a\u4ea4\u6613\u51b3\u7b56\u7684\u4ee3\u7406<\/strong>\u3002<\/li>\n\n\n\n<li><strong>\u7ed3\u679c\u8868\u660e\uff0cMDP\u548cRL\u5728\u80a1\u7968\u4ea4\u6613\u4e2d\u7684\u5e94\u7528\u53ef\u4ee5\u5e2e\u52a9\u6295\u8d44\u8005\u505a\u51fa\u66f4\u52a0\u660e\u667a\u7684\u51b3\u7b56\uff0c\u4ece\u800c\u6700\u5927\u5316\u6295\u8d44\u56de\u62a5<\/strong>\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u6211\u8fd8\u6709\u51e0\u7bc7\u4ecb\u7ecd\u501f\u52a9 RL \u5982\u4f55\u8fdb\u884c\u80a1\u7968\u4ea4\u6613\u7684\u76f8\u5173\u6587\u7ae0\uff0c\u6709\u5174\u8da3\u7684\u670b\u53cb\u53ef\u4ee5\u8fdb\u884c\u5ef6\u5c55\u9605\u8bfb\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzkzNzY0NjIyNQ==&amp;mid=2247485637&amp;idx=1&amp;sn=5fd9e16bb52361f0509898762eb1ee60&amp;chksm=c28d093bf5fa802d5c2468da3004e001433100a3649bc21271ea578f932474ebadb133958c4c&amp;token=1854235955&amp;lang=zh_CN#rd\" target=\"_blank\" rel=\"noreferrer noopener\">\u501f\u52a9<em>\u5f3a\u5316\u5b66\u4e60<\/em>\u6765\u4f18\u5316\u80a1\u7968\u4ea4\u6613\u7b56\u7565\u7684\u5165\u95e8\u6307\u5357<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzkzNzY0NjIyNQ==&amp;mid=2247485119&amp;idx=1&amp;sn=92841d2eb0ccbe9281180df96e4180fb&amp;chksm=c28d0741f5fa8e5778b7093d6b8f07b6985660f45661edb9b2dd103eaa2cebade9618b715d9a&amp;token=1854235955&amp;lang=zh_CN#rd\" target=\"_blank\" rel=\"noreferrer noopener\">\u89e3\u5bc6\uff01\u770b\u6df1\u5ea6<em>\u5f3a\u5316\u5b66\u4e60<\/em>\u5982\u4f55\u5b9e\u73b0\u81ea\u52a8\u80a1\u7968\u4ea4\u6613<\/a><\/li>\n<\/ul>\n\n\n\n<p><br><\/p>\n\n\n\n<p><p><em>\u611f\u8c22\u60a8\u9605\u8bfb\u5230\u6700\u540e\uff0c\u5e0c\u671b\u672c\u6587\u80fd\u7ed9\u60a8\u5e26\u6765\u65b0\u7684\u6536\u83b7\u3002\u795d\u60a8\u6295\u8d44\u987a\u5229\uff01\u5982\u679c\u5bf9\u6587\u4e2d\u7684\u5185\u5bb9\u6709\u4efb\u4f55\u7591\u95ee\uff0c\u8bf7\u7ed9\u6211\u7559\u8a00\uff0c\u5fc5\u590d\u3002<\/em><\/p><hr class=\"wp-block-separator has-alpha-channel-opacity\"><\/hr><br><p class=\"has-text-align-center\" id=\"a1c6\"><strong><mark style=\"background-color:#ffffff\" class=\"has-inline-color 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