Constrained Markov Decision Processes with Total Expected Cost Criteria

Eitan Altman; Said Boularouk; Didier Josselin

Constrained Markov Decision Processes with Total Expected Cost Criteria

Eitan Altman ^{1, 2, 3} Said Boularouk ^{2, 1} Didier Josselin ⁴

1 NEO - Network Engineering and Operations

CRISAM - Inria Sophia Antipolis - Méditerranée

2 LIA - Laboratoire Informatique d'Avignon

3 LINCS - Laboratory of Information, Network and Communication Sciences

4 ESPACE - Études des Structures, des Processus d’Adaptation et des Changements de l’Espace

Abstract : We study in this paper a multiobjective dynamic programm-ming where all the criteria are in the form of total expected sum of costs till absorption in some set of states M. We assume that instantaneous costs are strictly positive and make no assumption on the ergodic structure of the Markov Decision Process. Our main result is to extend the linear program solution approach that was previously derived for transient CMDPs (Constrained Markov Decision Processes) to general ergodic structure. Several (additive) cost met-rics are defined and (possibly randomized) routing policies are sought which minimize one of the costs subject to constraints over the other objectives.

Document type :

Conference papers

Domain :

Mathematics [math]

Mathematics [math] / Optimization and Control [math.OC]

Mathematics [math] / Probability [math.PR]

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https://hal.inria.fr/hal-02053360
Contributor : Eitan Altman <>
Submitted on : Friday, March 1, 2019 - 11:42:55 AM
Last modification on : Thursday, October 17, 2019 - 12:36:59 PM
Long-term archiving on : Thursday, May 30, 2019 - 1:59:42 PM

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