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Article Dans Une Revue Applied Mathematics and Optimization Année : 2016

Conditions for the Solvability of the Linear Programming Formulation for Constrained Discounted Markov Decision Processes

Résumé

We consider a discrete-time constrained discounted Markov decision process (MDP) with Borel state and action spaces, compact action sets, and lower semi-continuous cost functions. We introduce a set of hypotheses related to a positive weight function which allow us to consider cost functions that might not be bounded below by a constant, and which imply the solvability of the linear programming formulation of the constrained MDP. In particular, we establish the existence of a constrained optimal stationary policy. Our results are illustrated with an application to a fishery management problem.
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Dates et versions

hal-01246228 , version 1 (18-12-2015)

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François Dufour, T. Prieto-Rumeau. Conditions for the Solvability of the Linear Programming Formulation for Constrained Discounted Markov Decision Processes. Applied Mathematics and Optimization, 2016, 74 (1), pp.27 - 51. ⟨10.1007/s00245-015-9307-3⟩. ⟨hal-01246228⟩
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