Continuous-time Markov decision processes under the risk-sensitive average cost criterion

2015/12/21 by Qingda Wei, Xian Chen, Wei, Qingda +1
Computer Science · Decision Sciences · Engineering · Mathematics · #90C40 #93E20 #Action (physics) #Advanced Control Systems Optimization #Applied mathematics #Average cost #Bounded function #Computer science #Economics #FOS: Mathematics #Markov chain #Markov decision process #Markov model #Markov process #Mathematical analysis #Mathematical optimization #Mathematics #Optimization and Control (math.OC) #Reinforcement Learning in Robotics #Risk and Portfolio Optimization #Sensitivity (control systems) #Set (abstract data type) #Space (punctuation) #State space #Statistics #math.OC #msc:90C40 #msc:93E20

paper · pdf · doi:10.48550/arxiv.1512.06641

published in arXiv (Cornell University) (Cornell University) · 14 pages

arxiv created 2015/12/21 · openalex publication_date 2015/12/21 · arxiv updated 2015/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

This paper studies continuous-time Markov decision processes under the risk-sensitive average cost criterion. The state space is a finite set, the action space is a Borel space, the cost and transition rates are bounded, and the risk-sensitivity coefficient can take arbitrary positive real numbers. Under the mild conditions, we develop a new approach to establish the existence of a solution to the risk-sensitive average cost optimality equation and obtain the existence of an optimal deterministic stationary policy.

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