Zur konstruktfon ∊-optimaler polltiken in markovschen entscheidungsmodellen mit überabzämbarem zustandsraum

Abstract

In this note we consider time-discrete N-stages, Markovian decision models with arbitrary state space, especially a standard BOREL space. It is shown, how the minimal value function can be approximated by a construction of a sequence of programming problems with finite state spaces, by means of discretization.

For this an approximation procedures, developed by Hahnewald-Busch and Nollau, is modified and extended. Theorems about the accuracy of the approximation and convergence are proved and a procedure for construction of ∊ ɛ-optimal policies is given.

Keywords:

• Markovian decision models
• discretization
• ∊-optimal policies

AMS 1980 Subject Classification:

• Primary:90 C 39
• Secondary:90 C 48