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A Weighted Markov Decision Process

Author

Listed:
  • Dmitry Krass

    (University of Toronto, Toronto, Ontario, Canada)

  • Jerzy A. Filar

    (University of Maryland at Baltimore County, Baltimore, Maryland)

  • Sagnik S. Sinha

    (Indian Statistical Institute, New Delhi, India)

Abstract

The two most commonly considered reward criteria for Markov decision processes are the discounted reward and the long-term average reward. The first tends to “neglect” the future, concentrating on the short-term rewards, while the second one tends to do the opposite. We consider a new reward criterion consisting of the weighted combination of these two criteria, thereby allowing the decision maker to place more or less emphasis on the short-term versus the long-term rewards by varying their weights. The mathematical implications of the new criterion include: the deterministic stationary policies can be outperformed by the randomized stationary policies, which in turn can be outperformed by the nonstationary policies; an optimal policy might not exist. We present an iterative algorithm for computing an ε-optimal nonstationary policy with a very simple structure.

Suggested Citation

  • Dmitry Krass & Jerzy A. Filar & Sagnik S. Sinha, 1992. "A Weighted Markov Decision Process," Operations Research, INFORMS, vol. 40(6), pages 1180-1187, December.
  • Handle: RePEc:inm:oropre:v:40:y:1992:i:6:p:1180-1187
    DOI: 10.1287/opre.40.6.1180
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    Citations

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    Cited by:

    1. Hernández-Lerma, Onésimo & Romera, Rosario, 2000. "Pareto optimality in multiobjective Markov control processes," DES - Working Papers. Statistics and Econometrics. WS 9865, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Dmitry Krass & O. J. Vrieze, 2002. "Achieving Target State-Action Frequencies in Multichain Average-Reward Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 27(3), pages 545-566, August.
    3. Eugene A. Feinberg, 2000. "Constrained Discounted Markov Decision Processes and Hamiltonian Cycles," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 130-140, February.

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