Existence of optimal stationary policies in finite dynamic programs with nonnegative rewards: an alternative approach

摘要

This article concerns Markov decision chains with finite state and action spaces, and a control policy is graded via the expected total-reward criterion associated to a nonnegative reward function. Within this framework, a classical theorem guaran- tees the existence of an optimal stationary policy whenever the optimal value func- tion is finite, a result that is obtained via a limit process using the discounted criterion. The objective of this article is to present an alternative approach, based entirely on The properties of the expected total-reward index, to establish such an existence Result.