Approximation of average cost Markov decision processes using empirical distributions and concentration inequalities - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Stochastics: An International Journal of Probability and Stochastic Processes Année : 2015

Approximation of average cost Markov decision processes using empirical distributions and concentration inequalities

Résumé

We consider a discrete-time Markov decision process with Borel state and action spaces, and possibly unbounded cost function. We assume that the Markov transition kernel is absolutely continuous with respect to some probability measure . By replacing this probability measure with its empirical distribution for a sample of size n, we obtain a finite state space control problem, which is used to provide an approximation of the optimal value and an optimal policy of the original control model. We impose Lipschitz continuity properties on the control model and its associated density functions. We measure the accuracy of the approximation of the optimal value and an optimal policy by means of a non-asymptotic concentration inequality based on the 1-Wasserstein distance between and . Obtaining numerically the solution of the approximating control model is discussed and an application to an inventory management problem is presented.
Fichier non déposé

Dates et versions

hal-01246225 , version 1 (18-12-2015)

Identifiants

Citer

François Dufour, Tomás Prieto-Rumeau. Approximation of average cost Markov decision processes using empirical distributions and concentration inequalities. Stochastics: An International Journal of Probability and Stochastic Processes, 2015, 87 (2), pp.273 - 307. ⟨10.1080/17442508.2014.939979⟩. ⟨hal-01246225⟩
145 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More