LP Based Upper and Lower Bounds for Ces\`aro and Abel Limits of the Optimal Values in Problems of Control of Stochastic Discrete Time Systems

Abstract

In this paper, we study asymptotic properties of problems of control of stochastic discrete time systems (also known as Markov decision processes) with time averaging and time discounting optimality criteria, and we establish that the Ces\`aro and Abel limits of the optimal values in such problems can be evaluated with the help of a certain infinite-dimensional linear programming problem and its dual.