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Policy Bounds for Markov Decision Processes

Author

Listed:
  • William S. Lovejoy

    (Georgia Institute of Technology, Atlanta, Georgia)

Abstract

This paper demonstrates how a Markov decision process (MDP) can be approximated to generate a policy bound, i.e., a function that bounds the optimal policy from below or from above for all states. We present sufficient conditions for several computationally attractive approximations to generate rigorous policy bounds. These approximations include approximating the optimal value function, replacing the original MDP with a separable approximate MDP, and approximating a stochastic MDP with its deterministic counterpart. An example from the field of fisheries management demonstrates the practical applicability of the results.

Suggested Citation

  • William S. Lovejoy, 1986. "Policy Bounds for Markov Decision Processes," Operations Research, INFORMS, vol. 34(4), pages 630-637, August.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:4:p:630-637
    DOI: 10.1287/opre.34.4.630
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    Cited by:

    1. Dan Zhang & William L. Cooper, 2005. "Revenue Management for Parallel Flights with Customer-Choice Behavior," Operations Research, INFORMS, vol. 53(3), pages 415-431, June.
    2. Jie Ning & Matthew J. Sobel, 2019. "Easy Affine Markov Decision Processes," Operations Research, INFORMS, vol. 67(6), pages 1719-1737, November.
    3. Kannapha Amaruchkul & William L. Cooper & Diwakar Gupta, 2007. "Single-Leg Air-Cargo Revenue Management," Transportation Science, INFORMS, vol. 41(4), pages 457-469, November.
    4. Slotnick, Susan A. & Sobel, Matthew J., 2005. "Manufacturing lead-time rules: Customer retention versus tardiness costs," European Journal of Operational Research, Elsevier, vol. 163(3), pages 825-856, June.
    5. Drouin, Nicol & Gautier, Antoine & Lamond, Bernard F. & Lang, Pascal, 1996. "Piecewise affine approximations for the control of a one-reservoir hydroelectric system," European Journal of Operational Research, Elsevier, vol. 89(1), pages 53-69, February.

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