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Finite-Memory Strategies in POMDPs with Long-Run Average Objectives

Author

Listed:
  • Krishnendu Chatterjee

    (Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria)

  • Raimundo Saona

    (Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria)

  • Bruno Ziliotto

    (Centre de Recherche en Mathématiques de la Décision, Centre National de la Recherche Scientifique, Université Paris Dauphine, Université PSL, 75016 Paris, France)

Abstract

Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that in POMDPs with long-run average objective, the decision maker has approximately optimal strategies with finite memory. This implies notably that approximating the long-run value is recursively enumerable, as well as a weak continuity property of the value with respect to the transition function.

Suggested Citation

  • Krishnendu Chatterjee & Raimundo Saona & Bruno Ziliotto, 2022. "Finite-Memory Strategies in POMDPs with Long-Run Average Objectives," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 100-119, February.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:1:p:100-119
    DOI: 10.1287/moor.2020.1116
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    References listed on IDEAS

    as
    1. 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.
    2. Xavier Venel & Bruno Ziliotto, 2016. "Pathwise uniform value in gambling houses and Partially Observable Markov Decision Processes," Working Papers hal-01302567, HAL.
    3. Xavier Venel & Bruno Ziliotto, 2016. "Strong Uniform Value in Gambling Houses and Partially Observable Markov Decision Processes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01395429, HAL.
    4. Xavier Venel & Bruno Ziliotto, 2016. "Pathwise uniform value in gambling houses and Partially Observable Markov Decision Processes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01302567, HAL.
    5. Xavier Venel & Bruno Ziliotto, 2016. "Strong Uniform Value in Gambling Houses and Partially Observable Markov Decision Processes," Post-Print hal-01395429, HAL.
    6. Eilon Solan, 2003. "Continuity of the Value of Competitive Markov Decision Processes," Journal of Theoretical Probability, Springer, vol. 16(4), pages 831-845, October.
    7. Xavier Venel & Bruno Ziliotto, 2016. "Strong Uniform Value in Gambling Houses and Partially Observable Markov Decision Processes," PSE-Ecole d'économie de Paris (Postprint) hal-01395429, HAL.
    8. Abraham Neyman & Sylvain Sorin, 2010. "Repeated games with public uncertain duration process," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 29-52, March.
    9. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2000. "Blackwell Optimality in Markov Decision Processes with Partial Observation," Discussion Papers 1292, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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