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Technical Note—Successive Approximations in Value Determination for a Markov Decision Process

Author

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  • Theodore J. Sheskin

    (Cleveland State University, Cleveland, Ohio)

Abstract

We present a new procedure for solving the value-determination equations for an undiscounted Markov decision process by the successive approximations of a Gauss-Seidel or Jacobi iteration method. The key step is to use the Markov chain partitioning algorithm to compute the steady-state probabilities corresponding to a given policy. The gain, computed in terms of the steady-state probabilities, is substituted into the value-determination equations. After deleting one relative value and one value-determination equation, we show that the remaining system of equations satisfies the sufficient conditions for the convergence of a Gauss-Seidel or Jacobi iteration.

Suggested Citation

  • Theodore J. Sheskin, 1987. "Technical Note—Successive Approximations in Value Determination for a Markov Decision Process," Operations Research, INFORMS, vol. 35(5), pages 784-786, October.
    • Handle: RePEc:inm:oropre:v:35:y:1987:i:5:p:784-786
    DOI: 10.1287/opre.35.5.784
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