The value iteration method for countable state Markov decision processes
Coauthor(s): Yossi Aviv.
This paper deals with Markov decision processes with a countable state space. We demonstrate that a single, relatively simple condition suffices to guarantee that the value-iteration method converges and that an optimal policy can be computed via this method, once the existence of a solution to the average cost optimality equation has been established via any of the many available sets of existence conditions.
Source: Operations Research Letters
Aviv, Yossi, and Awi Federgruen. "The value iteration method for countable state Markov decision processes." Operations Research Letters 24, no. 5 (June 1999): 223-234.