Abstract.
In this paper, Discounted Markov Decision Processes with finite state and countable action set (semi-infinite DMDP for short) are considered. A policy improvement finite algorithm which finds a nearly optimal deterministic strategy is presented. The steps of the algorithm are based on the classical policy improvement algorithm for finite DMDPs. Singularly perturbed semi-infinite DMDPs are investigated. In case of perturbations, some sufficient condition is given to guarantee that there exists a nearly optimal deterministic strategy which can approximate nearly optimal strategies for a whole family of singularly perturbed semi-infinite DMDP.
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Manuscript received: December 2000/Final version received: March 2001
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Abbad, M., Rahhali, K. Semi-infinite discounted Markov decision processes: Policy improvement and singular perturbations. Mathematical Methods of OR 54, 279–290 (2001). https://doi.org/10.1007/s001860100143
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DOI: https://doi.org/10.1007/s001860100143