Stationary policies in dynamic programming models under compactness assumptions. (English) Zbl 0533.90093

Schäl, Manfred

Math. Oper. Res. 8, 366-372 (1983).

Summary: The present work deals with the usual stationary decision model of dynamic programming. The imposed convergence condition on the expected total rewards is so general that both the negative (unbounded) case and the positive (unbounded) case are included. However, the gambling model studied by Dubins and Savage is not covered by the present model. In addition to the convergence condition, a continuity and compactness condition is imposed. The main result states that the supremum of the expected total rewards under all stationary policies is equal to the supremum under all (possibly randomized and non-Markovian) policies.

MSC:

90C39	Dynamic programming
90C40	Markov and semi-Markov decision processes

Keywords:

stationary decision model; convergence condition; expected total rewards