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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Thompson sampling ： ウィキペディア英語版 Thompson sampling In artificial intelligence, Thompson sampling,〔 named after William R. Thompson, is a heuristic for choosing actions that addresses the exploration-exploitation dilemma in the multi-armed bandit problem. It consists in choosing the action that maximizes the expected reward with respect to a randomly drawn belief. == Description == Consider a set of contexts $\backslash mathcal$, a set of actions $\backslash mathcal$, and rewards in $\backslash mathbb$. In each round, the player obtains a context $x\; \backslash in\; \backslash mathcal$, plays an action $a\; \backslash in\; \backslash mathcal$ and receives a reward $r\; \backslash in\; \backslash mathbb$ following a distribution that depends on the context and the issued action. The aim of the player is to play actions such as to maximize the cumulative rewards. The elements of Thompson sampling are as follows: # a likelihood function $P(r|\backslash theta,a,x)$; # a set $\backslash Theta$ of parameters $\backslash theta$ of the distribution of r; # a prior distribution $P(\backslash theta)$ on these parameters; # past observations triplets $\backslash mathcal\; =\; \backslash$; # a posterior distribution $P(\backslash theta|\backslash mathcal)\; \backslash propto\; P(\backslash mathcal|\backslash theta)P(\backslash theta)$, where $P(\backslash mathcal|\backslash theta)$ is the likelihood function. Thompson sampling consists in playing the action $a^\backslash ast\; \backslash in\; \backslash mathcal$ according to the probability that it maximizes the expected reward, i.e. :$\backslash int\; \backslash mathbb(=\; \backslash max\_\; \backslash mathbb(r|a\text{'},x,\backslash theta))\; P(\backslash theta|\backslash mathcal)\; \backslash ,\; d\backslash theta,$ where $\backslash mathbb$ is the indicator function. In practice, the rule is implemented by sampling, in each round, a parameter $\backslash theta^\backslash ast$ from the posterior $P(\backslash theta|\backslash mathcal)$, and choosing the action $a^\backslash ast$ that maximizes $\backslash mathbb()$, i.e. the expected reward given the parameter, the action and the current context. Conceptually, this means that the player instantiates his beliefs randomly in each round, and then he acts optimally according to them. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Thompson sampling」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.