Contractive approximations in average Markov decision chains driven by a risk-seeking controller

This work concerns with Markov decision processes on a denumerable state space. It is assumed that the performance of a control policy is measured by the average criterion associated with a risk-seeking controller with constant risk-sensitivity coefficient. The structural assumptions on the model en...

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Bibliographic Details
Published inMathematical methods of operations research (Heidelberg, Germany) Vol. 98; no. 1; pp. 75 - 91
Main Authors Portillo-Ramírez, Gustavo, Cavazos-Cadena, Rolando, Cruz-Suárez, Hugo
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2023
Springer Nature B.V
Subjects
Approximation
Business and Management
Calculus of Variations and Optimal Control; Optimization
Controllers
Equality
Markov chains
Mathematics
Mathematics and Statistics
Operations research
Operations Research/Decision Theory
Original Article
Random variables
93E20
93C55
Hölder’s inequality
Contractive operator
Risk-lover decision maker
60J05
Exponential utility
Fixed point
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Summary:This work concerns with Markov decision processes on a denumerable state space. It is assumed that the performance of a control policy is measured by the average criterion associated with a risk-seeking controller with constant risk-sensitivity coefficient. The structural assumptions on the model ensure that the optimal average cost is constant, but it is possible that the optimalty equation does not admit a solution. In this context, a risk-sensitive version of the classical discounted approach is used to obtain convergent approximations to the optimal average cost, and to determine nearly optimal stationary policies.
ISSN:1432-2994
1432-5217
DOI:10.1007/s00186-023-00825-0