Uniform value in Dynamic Programming
Renault, Jérôme (2011), Uniform value in Dynamic Programming, Journal of the European Mathematical Society, 13, 2, p. 309-330. http://dx.doi.org/10.4171/JEMS/254
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/0803.2758v2
Journal nameJournal of the European Mathematical Society
European Mathematical Society
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Abstract (EN)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.
Subjects / KeywordsUniform value; dynamic programming; Markov decision processes; limit value; Blackwell optimality; average payoffs; long-run values; precompact state space; non expansive correspondence
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