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New Average Optimality Conditions for Semi-Markov Decision Processes in Borel Spaces

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  • Qingda Wei

    (Sun Yat-Sen University)

  • Xianping Guo

    (Sun Yat-Sen University)

Abstract

This paper deals with semi-Markov decision processes under the average expected criterion. The state and action spaces are Borel spaces, and the cost/reward function is allowed to be unbounded from above and from below. We give another set of conditions, under which the existence of an optimal (deterministic) stationary policy is proven by a new technique of two average optimality inequalities. Our conditions are slightly weaker than those in the existing literature, and some new sufficient conditions for the verifications of our assumptions are imposed on the primitive data of the model. Finally, we illustrate our results with three examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:3:d:10.1007_s10957-012-9986-8
    DOI: 10.1007/s10957-012-9986-8
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    References listed on IDEAS

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    1. Anna Jaśkiewicz, 2001. "An approximation approach to ergodic semi-Markov control processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(1), pages 1-19, October.
    2. Federgruen, A. & Hordijk, A. & Tijms, H. C., 1979. "Denumerable state semi-Markov decision processes with unbounded costs, average cost criterion," Stochastic Processes and their Applications, Elsevier, vol. 9(2), pages 223-235, November.
    3. 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.
    4. A. Jaśkiewicz, 2004. "On the Equivalence of Two Expected Average Cost Criteria for Semi-Markov Control Processes," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 326-338, May.
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    Cited by:

    1. Gabriel Zayas-Cabán & Mark E. Lewis, 2020. "Admission control in a two-class loss system with periodically varying parameters and abandonments," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 175-210, February.

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