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Journal of Applied Mathematics
Volume 2013, Article ID 271279, 5 pages
Research Article

Nonuniqueness versus Uniqueness of Optimal Policies in Convex Discounted Markov Decision Processes

1Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, Avenida San Rafael Atlixco 186, Col. Vicentina, 09340 México, DF, Mexico
2Universidad Anáhuac México-Norte, Avenida Universidad Anáhuac 46, Lomas Anáhuac, 52786 Huixquilucan, MEX, Mexico
3Facultad de Matemáticas, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán s/n, Zona Universitaria, 91000 Xalapa, VER, Mexico

Received 16 October 2012; Accepted 12 February 2013

Academic Editor: Debasish Roy

Copyright © 2013 Raúl Montes-de-Oca et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


From the classical point of view, it is important to determine if in a Markov decision process (MDP), besides their existence, the uniqueness of the optimal policies is guaranteed. It is well known that uniqueness does not always hold in optimization problems (for instance, in linear programming). On the other hand, in such problems it is possible for a slight perturbation of the functional cost to restore the uniqueness. In this paper, it is proved that the value functions of an MDP and its cost perturbed version stay close, under adequate conditions, which in some sense is a priority. We are interested in the stability of Markov decision processes with respect to the perturbations of the cost-as-you-go function.