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Sample-path optimality and variance-maximization for Markov decision processes

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  • Q. Zhu

Abstract

This paper studies both the average sample-path reward (ASPR) criterion and the limiting average variance criterion for denumerable discrete-time Markov decision processes. The rewards may have neither upper nor lower bounds. We give sufficient conditions on the system’s primitive data and under which we prove the existence of ASPR-optimal stationary policies and variance optimal policies. Our conditions are weaker than those in the previous literature. Moreover, our results are illustrated by a controlled queueing system. Copyright Springer-Verlag 2007

Suggested Citation

  • Q. Zhu, 2007. "Sample-path optimality and variance-maximization for Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 519-538, June.
    • Handle: RePEc:spr:mathme:v:65:y:2007:i:3:p:519-538
    DOI: 10.1007/s00186-006-0126-9
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    References listed on IDEAS

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    1. Arie Hordijk & Alexander A. Yushkevich, 1999. "Blackwell optimality in the class of all policies in Markov decision chains with a Borel state space and unbounded rewards," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 421-448, December.
    2. Keith W. Ross & Ravi Varadarajan, 1989. "Markov Decision Processes with Sample Path Constraints: The Communicating Case," Operations Research, INFORMS, vol. 37(5), pages 780-790, October.
    3. Arie Hordijk & Alexander A. Yushkevich, 1999. "Blackwell optimality in the class of stationary policies in Markov decision chains with a Borel state space and unbounded rewards," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(1), pages 1-39, March.
    4. Andrzej S. Nowak, 1999. "A note on strong 1-optimal policies in Markov decision chains with unbounded costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(3), pages 475-482, July.
    5. 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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