Risk-sensitive average continuous-time Markov decision processes with unbounded rates. (3rd April 2019)

• Record Type: Journal Article
• Authors: Wei, Qingda; Chen, Xian
• Is Part Of: Optimization. Volume 68:Number 4(2019)
• Page Start: 773
• Page End: 800
• Publication Date: 2019-04-03
• Subjects: Continuous-time Markov decision processes -- risk-sensitive average cost criterion -- risk-sensitive average optimality inequality -- unbounded cost and transition rates -- optimal policy; 93E20 -- 90C40; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1547382
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this paper we study the risk-sensitive average cost criterion for continuous-time Markov decision processes in the class of all randomized Markov policies. The state space is a denumerable set, and the cost and transition rates are allowed to be unbounded. Under the suitable conditions, we establish the optimality equation of the auxiliary risk-sensitive first passage optimization problem and obtain the properties of the corresponding optimal value function. Then by a technique of constructing the appropriate approximating sequences of the cost and transition rates and employing the results on the auxiliary optimization problem, we show the existence of a solution to the risk-sensitive average optimality inequality and develop a new approach called the risk-sensitive average optimality inequality approach to prove the existence of an optimal deterministic stationary policy. Furthermore, we give some sufficient conditions for the verification of the simultaneous Doeblin condition, use a controlled birth and death system to illustrate our conditions and provide an example for which the risk-sensitive average optimality strict inequality occurs.