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Constrained Markov Decision Processes with Non-constant Discount Factor

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Listed:
  • Héctor Jasso-Fuentes

    (CINVESTAV-IPN)

  • Tomás Prieto-Rumeau

    (UNED)

Abstract

This paper studies constrained Markov decision processes under the total expected discounted cost optimality criterion, with a state-action dependent discount factor that may take any value between zero and one. Both the state and the action space are assumed to be Borel spaces. By using the linear programming approach, consisting in stating the control problem as a linear problem on a set of occupation measures, we show the existence of an optimal stationary Markov policy. Our results are based on the study of both weak-strong topologies in the space of occupation measures and Young measures in the space of Markov policies.

Suggested Citation

  • Héctor Jasso-Fuentes & Tomás Prieto-Rumeau, 2024. "Constrained Markov Decision Processes with Non-constant Discount Factor," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 897-931, August.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:2:d:10.1007_s10957-024-02453-y
    DOI: 10.1007/s10957-024-02453-y
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    References listed on IDEAS

    as
    1. Erik J. Balder, 2001. "On ws-Convergence of Product Measures," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 494-518, August.
    2. 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.
    3. Jorge Alvarez-Mena & Onésimo Hernández-Lerma, 2002. "Convergence of the optimal values of constrained Markov control processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(3), pages 461-484, June.
    4. Héctor Jasso-Fuentes & José-Luis Menaldi & Tomás Prieto-Rumeau, 2020. "Discrete-time control with non-constant discount factor," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(2), pages 377-399, October.
    5. Jorge Alvarez-Mena & Onésimo Hernández-Lerma, 2002. "Convergence of the optimal values of constrained Markov control processes," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(3), pages 461-484, June.
    6. Balder, Erik J, 1991. "On Cournot-Nash Equilibrium Distributions for Games with Differential Information and Discontinuous Payoffs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(4), pages 339-354, October.
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