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Percentile Optimization for Markov Decision Processes with Parameter Uncertainty

Author

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  • Erick Delage

    (Department of Management Science, HEC Montréal, Montréal, Quebec H3T 2A7, Canada)

  • Shie Mannor

    (Department of Electrical and Computer Engineering, McGill University, Montreal, Quebec H3A 2A7, Canada)

Abstract

Markov decision processes are an effective tool in modeling decision making in uncertain dynamic environments. Because the parameters of these models typically are estimated from data or learned from experience, it is not surprising that the actual performance of a chosen strategy often differs significantly from the designer's initial expectations due to unavoidable modeling ambiguity. In this paper, we present a set of percentile criteria that are conceptually natural and representative of the trade-off between optimistic and pessimistic views of the question. We study the use of these criteria under different forms of uncertainty for both the rewards and the transitions. Some forms are shown to be efficiently solvable and others highly intractable. In each case, we outline solution concepts that take parametric uncertainty into account in the process of decision making.

Suggested Citation

  • Erick Delage & Shie Mannor, 2010. "Percentile Optimization for Markov Decision Processes with Parameter Uncertainty," Operations Research, INFORMS, vol. 58(1), pages 203-213, February.
  • Handle: RePEc:inm:oropre:v:58:y:2010:i:1:p:203-213
    DOI: 10.1287/opre.1080.0685
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    References listed on IDEAS

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    Cited by:

    1. Anthony Coache & Sebastian Jaimungal, 2021. "Reinforcement Learning with Dynamic Convex Risk Measures," Papers 2112.13414, arXiv.org, revised Nov 2022.
    2. 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.
    3. Wentao Ma & Zhiping Chen, 2024. "Multi-stage distributionally robust convex stochastic optimization with Bayesian-type ambiguity sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(2), pages 553-600, October.
    4. Saghafian, Soroush, 2018. "Ambiguous partially observable Markov decision processes: Structural results and applications," Journal of Economic Theory, Elsevier, vol. 178(C), pages 1-35.
    5. Li Xia, 2020. "Risk‐Sensitive Markov Decision Processes with Combined Metrics of Mean and Variance," Production and Operations Management, Production and Operations Management Society, vol. 29(12), pages 2808-2827, December.
    6. Boloori, Alireza & Saghafian, Soroush & Chakkera, Harini A. A. & Cook, Curtiss B., 2017. "Data-Driven Management of Post-transplant Medications: An APOMDP Approach," Working Paper Series rwp17-036, Harvard University, John F. Kennedy School of Government.
    7. David L. Kaufman & Andrew J. Schaefer, 2013. "Robust Modified Policy Iteration," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 396-410, August.
    8. Varagapriya, V & Singh, Vikas Vikram & Lisser, Abdel, 2024. "Rank-1 transition uncertainties in constrained Markov decision processes," European Journal of Operational Research, Elsevier, vol. 318(1), pages 167-178.
    9. 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.
    10. Huan Xu & Shie Mannor, 2012. "Distributionally Robust Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 288-300, May.
    11. 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.
    12. Chernonog, Tatyana & Avinadav, Tal, 2014. "Profit criteria involving risk in price setting of virtual products," European Journal of Operational Research, Elsevier, vol. 236(1), pages 351-360.
    13. Huan Xu & Constantine Caramanis & Shie Mannor, 2012. "Optimization Under Probabilistic Envelope Constraints," Operations Research, INFORMS, vol. 60(3), pages 682-699, June.
    14. Bren, Austin & Saghafian, Soroush, 2018. "Data-Driven Percentile Optimization for Multi-Class Queueing Systems with Model Ambiguity: Theory and Application," Working Paper Series rwp18-008, Harvard University, John F. Kennedy School of Government.
    15. Maximilian Blesch & Philipp Eisenhauer, 2023. "Robust Decision-Making under Risk and Ambiguity," Rationality and Competition Discussion Paper Series 463, CRC TRR 190 Rationality and Competition.
    16. Huan Xu & Constantine Caramanis & Shie Mannor, 2012. "A Distributional Interpretation of Robust Optimization," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 95-110, February.
    17. Shie Mannor & Ofir Mebel & Huan Xu, 2016. "Robust MDPs with k -Rectangular Uncertainty," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1484-1509, November.
    18. 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.
    19. Alireza Boloori & Soroush Saghafian & Harini A. Chakkera & Curtiss B. Cook, 2020. "Data-Driven Management of Post-transplant Medications: An Ambiguous Partially Observable Markov Decision Process Approach," Manufacturing & Service Operations Management, INFORMS, vol. 22(5), pages 1066-1087, September.
    20. Zahra Ghatrani & Archis Ghate, 2024. "Percentile optimization in multi-armed bandit problems," Annals of Operations Research, Springer, vol. 340(2), pages 837-862, September.
    21. Saghafian, Soroush & Tomlin, Brian & Biller, Stephan, 2018. "The Internet of Things and Information Fusion: Who Talks to Who?," Working Paper Series rwp18-009, Harvard University, John F. Kennedy School of Government.
    22. Wolfram Wiesemann & Daniel Kuhn & Berç Rustem, 2013. "Robust Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 153-183, February.
    23. Maximilian Blesch & Philipp Eisenhauer, 2021. "Robust Decision-Making Under Risk and Ambiguity," ECONtribute Discussion Papers Series 104, University of Bonn and University of Cologne, Germany.

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