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Structural Results for Partially Observable Markov Decision Processes

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  • S. Christian Albright

    (Indiana University, Bloomington, Indiana)

Abstract

This paper examines monotonicity results for a fairly general class of partially observable Markov decision processes. When there are only two actual states in the system and when the actions taken are primarily intended to improve the system, rather than to inspect it, we give reasonable conditions which ensure that the optimal reward function and the optimal action are both monotone in the current state of information. Examples of maintenance systems and advertising systems for which our results hold are given. Finally, we examine the case where there are three or more actual states and indicate the difficulties encountered when we attempt to extend the monotonicity results to this situation.

Suggested Citation

  • S. Christian Albright, 1979. "Structural Results for Partially Observable Markov Decision Processes," Operations Research, INFORMS, vol. 27(5), pages 1041-1053, October.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:5:p:1041-1053
    DOI: 10.1287/opre.27.5.1041
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    Cited by:

    1. Chiel van Oosterom & Lisa M. Maillart & Jeffrey P. Kharoufeh, 2017. "Optimal maintenance policies for a safety‐critical system and its deteriorating sensor," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(5), pages 399-417, August.
    2. Armando Z. Milioni & Stanley R. Pliska, 1988. "Optimal inspection under semi‐markovian deterioration: Basic results," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 373-392, October.
    3. Jingyu Zhang & Brian T. Denton & Hari Balasubramanian & Nilay D. Shah & Brant A. Inman, 2012. "Optimization of Prostate Biopsy Referral Decisions," Manufacturing & Service Operations Management, INFORMS, vol. 14(4), pages 529-547, October.
    4. Abraham Grosfeld‐Nir & Eyal Cohen & Yigal Gerchak, 2007. "Production to order and off‐line inspection when the production process is partially observable," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(8), pages 845-858, December.
    5. Ciriaco Valdez‐Flores & Richard M. Feldman, 1989. "A survey of preventive maintenance models for stochastically deteriorating single‐unit systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(4), pages 419-446, August.
    6. Givon, Moshe & Grosfeld-Nir, Abraham, 2008. "Using partially observed Markov processes to select optimal termination time of TV shows," Omega, Elsevier, vol. 36(3), pages 477-485, June.
    7. Miehling, Erik & Teneketzis, Demosthenis, 2020. "Monotonicity properties for two-action partially observable Markov decision processes on partially ordered spaces," European Journal of Operational Research, Elsevier, vol. 282(3), pages 936-944.
    8. Shoshana Anily & Abraham Grosfeld-Nir, 2006. "An Optimal Lot-Sizing and Offline Inspection Policy in the Case of Nonrigid Demand," Operations Research, INFORMS, vol. 54(2), pages 311-323, April.
    9. Chernonog, Tatyana & Avinadav, Tal, 2016. "A two-state partially observable Markov decision process with three actionsAuthor-Name: Ben-Zvi, Tal," European Journal of Operational Research, Elsevier, vol. 254(3), pages 957-967.
    10. Grosfeld-Nir, Abraham, 2007. "Control limits for two-state partially observable Markov decision processes," European Journal of Operational Research, Elsevier, vol. 182(1), pages 300-304, October.
    11. Li, Weiyu & Denton, Brian T. & Morgan, Todd M., 2023. "Optimizing active surveillance for prostate cancer using partially observable Markov decision processes," European Journal of Operational Research, Elsevier, vol. 305(1), pages 386-399.
    12. K. Waldmann, 1982. "On two-state quality control under Markovian deterioration," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 29(1), pages 249-260, December.

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