RISK-SENSITIVE AVERAGE OPTIMALITY FOR DISCRETE-TIME MARKOV DECISION PROCESSES

In this paper we study the risk-sensitive average optimality for discrete-time Markov decision processes with denumerable states and unbounded costs. We derive the multiplicative Poisson equation under the suitable ergodicity conditions via an approximation method. Moreover, we prove the existence of a unique solution to the risk-sensitive average cost optimality equation and give an equivalent characterization of the set of all optimal stationary policies. Finally, we present the policy iteration algorithm and show its convergence.

Automated summary

In this paper, we investigate the risk-sensitive average optimality in discrete-time Markov decision processes with denumerable states and unbounded costs. By utilizing an approximation method, we derive the multiplicative Poisson equation under suitable ergodicity conditions. Furthermore, we establish the existence of a unique solution to the risk-sensitive average cost optimality equation and provide an equivalent characterization of the set of all optimal stationary policies. Finally, we introduce the policy iteration algorithm and demonstrate its convergence.