Bellman\u65b9\u7a0b\u5f0f\u306f\u3001E=mc2\u306a\u3069\u3068\u9055\u3063\u3066\u30d1\u30c3\u3068\u898b\u3066\u3082\u3088\u304f\u308f\u304b\u308a\u307e\u305b\u3093\u3002
\n\u3044\u308d\u3044\u308d\u306a\u66f8\u304d\u65b9\u304c\u3067\u304d\u307e\u3059\u304c\u3001\u6dfb\u3048\u5b57\u7121\u3057\u3067\u66f8\u304f\u65b9\u6cd5\u3060\u3068
\nV(x)=max [F(x,a)+\u03b2V(T(x,a))]
\n\u3067\u3059\u3002\u3053\u306e\u8aac\u660e\u306b\u8b1b\u7fa9\u3067\u306f1\u6642\u9593\u4f7f\u3044\u307e\u3059\u304c\u3001\u7c21\u5358\u306b\u66f8\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002
\n\u56f2\u7881\u3084\u5c06\u68cb\u306a\u3069\u306e\u6226\u7565\u7684\u30b2\u30fc\u30e0\u3092\u4f8b\u306b\u3068\u308b\u3068\u3001x\u306f\u73fe\u5728\u306e\u76e4\u9762\u3001V(x)\u306f\u73fe\u5728\u306e\u76e4\u9762\u306e\u8a55\u4fa1\uff08\u3069\u306e\u304f\u3089\u3044\u826f\u3044\u304b\u3068\u3044\u3046\u70b9\u6570\u3002\u3075\u3064\u3046\u306f\u6700\u5927\u30921\u306b\u3057\u307e\u3059\uff09\u3002
\n\u53f3\u8fba\u306ea\u306f\u6b21\u306e1\u624b\u3067\u3059\u3002F(x,a)\u306f\u3001\u76e4\u9762x\u306b\u5bfe\u3057\u3066\u624ba\u3092\u58f2\u3063\u305f\u3068\u304d\u306e\u640d\u5f97\u3002T(x,a)\u306fx\u3068a\u306e\u7d44\u307f\u5408\u308f\u305b\u306b\u5bfe\u3057\u3066\u76f8\u624b\u304c\u6253\u3063\u305f\u5f8c\u306e\u76e4\u9762\u3067\u3001\u305d\u306e\u8a55\u4fa1\u304cV(T(x,a))\u3067\u3059\u3002
\n\u76f8\u624b\u304c\u6700\u5584\u624b\u3092\u6253\u3064\u3068\u3059\u308c\u3070\u6b21\u306e\u76e4\u9762T(x,a)\u306f\u4e00\u3064\u306b\u6c7a\u307e\u308a\u307e\u3059\u304c\u3001\u8272\u3005\u306a\u624b\u3092\u6253\u3064\u3053\u3068\u3092\u8003\u3048\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002
\n\u03b2\u306f\u3001\u4e00\u624b\u5148\u306e\u8a55\u4fa1\u304c\u73fe\u5728\u306e\u8a55\u4fa1\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u3092\u5f31\u3081\u308b\u305f\u3081\u306e\u5b9a\u6570\uff08\u9013\u6e1b\u7387\uff09\u3067\u3001\uff11\u3088\u308a\u5c11\u3057\u5c0f\u3055\u3044\u6570\u306b\u3057\u307e\u3059\u3002\u7d4c\u6e08\u5b66\u3067\u306f\u3001\u672a\u6765\u306e1\u4e07\u5186\u306f\u73fe\u5728\u306e9900\u5186\u306b\u5024\u3059\u308b\u306e\u3067\u03b2=0.99\u306a\u3069\u3068\u4f7f\u3044\u307e\u3059\u3002\u3053\u306e\u65b9\u7a0b\u5f0f\u304c\u8a00\u3063\u3066\u3044\u308b\u3053\u3068\u306f\u3001\u76e4\u9762x\u306b\u5bfe\u3059\u308b\u8a55\u4fa1V(x)\u306f\u3001\u3044\u308d\u3044\u308d\u306a\u624ba\u306b\u5bfe\u3057\u3066F(x,a)+\u03b2V(T(x,a))\u3092\u6c42\u3081\u305f\u3068\u304d\u306e\u6700\u5927\u5024\u3067\u3042\u308b\u3001\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002
