A characterization of the optimal risk-sensitive average cost in finite controlled Markov chains

2005/02/01 by Rolando Cavazos-Cadena, Daniel Hernandez-Hernandez, Daniel Hernández-Hernández
Business, Management and Accounting · Computer Science · Engineering · Mathematics · #Advanced Queuing Theory Analysis #Reinforcement Learning in Robotics #Stability and Control of Uncertain Systems #math.PR #msc:60F10 #msc:93C55 #msc:93E20

paper · pdf · doi:10.1214/105051604000000585

published as Annals of Applied Probability 2005, Vol. 15, No. 1A, 175-212 · Published at http://dx.doi.org/10.1214/105051604000000585 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2005/02/01 · arxiv created 2005/03/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This work concerns controlled Markov chains with finite state and action spaces. The transition law satisfies the simultaneous Doeblin condition, and the performance of a control policy is measured by the (long-run) risk-sensitive average cost criterion associated to a positive, but otherwise arbitrary, risk sensitivity coefficient. Within this context, the optimal risk-sensitive average cost is characterized via a minimization problem in a finite-dimensional Euclidean space.

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