Kybernetika 52 no. 1, 66-75, 2016

Uniqueness of optimal policies as a generic property of discounted Markov decision processes: Ekeland's variational principle approach

This article was granted Editor's award of the year 2016Editor's award 2016

R. Israel Ortega-Gutiérrez, Raúl Montes-de-Oca and Enrique Lemus-RodríguezDOI: 10.14736/kyb-2016-1-0066


Many examples in optimization, ranging from Linear Programming to Markov Decision Processes (MDPs), present more than one optimal solution. The study of this non-uniqueness is of great mathematical interest. In this paper the authors show that in a specific family of discounted MDPs, non-uniqueness is a "fragile'' property through Ekeland's Principle for each problem with at least two optimal policies; a perturbed model is produced with a unique optimal policy. This result not only supersedes previous papers on the subject, but it also renews the interest in the corresponding questions of well-posedness, genericity and structural stability of MDPs.


discounted Markov decision processes, dynamic programming, unique optimal policy, non-uniqueness of optimal policies, Ekeland's variational principle


90C40, 93E20


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