Risk-sensitive semi-Markov decision processes with general utilities and multiple criteria. (16th November 2018)

• Record Type: Journal Article
• Authors: Huang, Yonghui; Lian, Zhaotong; Guo, Xianping
• Is Part Of: Advances in applied probability. Volume 50:Number 3(2018)
• Page Start: 783
• Page End: 804
• Publication Date: 2018-11-16
• Subjects: Semi-Markov decision process, -- finite-horizon cost, -- occupation measure, -- expected utility, -- linear program; Primary 90C40, -- Secondary 93E20; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2018.36
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: In this paper we investigate risk-sensitive semi-Markov decision processes with a Borel state space, unbounded cost rates, and general utility functions. The performance criteria are several expected utilities of the total cost in a finite horizon. Our analysis is based on a type of finite-horizon occupation measure. We express the distribution of the finite-horizon cost in terms of the occupation measure for each policy, wherein the discount is not needed. For unconstrained and constrained problems, we establish the existence and computation of optimal policies. In particular, we develop a linear program and its dual program for the constrained problem and, moreover, establish the strong duality between the two programs. Finally, we provide two special cases of our results, one of which concerns the discrete-time model, and the other the chance-constrained problem.