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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 Markov decision process ： ウィキペディア英語版 Markov decision process Markov decision processes (MDPs) provide a mathematical framework for modeling decision making in situations where outcomes are partly random and partly under the control of a decision maker. MDPs are useful for studying a wide range of optimization problems solved via dynamic programming and reinforcement learning. MDPs were known at least as early as the 1950s (cf. Bellman 1957). A core body of research on Markov decision processes resulted from Ronald A. Howard's book published in 1960, ''Dynamic Programming and Markov Processes''. They are used in a wide area of disciplines, including robotics, automated control, economics, and manufacturing. More precisely, a Markov Decision Process is a discrete time stochastic control process. At each time step, the process is in some state $s$, and the decision maker may choose any action $a$ that is available in state $s$. The process responds at the next time step by randomly moving into a new state $s\text{'}$, and giving the decision maker a corresponding reward $R\_a(s,s\text{'})$. The probability that the process moves into its new state $s\text{'}$ is influenced by the chosen action. Specifically, it is given by the state transition function $P\_a(s,s\text{'})$. Thus, the next state $s\text{'}$ depends on the current state $s$ and the decision maker's action $a$. But given $s$ and $a$, it is conditionally independent of all previous states and actions; in other words, the state transitions of an MDP process satisfies the ''Markov property''. Markov decision processes are an extension of Markov chains; the difference is the addition of actions (allowing choice) and rewards (giving motivation). Conversely, if only one action exists for each state and all rewards are the same (e.g., zero), a Markov decision process reduces to a Markov chain. ==Definition== A Markov decision process is a 5-tuple $(S,A,P\_\backslash cdot(\backslash cdot,\backslash cdot),R\_\backslash cdot(\backslash cdot,\backslash cdot),\backslash gamma)$, where * $S$ is a finite set of states, * $A$ is a finite set of actions (alternatively, $A\_s$ is the finite set of actions available from state $s$), * $P\_a(s,s\text{'})\; =\; \backslash Pr(s\_=s\text{'}\; \backslash mid\; s\_t\; =\; s,\; a\_t=a)$ is the probability that action $a$ in state $s$ at time $t$ will lead to state $s\text{'}$ at time $t+1$, *$R\_a(s,s\text{'})$ is the immediate reward (or expected immediate reward) received after transition to state $s\text{'}$ from state $s$, *$\backslash gamma\; \backslash in\; ()$ is the discount factor, which represents the difference in importance between future rewards and present rewards. (Note: The theory of Markov decision processes does not state that $S$ or $A$ are finite, but the basic algorithms below assume that they are finite.) 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「Markov decision process」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.