A note on the convergence rate of the value iteration scheme in controlled Markov chains

摘要

This work is concerned with controlled Markov chains with bounded costs. Assuming that the transition probabilities satisfy a simultaneous Doeblin condition, it is shown that Schweitzer's transformation on the transition law yields a strong ergodicity condition that implies that the solution to the average cost optimality equation can be approximated, at a geometric rate, via the value iteration scheme. (C) 1998 Elsevier Science B.V. All rights reserved. [References: 16]