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Convex analytic approach to constrained discounted Markov decision processes with non-constant discount factors

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  • Yi Zhang

Abstract

In this paper we develop the convex analytic approach to a discounted discrete-time Markov decision process (DTMDP) in Borel state and action spaces with N constraints. Unlike the classic discounted models, we allow a non-constant discount factor. After defining and characterizing the corresponding occupation measures, the original constrained DTMDP is written as a convex program in the space of occupation measures, whose compactness and convexity we show. In particular, we prove that every extreme point of the space of occupation measures can be generated by a deterministic stationary policy for the DTMDP. For the resulting convex program, we prove that it admits a solution that can be expressed as a convex combination of N+1 extreme points of the space of occupation measures. One of its consequences is the existence of a randomized stationary optimal policy for the original constrained DTMDP. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • Yi Zhang, 2013. "Convex analytic approach to constrained discounted Markov decision processes with non-constant discount factors," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 378-408, July.
    • Handle: RePEc:spr:topjnl:v:21:y:2013:i:2:p:378-408
    DOI: 10.1007/s11750-011-0186-8
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    References listed on IDEAS

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    1. Xianping Guo & Alexei Piunovskiy, 2011. "Discounted Continuous-Time Markov Decision Processes with Constraints: Unbounded Transition and Loss Rates," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 105-132, February.
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