Average cost optimal stationary policies in infinite state Markov decision processes with unbounded costs. (English) Zbl 0675.90091

Sennott, Linn I.

Oper. Res. 37, No. 4, 626-633 (1989).

Summary: We deal with infinite state Markov decision processes with unbounded costs. Three simple conditions, based on the optimal discounted value function, guarantee the existence of an expected cost optimal stationary policy. Sufficient conditions are the existence of a distinguished state of smallest discounted value and a single stationary policy inducing an irreducible, ergodic Markov chain for which the average cost of a first passage from any state to the distinguished state is finite. A result to verify this is also given. Two examples illustrate the ease of applying the criteria.

MSC:

90C40

Markov and semi-Markov decision processes

Keywords:

infinite state Markov decision processes; unbounded costs; optimal discounted value function; existence of an expected cost optimal stationary policy