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Sensitivity analysis and optimal ultimately stationary deterministic policies in some constrained discounted cost models

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  • Krishnamurthy Iyer
  • Nandyala Hemachandra

Abstract

We consider a discrete time Markov Decision Process (MDP) under the discounted payoff criterion in the presence of additional discounted cost constraints. We study the sensitivity of optimal Stationary Randomized (SR) policies in this setting with respect to the upper bound on the discounted cost constraint functionals. We show that such sensitivity analysis leads to an improved version of the Feinberg–Shwartz algorithm (Math Oper Res 21(4):922–945, 1996) for finding optimal policies that are ultimately stationary and deterministic. Copyright Springer-Verlag 2010

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  • Krishnamurthy Iyer & Nandyala Hemachandra, 2010. "Sensitivity analysis and optimal ultimately stationary deterministic policies in some constrained discounted cost models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 401-425, June.
    • Handle: RePEc:spr:mathme:v:71:y:2010:i:3:p:401-425
    DOI: 10.1007/s00186-010-0303-8
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    References listed on IDEAS

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    1. Eugene A. Feinberg & Adam Shwartz, 1994. "Markov Decision Models with Weighted Discounted Criteria," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 152-168, February.
    2. Stratton C. Jaquette, 1976. "A Utility Criterion for Markov Decision Processes," Management Science, INFORMS, vol. 23(1), pages 43-49, September.
    3. Eugene A. Feinberg & Adam Shwartz, 1996. "Constrained Discounted Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 922-945, November.
    4. Cyrus Derman & Morton Klein, 1965. "Some Remarks on Finite Horizon Markovian Decision Models," Operations Research, INFORMS, vol. 13(2), pages 272-278, April.
    5. Eugene A. Feinberg & Adam Shwartz, 1995. "Constrained Markov Decision Models with Weighted Discounted Rewards," Mathematics of Operations Research, INFORMS, vol. 20(2), pages 302-320, May.
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    Cited by:

    1. Nandyala Hemachandra & Kamma Sri Naga Rajesh & Mohd. Abdul Qavi, 2016. "A model for equilibrium in some service-provider user-set interactions," Annals of Operations Research, Springer, vol. 243(1), pages 95-115, August.
    2. Kumar, Uday M & Bhat, Sanjay P. & Kavitha, Veeraruna & Hemachandra, Nandyala, 2023. "Approximate solutions to constrained risk-sensitive Markov decision processes," European Journal of Operational Research, Elsevier, vol. 310(1), pages 249-267.

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