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A Compromise Programming Approach To Multiobjective Markov Decision Processes

Author

Listed:
  • WLODZIMIERZ OGRYCZAK

    () (ICCE, Warsaw University of Technology, Poland)

  • PATRICE PERNY

    (LIP6, University Pierre and Marie Curie, Paris, France)

  • PAUL WENG

    (LIP6, University Pierre and Marie Curie, Paris, France)

Abstract

A Markov decision process (MDP) is a general model for solving planning problems under uncertainty. It has been extended to multiobjective MDP to address multicriteria or multiagent problems in which the value of a decision must be evaluated according to several viewpoints, sometimes conflicting. Although most of the studies concentrate on the determination of the set of Pareto-optimal policies, we focus here on a more specialized problem that concerns the direct determination of policies achieving well-balanced tradeoffs. To this end, we introduce a reference point method based on the optimization of a weighted ordered weighted average (WOWA) of individual disachievements. We show that the resulting notion of optimal policy does not satisfy the Bellman principle and depends on the initial state. To overcome these difficulties, we propose a solution method based on a linear programming (LP) reformulation of the problem. Finally, we illustrate the feasibility of the proposed method on two types of planning problems under uncertainty arising in navigation of an autonomous agent and in inventory management.

Suggested Citation

  • Wlodzimierz Ogryczak & Patrice Perny & Paul Weng, 2013. "A Compromise Programming Approach To Multiobjective Markov Decision Processes," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 12(05), pages 1021-1053.
  • Handle: RePEc:wsi:ijitdm:v:12:y:2013:i:05:n:s0219622013400075
    DOI: 10.1142/S0219622013400075
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