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

Author

Listed:
  • Eitan Altman
  • Konstantin E. Avrachenkov
  • Jerzy A. Filar

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. Copyright Springer-Verlag Berlin Heidelberg 1999

Suggested Citation

  • Eitan Altman & Konstantin E. Avrachenkov & Jerzy A. Filar, 1999. "Asymptotic linear programming and policy improvement for singularly perturbed Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(1), pages 97-109, March.
    • Handle: RePEc:spr:mathme:v:49:y:1999:i:1:p:97-109
    DOI: 10.1007/s001860050015
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    Cited by:

    1. L. Cayton & R. Herring & A. Holder & J. Holzer & C. Nightingale & T. Stohs, 2006. "Asymptotic sign-solvability, multiple objective linear programming, and the nonsubstitution theorem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 541-555, December.
    2. Eilon Solan & Nicolas Vieille, 2010. "Computing uniformly optimal strategies in two-player stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 237-253, January.

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