The value functions of Markov decision processes

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• 作者：Ehud Lehrer^a ; ^b ; ^{lehrer@post.tau.ac.il" class="auth_mail" title="E-mail the corresponding author} ; Eilon Solan^a ; ^{eilons@post.tau.ac.il" class="auth_mail" title="E-mail the corresponding author} ; Omri N. Solan^a ; ^{omrisola@post.tau.ac.il" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Markov decision problems ; Value function ; Characterization
• 刊名：Operations Research Letters
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：44
• 期：5
• 页码：587-591
• 全文大小：432 K

文摘

It is known that the value function of a Markov decision process, as a function of the discount factor URL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0167637716300487&_mathId=si2.gif&_user=111111111&_pii=S0167637716300487&_rdoc=1&_issn=01676377&md5=8cd069c5799882edd288853ca003bd08" title="Click to view the MathML source">λ$\lambda$, is the maximum of finitely many rational functions in urce">λ$\lambda$. Moreover, each root of the denominators of the rational functions either lies outside the unit ball in the complex plane, or is a unit root with multiplicity 1. We prove the converse of this result, namely, every function that is the maximum of finitely many rational functions in urce">λ$\lambda$, satisfying the property that each root of the denominators of the rational functions either lies outside the unit ball in the complex plane, or is a unit root with multiplicity 1, is the value function of some Markov decision process. We thereby provide a characterization of the set of value functions of Markov decision processes.