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Myopic Bounds for Optimal Policy of POMDPs: An Extension of Lovejoy’s Structural Results

Author

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  • Vikram Krishnamurthy

    (Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada)

  • Udit Pareek

    (Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada)

Abstract

This paper provides a relaxation of the sufficient conditions and an extension of the structural results for partially observed Markov decision processes (POMDPs) obtained by Lovejoy in 1987. Sufficient conditions are provided so that the optimal policy can be upper and lower bounded by judiciously chosen myopic policies. These myopic policy bounds are constructed to maximize the volume of belief states where they coincide with the optimal policy. Numerical examples illustrate these myopic bounds for both continuous and discrete observation sets.

Suggested Citation

  • Vikram Krishnamurthy & Udit Pareek, 2015. "Myopic Bounds for Optimal Policy of POMDPs: An Extension of Lovejoy’s Structural Results," Operations Research, INFORMS, vol. 63(2), pages 428-434, April.
    • Handle: RePEc:inm:oropre:v:63:y:2015:i:2:p:428-434
    DOI: 10.1287/opre.2014.1332
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    References listed on IDEAS

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    1. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities II. Multivariate reverse rule distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 499-516, December.
    2. William S. Lovejoy, 1987. "Some Monotonicity Results for Partially Observed Markov Decision Processes," Operations Research, INFORMS, vol. 35(5), pages 736-743, October.
    3. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    4. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
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