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Markov Decision Processes with Imprecise Transition Probabilities

Author

Listed:
  • Chelsea C. White

    (University of Michigan, Ann Arbor, Michigan)

  • Hany K. Eldeib

    (INTELSAT Corporation, Washington, D.C.)

Abstract

We present new numerical algorithms and bounds for the infinite horizon, discrete stage, finite state and action Markov decision process with imprecise transition probabilities. We assume that the transition probability mass vector for each state and action is described by a finite number of linear inequalities. This model of imprecision appears to be well suited for describing statistically determined confidence limits and/or natural language statements of likelihood. The numerical procedures for calculating an optimal max-min strategy are based on successive approximations, reward revision, and modified policy iteration. The bounds that are determined are at least as tight as currently available bounds for the case where the transition probabilities are precise.

Suggested Citation

  • Chelsea C. White & Hany K. Eldeib, 1994. "Markov Decision Processes with Imprecise Transition Probabilities," Operations Research, INFORMS, vol. 42(4), pages 739-749, August.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:4:p:739-749
    DOI: 10.1287/opre.42.4.739
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    Cited by:

    1. Abhijit Gosavi, 2009. "Reinforcement Learning: A Tutorial Survey and Recent Advances," INFORMS Journal on Computing, INFORMS, vol. 21(2), pages 178-192, May.
    2. Zhu, Zhicheng & Xiang, Yisha & Zhao, Ming & Shi, Yue, 2023. "Data-driven remanufacturing planning with parameter uncertainty," European Journal of Operational Research, Elsevier, vol. 309(1), pages 102-116.
    3. Zeynep Turgay & Fikri Karaesmen & Egemen Lerzan Örmeci, 2018. "Structural properties of a class of robust inventory and queueing control problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 699-716, December.
    4. Arnab Nilim & Laurent El Ghaoui, 2005. "Robust Control of Markov Decision Processes with Uncertain Transition Matrices," Operations Research, INFORMS, vol. 53(5), pages 780-798, October.
    5. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.
    6. D. Škulj & R. Hable, 2013. "Coefficients of ergodicity for Markov chains with uncertain parameters," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 107-133, January.
    7. Garud N. Iyengar, 2005. "Robust Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 257-280, May.
    8. Peter Buchholz & Dimitri Scheftelowitsch, 2019. "Computation of weighted sums of rewards for concurrent MDPs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 1-42, February.
    9. Wolfram Wiesemann & Daniel Kuhn & Berç Rustem, 2010. "Robust Markov Decision Processes," Working Papers 034, COMISEF.
    10. Xiaoting Ji & Yifeng Niu & Lincheng Shen, 2016. "Robust Satisficing Decision Making for Unmanned Aerial Vehicle Complex Missions under Severe Uncertainty," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-35, November.
    11. Schapaugh, Adam W. & Tyre, Andrew J., 2013. "Accounting for parametric uncertainty in Markov decision processes," Ecological Modelling, Elsevier, vol. 254(C), pages 15-21.
    12. David L. Kaufman & Andrew J. Schaefer, 2013. "Robust Modified Policy Iteration," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 396-410, August.
    13. Felipe Caro & Aparupa Das Gupta, 2022. "Robust control of the multi-armed bandit problem," Annals of Operations Research, Springer, vol. 317(2), pages 461-480, October.
    14. Wolfram Wiesemann & Daniel Kuhn & Berç Rustem, 2013. "Robust Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 153-183, February.
    15. V Varagapriya & Vikas Vikram Singh & Abdel Lisser, 2023. "Joint chance-constrained Markov decision processes," Annals of Operations Research, Springer, vol. 322(2), pages 1013-1035, March.
    16. Hyeong Chang, 2006. "Perfect information two-person zero-sum markov games with imprecise transition probabilities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 335-351, October.
    17. Erim Kardeş & Fernando Ordóñez & Randolph W. Hall, 2011. "Discounted Robust Stochastic Games and an Application to Queueing Control," Operations Research, INFORMS, vol. 59(2), pages 365-382, April.
    18. Arthur Flajolet & Sébastien Blandin & Patrick Jaillet, 2018. "Robust Adaptive Routing Under Uncertainty," Operations Research, INFORMS, vol. 66(1), pages 210-229, January.

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