A note on the vanishing interest rate approach in average Markov decision chains with continuous and bounded costs

Abstract

This work considers denumerable state Markov decision processes with discrete time parameter. The performance of a control policy is measured by the (lim sup) expected average cost criterion, the action sets are compact metric and the cost function is continuous and bounded. Within this framework, necessary and sufficient conditions are given so that the vanishing interest rate (VIR) method — also known as the vanishing discount effect approach — yields an average optimal stationary policy.