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Computable approximations for continuous-time Markov decision processes on Borel spaces based on empirical measures

hal.structure.identifierQuality control and dynamic reliability [CQFD]
dc.contributor.authorANSELMI, Jonatha
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.accessioned2024-04-04T03:12:23Z
dc.date.available2024-04-04T03:12:23Z
dc.date.issued2016
dc.identifier.issn0022-247X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193866
dc.description.abstractEnIn this paper, we propose an approach for approximating the value function and an ϵ-optimal policy of continuous-time Markov decision processes with Borel state and action spaces, with possibly unbounded cost and transition rates, under the total expected discounted cost optimality criterion. Under adequate assumptions, which in particular include that the transition rate has a density function with respect to a reference measure, together with piecewise Lipschitz continuity of the elements of the control model, we approximate the original controlled process by a model with finite state and action spaces. The approximation error is related to the 1-Wasserstein distance between suitably defined probability measures and approximating measures with finite support. We also study the case when the reference measure is approximated with empirical distributions and we show that convergence of the approximations takes place at an exponential rate in probability.
dc.language.isoen
dc.publisherElsevier
dc.subject.enLinear programming approach to control problems
dc.subject.enApproximation of Markov decision processes
dc.subject.enConstrained Markov decision processes
dc.title.enComputable approximations for continuous-time Markov decision processes on Borel spaces based on empirical measures
dc.typeArticle de revue
dc.identifier.doi10.1016/j.jmaa.2016.05.055
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
bordeaux.journalJournal of Mathematical Analysis and Applications
bordeaux.page1323 - 1361
bordeaux.volume443
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01412615
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01412615v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Mathematical%20Analysis%20and%20Applications&rft.date=2016&rft.volume=443&rft.issue=2&rft.spage=1323%20-%201361&rft.epage=1323%20-%201361&rft.eissn=0022-247X&rft.issn=0022-247X&rft.au=ANSELMI,%20Jonatha&DUFOUR,%20Fran%C3%A7ois&PRIETO-RUMEAU,%20Tom%C3%A1s&rft.genre=article


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