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Average optimality inequality for continuous-time Markov decision processes in Polish spaces

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  • Quanxin Zhu

Abstract

In this paper, we study the average optimality for continuous-time controlled jump Markov processes in general state and action spaces. The criterion to be minimized is the average expected costs. Both the transition rates and the cost rates are allowed to be unbounded. We propose another set of conditions under which we first establish one average optimality inequality by using the well-known “vanishing discounting factor approach”. Then, when the cost (or reward) rates are nonnegative (or nonpositive), from the average optimality inequality we prove the existence of an average optimal stationary policy in all randomized history dependent policies by using the Dynkin formula and the Tauberian theorem. Finally, when the cost (or reward) rates have neither upper nor lower bounds, we also prove the existence of an average optimal policy in all (deterministic) stationary policies by constructing a “new” cost (or reward) rate. Copyright Springer-Verlag 2007

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:66:y:2007:i:2:p:299-313
    DOI: 10.1007/s00186-007-0157-x
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    1. Quanxin Zhu & Xianping Guo & Yonglong Dai, 2005. "Unbounded cost Markov decision processes with limsup and liminf average criteria: new conditions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 469-482, July.
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    Cited by:

    1. Liuer Ye & Xianping Guo, 2010. "New sufficient conditions for average optimality in continuous-time Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 75-94, August.

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