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Asymptotic linear programming and policy improvement for singularly perturbed Markov decision processes

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Abstract.

In this paper we consider a singularly perturbed Markov decision process with finitely many states and actions and the limiting expected average reward criterion. We make no assumptions about the underlying ergodic structure. We present algorithms for the computation of a uniformly optimal deterministic control, that is, a control which is optimal for all values of the perturbation parameter that are sufficiently small. Our algorithms are based on Jeroslow's Asymptotic Linear Programming.

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Authors and Affiliations

  1. INRIA, Centre Sophia-Antipolis, 2004 Route des Lucioles, B.P. 93, F-06902 Sophia-Antipolis Cedex, France (e-mail: eitan.altman@sophia.inria.fr), , , , , , FR

    Eitan Altman

  2. Centre for the Industrial and Applicable Mathematics, School of Mathematics, University of South Australia, The Levels, SA 5095, Australia (e-mail: matkea@zarniwoop.levels.unisa.edu.au), , , , , , AU

    Konstantin E. Avrachenkov & Jerzy A. Filar

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  1. Eitan Altman
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  2. Konstantin E. Avrachenkov
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  3. Jerzy A. Filar
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Manuscript received: July 1997/final version received: July 1998

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Altman, E., Avrachenkov, K. & Filar, J. Asymptotic linear programming and policy improvement for singularly perturbed Markov decision processes. Mathematical Methods of OR 49, 97–109 (1999). https://doi.org/10.1007/s001860050015

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  • DOI: https://doi.org/10.1007/s001860050015

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