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hal.structure.identifierInstitut Polytechnique de Bordeaux [Bordeaux INP]
hal.structure.identifierQuality control and dynamic reliability [CQFD]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorDUFOUR, François
hal.structure.identifierUniversidad Estatal a Distancia [UNED]
dc.contributor.authorPRIETO-RUMEAU, Tomás
dc.date.accessioned2024-04-04T03:03:19Z
dc.date.available2024-04-04T03:03:19Z
dc.date.issued2019
dc.identifier.issn2153-0785
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193060
dc.description.abstractEnThis paper is concerned with a minimax control problem (also known as a robust Markov decision process (MDP) or a game against nature) with general state and action spaces under the discounted cost optimality criterion. We are interested in approximating numerically the value function and an optimal strategy of this general discounted minimax control problem. To this end, we derive structural Lipschitz continuity properties of the solution of this robust MDP by imposing suitable conditions on the model, including Lipschitz continuity of the elements of the model and absolute continuity of the Markov transition kernel with respect to some probability measure μ. Then, we are able to provide an approximating minimax control model with finite state and action spaces, and hence computationally tractable, by combining these structural properties with a suitable discretization procedure of the state space (related to a probabilistic criterion) and the action spaces (associated to a geometric criterion). Finally, it is shown that the corresponding approximation errors for the value function and the optimal strategy can be controlled in terms of the discretization parameters. These results are also extended to a two-player zero-sum Markov game
dc.language.isoen
dc.publisherSpringer Verlag
dc.subject.enRobust Markov decision process
dc.subject.enApproximation of control models
dc.subject.enWasserstein distance
dc.subject.enMinimax control problem
dc.title.enApproximation of Discounted Minimax Markov Control Problems and Zero-Sum Markov Games Using Hausdorff and Wasserstein Distances
dc.typeArticle de revue
dc.identifier.doi10.1007/s13235-018-0253-y
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
bordeaux.journalDynamic Games and Applications
bordeaux.page68-102
bordeaux.volume9
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01953983
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01953983v1
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