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The expected total cost criterion for Markov decision processes under constraints

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierQuality control and dynamic reliability [CQFD]
dc.contributor.authorDUFOUR, François
hal.structure.identifierDepartment of Mathematical Sciences [Liverpool]
dc.contributor.authorPIUNOVSKIY, Alexei
dc.date.accessioned2024-04-04T02:20:27Z
dc.date.available2024-04-04T02:20:27Z
dc.date.issued2013
dc.identifier.issn0001-8678
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189493
dc.description.abstractEnIn this work, we study discrete-time Markov decision processes (MDPs) with constraints when all the objectives have the same form of expected total cost over the infinite time horizon. Our objective is to analyze this problem by using the linear programming approach. Under some technical hypotheses, it is shown that if there exists an optimal solution for the associated linear program then there exists a randomized stationary policy which is optimal for the MDP, and that the optimal value of the linear program coincides with the optimal value of the constrained control problem. A second important result states that the set of randomized stationary policies provides a sufficient set for solving this MDP. It is important to note that, in contrast with the classical results of the literature, we do not assume the MDP to be transient or absorbing. More importantly, we do not impose the cost functions to be nonnegative or to be bounded below. Several examples are presented to illustrate our results.
dc.language.isoen
dc.publisherApplied Probability Trust
dc.title.enThe expected total cost criterion for Markov decision processes under constraints
dc.typeArticle de revue
dc.identifier.doi10.1017/S0001867800006601
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
bordeaux.journalAdvances in Applied Probability
bordeaux.page837-859
bordeaux.volume45
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-00925859
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00925859v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Advances%20in%20Applied%20Probability&rft.date=2013&rft.volume=45&rft.issue=3&rft.spage=837-859&rft.epage=837-859&rft.eissn=0001-8678&rft.issn=0001-8678&rft.au=DUFOUR,%20Fran%C3%A7ois&PIUNOVSKIY,%20Alexei&rft.genre=article


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