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Conditions for the uniqueness of optimal policies of discounted Markov decision processes

Author

Listed:
  • Daniel Cruz-Suárez
  • Raúl Montes-de-Oca
  • Francisco Salem-Silva

Abstract

This paper presents three conditions. Each of them guarantees the uniqueness of optimal policies of discounted Markov decision processes. The conditions presented here impose hypotheses specifically on the state space X, the action space A, the admissible action sets A(x),x∈X, the transition probability Q, and on the cost function c. Two of these conditions require mainly convexity assumptions, but the third one does not need this kind of assumptions. However, it needs certain stochastic order relations in Q, and the cost function c to reach its minimum with respect to the actions, just in one action. We illustrate the conditions with several examples including, in particular, discrete models, the linear regulator problem, and also a model of an inventory control system. Copyright Springer-Verlag 2004

Suggested Citation

  • Daniel Cruz-Suárez & Raúl Montes-de-Oca & Francisco Salem-Silva, 2004. "Conditions for the uniqueness of optimal policies of discounted Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(3), pages 415-436, December.
    • Handle: RePEc:spr:mathme:v:60:y:2004:i:3:p:415-436
    DOI: 10.1007/s001860400372
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    Cited by:

    1. Hugo Cruz-Suárez & Raúl Montes-de-Oca, 2008. "An envelope theorem and some applications to discounted Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 299-321, April.
    2. Gladys Denisse Salgado Su¨¢rez & Hugo Cruz-Su¨¢rez & Jos¨¦ Dionicio Zacar¨ªas Flores, 2018. "Asymptotic Analysis of a Deterministic Control System via Euler's Equation Approach," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(1), pages 115-123, February.
    3. Torpong Cheevaprawatdomrong & Irwin E. Schochetman & Robert L. Smith & Alfredo Garcia, 2007. "Solution and Forecast Horizons for Infinite-Horizon Nonhomogeneous Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 51-72, February.

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