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Existence of optimal policy for time non-homogeneous discounted Markovian decision programming. (English) Zbl 0734.90113

Summary: We discuss the discrete time non-homogeneous discounted Markovian decision programming, where the state space and all action sets are countable. Suppose that the optimum value function is finite. We give necessary and sufficient conditions for the existence of an optimal policy. Suppose that the absolute mean of rewards is relatively bounded. We also give necessary and sufficient conditions for the existence of an optimal policy.

MSC:

90C40 Markov and semi-Markov decision processes
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References:

[1] Fedrgruen, A.; Schweitzer, P. J., Nonstationary Markov Decision Problems with Converging Parameter,JOTA,34: 2 (1981), 107–241. · Zbl 0426.90091
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[4] Guo Shizhen, Optimal Policies for Discounted Markovian Decision Programming,Mathematics in Economics,1: 1 (1984), 109–120.
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