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A structured pattern matrix algorithm for multichain Markov decision processes

Author

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  • Tetsuichiro Iki
  • Masayuki Horiguchi
  • Masami Kurano

Abstract

In this paper, we are concerned with a new algorithm for multichain finite state Markov decision processes which finds an average optimal policy through the decomposition of the state space into some communicating classes and a transient class. For each communicating class, a relatively optimal policy is found, which is used to find an optimal policy by applying the value iteration algorithm. Using a pattern matrix determining the behaviour pattern of the decision process, the decomposition of the state space is effectively done, so that the proposed algorithm simplifies the structured one given by the excellent Leizarowitz’s paper (Math Oper Res 28:553–586, 2003). Also, a numerical example is given to comprehend the algorithm. Copyright Springer-Verlag 2007

Suggested Citation

  • Tetsuichiro Iki & Masayuki Horiguchi & Masami Kurano, 2007. "A structured pattern matrix algorithm for multichain Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 545-555, December.
    • Handle: RePEc:spr:mathme:v:66:y:2007:i:3:p:545-555
    DOI: 10.1007/s00186-006-0138-5
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    References listed on IDEAS

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    1. Arie Leizarowitz, 2003. "An Algorithm to Identify and Compute Average Optimal Policies in Multichain Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 553-586, August.
    2. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    3. Arie Hordijk & Martin L. Puterman, 1987. "On the Convergence of Policy Iteration in Finite State Undiscounted Markov Decision Processes: The Unichain Case," Mathematics of Operations Research, INFORMS, vol. 12(1), pages 163-176, February.
    4. A. Hordijk & L. C. M. Kallenberg, 1979. "Linear Programming and Markov Decision Chains," Management Science, INFORMS, vol. 25(4), pages 352-362, April.
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