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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.
Renault, Jérôme. "Uniform value in dynamic programming." Journal of the European Mathematical Society 013.2 (2011): 309-330. <http://eudml.org/doc/277283>.
@article{Renault2011, abstract = {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.}, author = {Renault, Jérôme}, journal = {Journal of the European Mathematical Society}, keywords = {uniform value; dynamic programming; Markov decision processes; limit value; Blackwell optimality; average payoffs; long-run values; precompact state space; non expansive correspondence}, language = {eng}, number = {2}, pages = {309-330}, publisher = {European Mathematical Society Publishing House}, title = {Uniform value in dynamic programming}, url = {http://eudml.org/doc/277283}, volume = {013}, year = {2011}, }
TY - JOUR AU - Renault, Jérôme TI - Uniform value in dynamic programming JO - Journal of the European Mathematical Society PY - 2011 PB - European Mathematical Society Publishing House VL - 013 IS - 2 SP - 309 EP - 330 AB - 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. LA - eng KW - uniform value; dynamic programming; Markov decision processes; limit value; Blackwell optimality; average payoffs; long-run values; precompact state space; non expansive correspondence UR - http://eudml.org/doc/277283 ER -
