Discounted Approximations for Risk-Sensitive Average Criteria in Markov Decision Chains with Finite State Space

Authors:
Rolando Cavazos-Cadena;Daniel Hernández-Hernández
Affiliations:
Departamento de Estadística y Cálculo 25315, Universidad Autónoma Agraria Antonio Narro, Buenavista, 25315 Saltillo, COAH México;Centro de Investigación en Matemáticas, 36000 Guanajuato, GTO México
Venue:
Mathematics of Operations Research
Year:
2011

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Abstract

This work concerns Markov decision processes with finite state space and compact action set. The performance of a control policy is measured by a risk-sensitive average cost criterion and, under standard continuity-compactness conditions, it is shown that the discounted approximations converge to the optimal value function, and that the superior and inferior limit average criteria have the same optimal value function. These conclusions are obtained for every nonnull risk-sensitivity coefficient, and regardless of the communication structure induced by the transition law.