The Discounted Method and Equivalence of Average Criteria for Risk-Sensitive Markov Decision Processes on Borel Spaces |
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Authors: | Rolando Cavazos-Cadena Francisco Salem-Silva |
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Institution: | 1. Departamento de Estadística y Cálculo, Universidad Autónoma Agraria Antonio Narro, Buenavista, Saltillo, COAH 25315, Mexico 2. Facultad de Matemáticas, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán s/n, Zona Universitaria, Xalapa, VER 91000, Mexico
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Abstract: | This note concerns discrete-time controlled Markov chains with Borel state and action spaces. Given a nonnegative cost function,
the performance of a control policy is measured by the superior limit risk-sensitive average criterion associated with a constant
and positive risk sensitivity coefficient. Within such a framework, the discounted approach is used (a) to establish the existence
of solutions for the corresponding optimality inequality, and (b) to show that, under mild conditions on the cost function,
the optimal value functions corresponding to the superior and inferior limit average criteria coincide on a certain subset
of the state space. The approach of the paper relies on standard dynamic programming ideas and on a simple analytical derivation
of a Tauberian relation. |
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Keywords: | |
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