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Policy Iteration for Continuous‐Time Average Reward Markov Decision Processes in Polish Spaces

Author

Listed:
  • Quanxin Zhu
  • Xinsong Yang
  • Chuangxia Huang

Abstract

We study the policy iteration algorithm (PIA) for continuous‐time jump Markov decision processes in general state and action spaces. The corresponding transition rates are allowed to be unbounded, and the reward rates may have neither upper nor lower bounds. The criterion that we are concerned with is expected average reward. We propose a set of conditions under which we first establish the average reward optimality equation and present the PIA. Then under two slightly different sets of conditions we show that the PIA yields the optimal (maximum) reward, an average optimal stationary policy, and a solution to the average reward optimality equation.

Suggested Citation

  • Quanxin Zhu & Xinsong Yang & Chuangxia Huang, 2009. "Policy Iteration for Continuous‐Time Average Reward Markov Decision Processes in Polish Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    • Handle: RePEc:wly:jnlaaa:v:2009:y:2009:i:1:n:103723
    DOI: 10.1155/2009/103723
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    References listed on IDEAS

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    1. Iosif Il’ich Gihman & Anatoliĭ Vladimirovich Skorohod, 1979. "Discrete-Parameter Controlled Stochastic Processes," Springer Books, in: Controlled Stochastic Processes, chapter 1, pages 1-78, Springer.
    2. 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.
    3. A. Y. Golubin, 2003. "A Note on the Convergence of Policy Iteration in Markov Decision Processes with Compact Action Spaces," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 194-200, February.
    4. Iosif Il’ich Gihman & Anatoliĭ Vladimirovich Skorohod, 1979. "Controlled Stochastic Processes," Springer Books, Springer, number 978-1-4612-6202-2, March.
    5. Quanxin Zhu, 2007. "Average optimality inequality for continuous-time Markov decision processes in Polish spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 299-313, October.
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