\n\u3053\u308c\u3060\u3051\u3067\u306f\u4f55\u3082\u6c42\u307e\u308a\u307e\u305b\u3093\u304c\u3001\u52dd\u5229\u3057\u305f\u77ac\u9593\u306e\u76e4\u9762\u304cT(x,a)\u3068\u3059\u308b\u3068\u3001\u52dd\u5229\u3057\u305f\u76e4\u9762\u306eV(T(x,a))\u306f\uff11\uff08\u6700\u5927\u5024\uff09\u3067\u3001\u640d\u5f97F(x,a)\u3082\u6b63\u306e\u5927\u304d\u306a\u5024\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u308c\u306b\u3088\u308a\uff11\u624b\u524d\u306e\u72b6\u614bx\u306b\u5bfe\u3059\u308b\u8a55\u4fa1V(x)\u3068\u52dd\u5229\u306b\u3064\u306a\u304c\u3063\u305f\u6700\u5584\u624ba\u304c\u6c42\u307e\u308a\u307e\u3059\u3002\u3053\u3046\u3057\u3066\u305f\u3069\u3063\u3066\u3044\u304f\u3068\u5404\u76e4\u9762x\u306eV(x)\u3068\u6700\u5584\u624ba\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u76e4\u9762x\u306b\u5bfe\u3057\u3066\u3068\u308c\u308b\u3044\u308d\u3044\u308d\u306a\u624ba\u306e\u70b9\u6570\u3092Q(x,a)\u3068\u3057\u3066\u3001\u70b9\u6570\u306b\u6bd4\u4f8b\u3057\u305f\u78ba\u7387\u3067\u624b\u3092\u9078\u3073\u307e\u3059\u3002\u6700\u521d\u306f\u8a66\u884c\u932f\u8aa4\u306e\u305f\u3081Q(x,a)\u306b\u306f\u4e71\u6570\u3067\u9069\u5f53\u306a\u6570\u5024\u3092\u5165\u308c\u3066\u304a\u3044\u3066\u3001\u7e70\u308a\u8fd4\u3057\u30b2\u30fc\u30e0\u3092\u3059\u308b\u3068V\u3068Q\u304c\u66f4\u65b0\u30fb\u6539\u5584\u3055\u308c\u3001\u52dd\u3066\u308b\u3088\u3046\u306b\u306a\u3063\u3066\u304d\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u81ea\u3089\u306e\u884c\u52d5\u306e\u7d50\u679c\u3092\u53d6\u308a\u5165\u308c\u3066\u884c\u52d5\u898f\u7bc4\u3092\u4fee\u6b63\u3059\u308b\u3053\u3068\u3092\u300c\u5f37\u5316\u5b66\u7fd2\u300d\u3068\u547c\u3073\u3001\u6a5f\u68b0\u5b66\u7fd2\u306e\u91cd\u8981\u306a\u4e00\u5206\u91ce\u3067\u3059\u3002\u5f37\u5316\u5b66\u7fd2\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u306f\u3044\u308d\u3044\u308d\u306a\u3082\u306e\u304c\u63d0\u6848\u3055\u308c\u3066\u3044\u307e\u3059\u3002
\nBellman\u65b9\u7a0b\u5f0f\u306f1953\u5e74\u767a\u8868\u3067\u3059\u304c\u3001\u5f37\u5316\u5b66\u7fd2\u306f\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u767a\u9054\u306b\u3088\u308a2000\u5e74\u3053\u308d\u304b\u3089\u5b9f\u7528\u7684\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u6642\u4ee3\u309250\u5e74\u5148\u53d6\u308a\u3057\u305f\u5049\u5927\u306a\u767a\u660e\u3067\u3059\u3002
\n\u03b2\u306e\u9078\u3073\u65b9\uff08\u30cf\u30a4\u30d1\u30fc\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3044\u3046\uff09\u3084\u6539\u5584\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u5c40\u9762\u306b\u3082\u4f9d\u5b58\u3059\u308b\u306e\u3067\u3001\u305d\u308c\u81ea\u8eab\u3092\u5b66\u7fd2\u306b\u3088\u308a\u6539\u826f\u3059\u308b\u3053\u3068\u3082\u5f37\u3044\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u306f\u884c\u308f\u308c\u3066\u3044\u307e\u3059\u3002\u68cb\u8b5c\u3092\u8aad\u307f\u8fbc\u307e\u305b\u305f\u308a\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