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Article Dans Une Revue Operations Research Letters Année : 2022

Joint Chance-Constrained Markov Decision Processes

Abdel Lisser
Vikas Vikram Singh
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V Varagapriya
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Résumé

We consider a finite state-action uncertain constrained Markov decision process under discounted and average cost criteria. The running costs are defined by random variables and the transition probabilities are known. The uncertainties present in the objective function and the constraints are modelled using chance constraints. The dependence among the random constraint vectors is driven by a Gumbel-Hougaard copula. We propose two second order cone programming problems whose optimal values give upper and lower bounds of the optimal value of the uncertain constrained Markov decision process. As an application, we study a stochastic version of a service and admission control problem in a queueing system and illustrate the proposed approximation methods on randomly generated instances of different sizes.
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Dates et versions

hal-04375403 , version 1 (05-01-2024)

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Abdel Lisser, Vikas Vikram Singh, V Varagapriya. Joint Chance-Constrained Markov Decision Processes. Operations Research Letters, 2022, 50 (2), pp.218-223. ⟨10.1016/j.orl.2022.02.001⟩. ⟨hal-04375403⟩
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