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Acceleration Operators in the Value Iteration Algorithms for Markov Decision Processes

Author

Listed:
  • Oleksandr Shlakhter

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada)

  • Chi-Guhn Lee

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada)

  • Dmitry Khmelev

    (Deceased---Formerly with Department of Mathematics, University of Toronto, Toronto, Ontario, Canada)

  • Nasser Jaber

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada)

Abstract

We study the general approach to accelerating the convergence of the most widely used solution method of Markov decision processes (MDPs) with the total expected discounted reward. Inspired by the monotone behavior of the contraction mappings in the feasible set of the linear programming problem equivalent to the MDP, we establish a class of operators that can be used in combination with a contraction mapping operator in the standard value iteration algorithm and its variants. We then propose two such operators, which can be easily implemented as part of the value iteration algorithm and its variants. Numerical studies show that the computational savings can be significant especially when the discount factor approaches one and the transition probability matrix becomes dense, in which the standard value iteration algorithm and its variants suffer from slow convergence.

Suggested Citation

  • Oleksandr Shlakhter & Chi-Guhn Lee & Dmitry Khmelev & Nasser Jaber, 2010. "Acceleration Operators in the Value Iteration Algorithms for Markov Decision Processes," Operations Research, INFORMS, vol. 58(1), pages 193-202, February.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:1:p:193-202
    DOI: 10.1287/opre.1090.0705
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    References listed on IDEAS

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    1. Herzberg, Meir & Yechiali, Uri, 1996. "A K-step look-ahead analysis of value iteration algorithms for Markov decision processes," European Journal of Operational Research, Elsevier, vol. 88(3), pages 622-636, February.
    2. Meir Herzberg & Uri Yechiali, 1994. "Accelerating Procedures of the Value Iteration Algorithm for Discounted Markov Decision Processes, Based on a One-Step Lookahead Analysis," Operations Research, INFORMS, vol. 42(5), pages 940-946, October.
    3. D. P. de Farias & B. Van Roy, 2003. "The Linear Programming Approach to Approximate Dynamic Programming," Operations Research, INFORMS, vol. 51(6), pages 850-865, December.
    4. Trick, Michael A. & Zin, Stanley E., 1997. "Spline Approximations To Value Functions," Macroeconomic Dynamics, Cambridge University Press, vol. 1(1), pages 255-277, January.
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    Cited by:

    1. Oleksandr Shlakhter & Chi-Guhn Lee, 2013. "Accelerated modified policy iteration algorithms for Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(1), pages 61-76, August.

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