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Blackwell optimality in the class of stationary policies in Markov decision chains with a Borel state space and unbounded rewards

Author

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  • Arie Hordijk
  • Alexander A. Yushkevich

Abstract

This paper is the first part of a study of Blackwell optimal policies in Markov decision chains with a Borel state space and unbounded rewards. We prove here the existence of deterministic stationary policies which are Blackwell optimal in the class of all, in general randomized, stationary policies. We establish also a lexicographical policy improvement algorithm leading to Blackwell optimal policies and the relation between such policies and the Blackwell optimality equation. Our technique is a combination of the weighted norms approach developed in Dekker and Hordijk (1988) for countable models with unbounded rewards and of the weak-strong topology approach used in Yushkevich (1997a) for Borel models with bounded rewards. Copyright Springer-Verlag Berlin Heidelberg 1999

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:49:y:1999:i:1:p:1-39
    DOI: 10.1007/s001860050011
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    Citations

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    Cited by:

    1. Bernd Heidergott & Arie Hordijk & Haralambie Leahu, 2009. "Strong bounds on perturbations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(1), pages 99-127, August.
    2. 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.
    3. Bernd Heidergott & Arie Hordijk & Heinz Weisshaupt, 2006. "Measure-Valued Differentiation for Stationary Markov Chains," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 154-172, February.
    4. Bernd Heidergott & Haralambie Leahu, 2010. "Weak Differentiability of Product Measures," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 27-51, February.
    5. Heidergott, B. & Leahu, H., 2008. "Differentiability of Product Measures," Serie Research Memoranda 0005, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    6. Nicole Leder & Bernd Heidergott & Arie Hordijk, 2010. "An Approximation Approach for the Deviation Matrix of Continuous-Time Markov Processes with Application to Markov Decision Theory," Operations Research, INFORMS, vol. 58(4-part-1), pages 918-932, August.

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