Contractive Approximations in Risk-Sensitive Average Semi-Markov Decision Chains on a Finite State Space

Abstract

This work concerns with semi-Markov decision chains evolving on a finite state space. The controller has a positive and constant risk sensitivity coefficient, and the performance of a control policy is measured by the risk-sensitive average cost criterion. Under conditions ensuring that the optimal value function is determined via a single optimality equation, the fixed points of a family of contractive operators are used to obtain convergent approximations to the optimal average cost and to a solution of optimality equation, extending the classical discounted approach to the context of the paper. In contrast with the Markovian case, the contractive operators utilized in this work depend on two parameters.