Uniform value in Dynamic Programming

Jérôme Renault (1, 2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 X-DEP-ECO - Département d'Économie de l'École Polytechnique

We consider dynamic programming problems with a large time horizon, and give sufficient conditions for the existence of the uniform value. As a consequence, we obtain an existence result when the state space is precompact, payoffs are uniformly continuous and the transition correspondence is non expansive. In the same spirit, we give an existence result for the limit value. We also apply our results to Markov decision processes and obtain a few generalizations of existing results.

Mots clés: Uniform value; Dynamic programming; Markov decision processes; limit value; Blackwell optimality; average payoffs; long-run values; precompact state space; non expansive correspondence.

Mots clés: non expansive correspondence

Domaines: Optimisation et contrôle [math.OC]

Jérôme Renault. Uniform value in Dynamic Programming. 2008. ⟨hal-00265257v2⟩