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New sufficient conditions for average optimality in continuous-time Markov decision processes

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  • Liuer Ye
  • Xianping Guo

Abstract

This paper is devoted to studying continuous-time Markov decision processes with general state and action spaces, under the long-run expected average reward criterion. The transition rates of the underlying continuous-time Markov processes are allowed to be unbounded, and the reward rates may have neither upper nor lower bounds. We provide new sufficient conditions for the existence of average optimal policies. Moreover, such sufficient conditions are imposed on the controlled process’ primitive data and thus they are directly verifiable. Finally, we apply our results to two new examples. Copyright Springer-Verlag 2010

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:72:y:2010:i:1:p:75-94
    DOI: 10.1007/s00186-010-0307-4
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    References listed on IDEAS

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    1. Doshi, Bharat T., 1976. "Continuous time control of Markov processes on an arbitrary state space: Average return criterion," Stochastic Processes and their Applications, Elsevier, vol. 4(1), pages 55-77, January.
    2. 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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    Cited by:

    1. Xianping Guo & Yi Zhang, 2016. "Optimality of Mixed Policies for Average Continuous-Time Markov Decision Processes with Constraints," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1276-1296, November.
    2. Ping Cao & Jingui Xie, 2016. "Optimal control of a multiclass queueing system when customers can change types," Queueing Systems: Theory and Applications, Springer, vol. 82(3), pages 285-313, April.
    3. Qingda Wei & Xianping Guo, 2012. "New Average Optimality Conditions for Semi-Markov Decision Processes in Borel Spaces," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 709-732, June.

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