Geodesic
Uniform value in dynamic programming
Journal of the European Mathematical Society, Tome 13 (2011) no. 2, pp. 309-330.

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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.
DOI : 10.4171/jems/254
Classification : 60-XX, 68-XX, 00-XX
Keywords: Uniform 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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     author = {J\'er\^ome Renault},
     title = {Uniform value in dynamic programming},
     journal = {Journal of the European Mathematical Society},
     pages = {309--330},
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     year = {2011},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/254/}
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Jérôme Renault. Uniform value in dynamic programming. Journal of the European Mathematical Society, Tome 13 (2011) no. 2, pp. 309-330. doi : 10.4171/jems/254. http://geodesic.mathdoc.fr/articles/10.4171/jems/254/

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