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The expected total cost criterion for Markov decision processes under constraints: a convex analytic approach

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierQuality control and dynamic reliability [CQFD]
dc.contributor.authorDUFOUR, François
hal.structure.identifierDepartment of Mathematics
dc.contributor.authorHORIGUCHI, Masayuki
hal.structure.identifierDepartment of Mathematical Sciences [Liverpool]
dc.contributor.authorPIUNOVSKIY, Alexei
dc.date.accessioned2024-04-04T02:23:53Z
dc.date.available2024-04-04T02:23:53Z
dc.date.issued2012
dc.identifier.issn0001-8678
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189777
dc.description.abstractEnThis paper deals with discrete-time Markov Decision Processes (MDP's) under constraints where all the objectives have the same form of an expected total cost over the infinite time horizon. The existence of an optimal control policy is discussed by using the convex analytic approach. We work under the assumptions that the state and action spaces are general Borel spaces and the model is non-negative, semi-continuous and there exists an admissible solution with finite cost for the associated linear program. It is worth noting that, in contrast with the classical results of the literature, our hypotheses do not require the MDP to be transient or absorbing. Our first result ensures the existence of an optimal solution to the linear program given by an occupation measure of the process generated by a randomized stationary policy. Moreover, it is shown that this randomized stationary policy provides an optimal solution to this Markov control problem. As a consequence, these results imply that the set of randomized stationary policies is a sufficient set for this optimal control problem. Finally, our last main result states that all optimal solutions of the linear program coincide on a special set with an optimal occupation measure generated by a randomized stationary policy. Several examples are presented to illustrate some theoretical issues and the possible applications of the results developed in the paper.
dc.language.isoen
dc.publisherApplied Probability Trust
dc.title.enThe expected total cost criterion for Markov decision processes under constraints: a convex analytic approach
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
bordeaux.journalAdvances in Applied Probability
bordeaux.page774-793
bordeaux.volume44
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00759717
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00759717v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Advances%20in%20Applied%20Probability&rft.date=2012&rft.volume=44&rft.issue=3&rft.spage=774-793&rft.epage=774-793&rft.eissn=0001-8678&rft.issn=0001-8678&rft.au=DUFOUR,%20Fran%C3%A7ois&HORIGUCHI,%20Masayuki&PIUNOVSKIY,%20Alexei&rft.genre=article


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