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Sample path optimality for a Markov optimization problem

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  • Hunt, F.Y.

Abstract

We study a unichain Markov decision process i.e. a controlled Markov process whose state process under a stationary policy is an ergodic Markov chain. Here the state and action spaces are assumed to be either finite or countable. When the state process is uniformly ergodic and the immediate cost is bounded then a policy that minimizes the long-term expected average cost also has an nth stage sample path cost that with probability one is asymptotically less than the nth stage sample path cost under any other non-optimal stationary policy with a larger expected average cost. This is a strengthening in the Markov model case of the a.s. asymptotically optimal property frequently discussed in the literature.

Suggested Citation

  • Hunt, F.Y., 2005. "Sample path optimality for a Markov optimization problem," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 769-779, May.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:5:p:769-779
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    References listed on IDEAS

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    1. Glynn, Peter W. & Ormoneit, Dirk, 2002. "Hoeffding's inequality for uniformly ergodic Markov chains," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 143-146, January.
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    Cited by:

    1. Hachicha, Wafik & Ammeri, Ahmed & Masmoudi, Faouzi & Chachoub, Habib, 2010. "A comprehensive literature classification of simulation optimisation methods," MPRA Paper 27652, University Library of Munich, Germany.
    2. Rolando Cavazos-Cadena & Raúl Montes-de-Oca & Karel Sladký, 2014. "A Counterexample on Sample-Path Optimality in Stable Markov Decision Chains with the Average Reward Criterion," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 674-684, November.

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