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Computationally Feasible Bounds for Partially Observed Markov Decision Processes

Author

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  • William S. Lovejoy

    (Stanford University, Stanford, California)

Abstract

A partially observed Markov decision process (POMDP) is a sequential decision problem where information concerning parameters of interest is incomplete, and possible actions include sampling, surveying, or otherwise collecting additional information. Such problems can theoretically be solved as dynamic programs, but the relevant state space is infinite, which inhibits algorithmic solution. This paper explains how to approximate the state space by a finite grid of points, and use that grid to construct upper and lower value function bounds, generate approximate nonstationary and stationary policies, and bound the value loss relative to optimal for using these policies in the decision problem. A numerical example illustrates the methodology.

Suggested Citation

  • William S. Lovejoy, 1991. "Computationally Feasible Bounds for Partially Observed Markov Decision Processes," Operations Research, INFORMS, vol. 39(1), pages 162-175, February.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:1:p:162-175
    DOI: 10.1287/opre.39.1.162
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    Cited by:

    1. Burhaneddin Sandıkçı & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2013. "Alleviating the Patient's Price of Privacy Through a Partially Observable Waiting List," Management Science, INFORMS, vol. 59(8), pages 1836-1854, August.
    2. Satya S. Malladi & Alan L. Erera & Chelsea C. White, 2021. "Managing mobile production-inventory systems influenced by a modulation process," Annals of Operations Research, Springer, vol. 304(1), pages 299-330, September.
    3. Compare, Michele & Baraldi, Piero & Marelli, Paolo & Zio, Enrico, 2020. "Partially observable Markov decision processes for optimal operations of gas transmission networks," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    4. Hao Zhang, 2010. "Partially Observable Markov Decision Processes: A Geometric Technique and Analysis," Operations Research, INFORMS, vol. 58(1), pages 214-228, February.
    5. Robert Kraig Helmeczi & Can Kavaklioglu & Mucahit Cevik & Davood Pirayesh Neghab, 2023. "A multi-objective constrained partially observable Markov decision process model for breast cancer screening," Operational Research, Springer, vol. 23(2), pages 1-42, June.
    6. Nguyen, Khanh T. P. & Do, Phuc & Huynh, Khac Tuan & Bérenguer, Christophe & Grall, Antoine, 2019. "Joint optimization of monitoring quality and replacement decisions in condition-based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 177-195.
    7. Yu Zhang & Jason Leezer, 2010. "Simulating human-like decisions in a memory-based agent model," Computational and Mathematical Organization Theory, Springer, vol. 16(4), pages 373-399, December.
    8. Jingyu Zhang & Brian T. Denton & Hari Balasubramanian & Nilay D. Shah & Brant A. Inman, 2012. "Optimization of PSA Screening Policies," Medical Decision Making, , vol. 32(2), pages 337-349, March.
    9. 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.
    10. Williams, Byron K., 2011. "Resolving structural uncertainty in natural resources management using POMDP approaches," Ecological Modelling, Elsevier, vol. 222(5), pages 1092-1102.
    11. KarabaÄŸ, Oktay & Eruguz, Ayse Sena & Basten, Rob, 2020. "Integrated optimization of maintenance interventions and spare part selection for a partially observable multi-component system," Reliability Engineering and System Safety, Elsevier, vol. 200(C).
    12. 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.
    13. Lyn C. Thomas & James N. Eagle, 1995. "Criteria and approximate methods for path‐constrained moving‐target search problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(1), pages 27-38, February.
    14. Harun Avci & Kagan Gokbayrak & Emre Nadar, 2020. "Structural Results for Average‐Cost Inventory Models with Markov‐Modulated Demand and Partial Information," Production and Operations Management, Production and Operations Management Society, vol. 29(1), pages 156-173, January.
    15. Yossi Aviv & Amit Pazgal, 2005. "A Partially Observed Markov Decision Process for Dynamic Pricing," Management Science, INFORMS, vol. 51(9), pages 1400-1416, September.
    16. Fackler, Paul L. & Haight, Robert G., 2014. "Monitoring as a partially observable decision problem," Resource and Energy Economics, Elsevier, vol. 37(C), pages 226-241.
    17. 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.
    18. Juri Hinz, 2021. "On Approximate Solutions for Partially Observable Decision Problems," Research Paper Series 421, Quantitative Finance Research Centre, University of Technology, Sydney.
    19. Memarzadeh, Milad & Pozzi, Matteo, 2016. "Value of information in sequential decision making: Component inspection, permanent monitoring and system-level scheduling," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 137-151.
    20. Vishal Ahuja & John R. Birge, 2020. "An Approximation Approach for Response-Adaptive Clinical Trial Design," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 877-894, October.
    21. Vikram Krishnamurthy & Bo Wahlberg, 2009. "Partially Observed Markov Decision Process Multiarmed Bandits---Structural Results," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 287-302, May.

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