u540c\u58eb\u3067\u6226\u308f\u305b\u305f\u308a\u3057\u3066\u3001\u56f2\u7881\u3001\u5c06\u68cb\u3001\u30c1\u30a7\u30b9\u306a\u3069\u306f\u4eba\u9593\u3088\u308a\u5f37\u304f\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u9069\u5207\u306b\u5b9f\u793e\u4f1a\u3092\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306b\u8a8d\u8b58\u3055\u305b\u3089\u308c\u308c\u3070\u3001\u6211\u3005\u306e\u554f\u984c\u89e3\u6c7a\u306b\u3082\u4f7f\u3048\u308b\u306e\u3067\u306f\uff1f\u3068\u3044\u3046\u306e\u306f\u8aac\u5f97\u529b\u306e\u3042\u308b\u8ad6\u3067\u3059\u3002\u3044\u308d\u3044\u308d\u306a\u672c\u304c\u51fa\u3066\u3044\u3066\u3001\u793e\u4f1a\u306e\u554f\u984c\u306fAI\u88c1\u5224\u5b98\u3084AI\u653f\u6cbb\u5bb6\u306b\u4efb\u305b\u305f\u65b9\u304c\u3088\u3044\u3068\u3044\u3046\u4eba\u3068\u3001\u3069\u3053\u306b\u9023\u308c\u3066\u3044\u304b\u308c\u308b\u304b\u308f\u304b\u3089\u306a\u3044\u306e\u3067AI\u306b\u793e\u4f1a\u306e\u554f\u984c\u3092\u4efb\u305b\u3066\u306f\u3044\u3051\u306a\u3044\u3001\u3068\u3044\u3046\u4eba\u304c\u3044\u307e\u3059\u3002\u9060\u304f\u306a\u3044\u5c06\u6765\u306b\u56fd\u3054\u3068\u306b\u3069\u3063\u3061\u306b\u3059\u308b\u304b\u5206\u304b\u308c\u308b\u3068\u4e88\u60f3\u3057\u307e\u3059\u3002\u5c11\u5b50\u5316\u554f\u984c\u3092\u7a0e\u5236\u3084\u88dc\u52a9\u91d1\u306a\u3069\u306e\u65b9\u7b56\u3067\u89e3\u6c7a\u3067\u304d\u308b\u304b\u3069\u3046\u304b\u304c\u8a66\u91d1\u77f3\u3067\u306f\u306a\u3044\u304b\u3068\u601d\u3044\u307e\u3059\u304c\u3001\u5b66\u7fd2\u904e\u7a0b\u3067\u306e\u8a66\u884c\u932f\u8aa4\u3067\u5927\u304d\u306a\u5931\u6557\u306f\u8a31\u3055\u308c\u306a\u3044\u3068\u3053\u308d\u304c\u96e3\u3057\u3044\u3067\u3059\u3002<\/p>\n
\u82f1\u8a9e\u306f\u3000https:\/\/en.wikipedia.org\/wiki\/Bellman_equation \u304b\u3089\u3002\u3000\u3053\u306ewikipedia\u306f\u308f\u304b\u308a\u306b\u304f\u3044\u3067\u3059\u3002
\na necessary condition \u5fc5\u8981\u6761\u4ef6
\na sufficient condition \u5341\u5206\u6761\u4ef6
\na necessary and sufficient condition \u5fc5\u8981\u5341\u5206\u6761\u4ef6
\n\u201dThis breaks a dynamic optimization problem into a sequence of simpler subproblems, as Bellman’s \u201cprinciple of optimality” prescribes.\u201d
\nbreak \u5206\u5272\u3059\u308b
\na sequence of simpler subproblems \u4e00\u9023\u306e\u3088\u308a\u5358\u7d14\u306a\u554f\u984c
\nprescribe \u51e6\u65b9\u3059\u308b
\nprescription drugs \u51e6\u65b9\u85ac\uff08\u51e6\u65b9\u7b8b a medical prescription\uff09\u304c\u306a\u3044\u3068\u8ca9\u58f2\u3067\u304d\u306a\u3044\u85ac
\n“In discrete time any multi-stage optimization problem can be solved by analyzing the appropriate Bellman equation. The appropriate Bellman equation can be found by introducing new state variables (state augmentation).”
