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Reward Revision for Discounted Markov Decision Problems

Author

Listed:
  • Chelsea C. White

    (University of Virginia, Charlottesville, Virginia)

  • Lyn C. Thomas

    (The University of Manchester, Manchester, England)

  • William T. Scherer

    (University of Virginia, Charlottesville, Virginia)

Abstract

We present a numerical procedure for determining the optimal total expected discounted reward vector f * for an infinite horizon, discrete stage, finite state and action Markov decision process (MDP). This procedure exploits the fact that many MDPs generate the same vector f *. The objective of the procedure is to simultaneously construct and solve one such MDP that has a computationally attractive transition structure. The construction of this MDP requires the periodic revision of its reward structure. We then present a simple, a priori method for estimating the impact of the new procedure on operation counts as compared to standard successive approximations. This method is useful for determining whether or not the new procedure should be used and for selecting an important design parameter. We also describe two extensions of the new procedure, one generalizing a standard extrapolation and the other a modified policy iteration algorithm. A numerical evaluation indicates that for MDPs having transition structures with a small number of dominant probabilities per row, the new procedure can significantly reduce CPU time.

Suggested Citation

  • Chelsea C. White & Lyn C. Thomas & William T. Scherer, 1985. "Reward Revision for Discounted Markov Decision Problems," Operations Research, INFORMS, vol. 33(6), pages 1299-1315, December.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:6:p:1299-1315
    DOI: 10.1287/opre.33.6.1299
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    Cited by:

    1. Awi Federgruen & Michal Tzur, 1996. "Detection of minimal forecast horizons in dynamic programs with multiple indicators of the future," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(2), pages 169-189, March.
    2. David L. Kaufman & Andrew J. Schaefer, 2013. "Robust Modified Policy Iteration," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 396-410, August.

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