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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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    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. Eugene A. Feinberg, 2000. "Constrained Discounted Markov Decision Processes and Hamiltonian Cycles," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 130-140, February.
    3. 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.

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