Computable approximations for average Markov decision processes in continuous time - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Applied Probability Année : 2018

Computable approximations for average Markov decision processes in continuous time

Résumé

In this paper we study the numerical approximation of the optimal long-run average cost of a continuous-time Markov decision process, with Borel state and action spaces, and with bounded transition and reward rates. Our approach uses a suitable discretization of the state and action spaces to approximate the original control model. The approximation error for the optimal average reward is then bounded by a linear combination of coefficients related to the discretization of the state and action spaces, namely, the Wasserstein distance between an underlying probability measure μ and a measure with finite support, and the Hausdorff distance between the original and the discretized actions sets. When approximating μ with its empirical probability measure we obtain convergence in probability at an exponential rate. An application to a queueing system is presented.
Fichier non déposé

Dates et versions

hal-01949945 , version 1 (10-12-2018)

Identifiants

Citer

Jonatha Anselmi, François Dufour, Tomás Prieto-Rumeau. Computable approximations for average Markov decision processes in continuous time. Journal of Applied Probability, 2018, 55 (02), pp.571-592. ⟨10.1017/jpr.2018.36⟩. ⟨hal-01949945⟩
34 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More