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Conditions for the uniqueness of optimal policies of discounted Markov decision processes. (English) Zbl 1104.90053
Summary: This paper presents three conditions. Each of them guarantees the uniqueness of optimal policies of discounted Markov decision processes. The conditions presented here impose hypotheses specifically on the state space $$X$$, the action space $$A$$, the admissible action sets $$A(x)$$, $$x \in X$$, the transition probability $$Q$$, and on the cost function $$c$$. Two of these conditions require mainly convexity assumptions, but the third one does not need this kind of assumptions. However, it needs certain stochastic order relations in $$Q$$, and the cost function $$c$$ to reach its minimum with respect to the actions, just in one action. We illustrate the conditions with several examples including, in particular, discrete models, the linear regulator problem, and also a model of an inventory control system.

##### MSC:
 90C40 Markov and semi-Markov decision processes 93E20 Optimal stochastic control
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