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On the Expected Total Reward with Unbounded Returns for Markov Decision Processes

Abstract : We consider a discrete-time Markov decision process with Borel state and action spaces. The performance criterion is to maximize a total expected utility determined by unbounded return function. It is shown the existence of optimal strategies under general conditions allowing the reward function to be unbounded both from above and below and the action sets available at each step to the decision maker to be not necessarily compact. To deal with unbounded reward functions, a new characterization for the weak convergence of probability measures is derived. Our results are illustrated by examples.
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https://hal.inria.fr/hal-01953985
Contributor : François Dufour <>
Submitted on : Thursday, December 13, 2018 - 1:35:12 PM
Last modification on : Wednesday, December 2, 2020 - 1:41:52 PM

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François Dufour, Alexandre Genadot. On the Expected Total Reward with Unbounded Returns for Markov Decision Processes. Applied Mathematics and Optimization, Springer Verlag (Germany), 2020, 82 (2), pp.433-450. ⟨10.1007/s00245-018-9533-6⟩. ⟨hal-01953985⟩

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