\ndiscrete time \u96e2\u6563\u6642\u9593\uff08\u56f2\u7881\u3084\u5c06\u68cb\u306e\u3088\u3046\u306b\u3001\u300c\u624b\u300d\u304c\uff11\u3064\uff11\u3064\u6570\u3048\u3089\u308c\u308b\u5834\u5408\uff09
\nnew state variables \u65b0\u3057\u3044\u72b6\u614b\u5909\u6570
\naugmentation \u30aa\u30fc\u30b0\u30e1\u30f3\u30c6\u30a4\u30b7\u30e7\u30f3\u3000\u62e1\u5f35\u3000AR augmented reality \u62e1\u5f35\u73fe\u5b9f
\ncurse of dimensionality \u6b21\u5143\u306e\u546a\u3044
\n“Alternatively, it has been shown that if the cost function of the multi-stage optimization problem satisfies a “backward separable” structure, then the appropriate Bellman equation can be found without state augmentation.”
\nalternatively \u4ee3\u308f\u308a\u306b
\ncost function \u30b3\u30b9\u30c8\u95a2\u6570\u3000(\u4e0a\u8a18\u306eF\u306e\u3053\u3068)<\/p>\n","protected":false},"excerpt":{"rendered":"
Bellman\u65b9\u7a0b\u5f0f\u306f\u3001E=mc2\u306a\u3069\u3068\u9055\u3063\u3066\u30d1\u30c3\u3068\u898b\u3066\u3082\u3088\u304f\u308f\u304b\u308a\u307e\u305b\u3093\u3002 \u3044\u308d\u3044\u308d\u306a\u66f8\u304d\u65b9\u304c\u3067\u304d\u307e\u3059\u304c\u3001\u6dfb\u3048\u5b57\u7121\u3057\u3067\u66f8\u304f\u65b9\u6cd5\u3060\u3068 V(x)=max [F(x,a)+\u03b2V(T(x,a))] \u3067\u3059\u3002\u3053\u306e\u8aac\u660e\u306b\u8b1b\u7fa9\u3067\u306f1\u6642\u9593\u4f7f\u3044\u307e\u3059\u304c\u3001\u7c21\u5358\u306b\u66f8\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002 \u56f2\u7881\u3084\u5c06\u68cb\u306a\u3069\u306e\u6226\u7565\u7684\u30b2\u30fc\u30e0\u3092\u4f8b\u306b\u3068\u308b\u3068\u3001x\u306f\u73fe\u5728\u306e\u76e4\u9762\u3001V(x)\u306f\u73fe\u5728\u306e\u76e4\u9762\u306e\u8a55\u4fa1\uff08\u3069\u306e\u304f\u3089\u3044\u826f\u3044\u304b\u3068\u3044\u3046\u70b9\u6570\u3002\u3075\u3064\u3046\u306f\u6700\u5927\u30921\u306b\u3057\u307e\u3059\uff09\u3002 \u53f3\u8fba\u306ea\u306f\u6b21\u306e1\u624b\u3067\u3059\u3002F(x,a)\u306f\u3001\u76e4\u9762x\u306b\u5bfe\u3057\u3066\u624ba\u3092\u58f2\u3063\u305f\u3068\u304d\u306e\u640d\u5f97\u3002T(x,a)\u306fx\u3068a\u306e\u7d44\u307f\u5408\u308f\u305b\u306b\u5bfe\u3057\u3066\u76f8\u624b\u304c\u6253\u3063\u305f\u5f8c\u306e\u76e4\u9762\u3067\u3001\u305d\u306e\u8a55\u4fa1\u304cV(T(x,a))\u3067\u3059\u3002 \u76f8\u624b\u304c\u6700\u5584\u624b\u3092\u6253\u3064…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[42],"tags":[5],"class_list":["post-2062","post","type-post","status-publish","format-standard","hentry","category-tech","tag-tech"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.sekaiken.com\/index.php?rest_route=\/wp\/v2\/posts\/2062","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sekaiken.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sekaiken.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sekaiken.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sekaiken.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2062"}],"version-history":[{"count":0,"href":"https:\/\/www.sekaiken.com\/index.php?rest_route=\/wp\/v2\/posts\/2062\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sekaiken.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2062"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sekaiken.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2062"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sekaiken.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2062"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}