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

Author

Listed:
  • Arie Hordijk
  • Alexander A. Yushkevich

Abstract

This paper is the second part of our study of Blackwell optimal policies in Markov decision chains with a Borel state space and unbounded rewards. We prove that a stationary policy is Blackwell optimal in the class of all history-dependent policies if it is Blackwell optimal in the class of stationary policies. We also develop recurrence and drift conditions which ensure ergodicity and integrability assumptions made in the previous paper, and which are more suitable for applications. As an example we study a cash-balance model. Copyright Springer-Verlag Berlin Heidelberg 1999

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:50:y:1999:i:3:p:421-448
    DOI: 10.1007/s001860050079
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    Cited by:

    1. Bernd Heidergott & Haralambie Leahu, 2010. "Weak Differentiability of Product Measures," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 27-51, February.
    2. 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.
    3. J. Minjárez-Sosa, 2015. "Markov control models with unknown random state–action-dependent discount factors," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 743-772, October.
    4. 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.
    5. 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.
    6. 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.
    7. Heidergott, B. & Leahu, H., 2008. "Differentiability of Product Measures," Serie Research Memoranda 0005, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.

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