Finite-Memory Strategies in POMDPs with Long-Run Average Objectives

Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that POMDPs long-run average objective, the maker has approximately optimal strategies finite memory. This implies notably approximating value is recursively enumerable, as well a weak continuity property of respect to transition function.