Fixed Points of the Set-Based Bellman Operator (2001.04535v2)

Abstract: Motivated by uncertain parameters encountered in Markov decision processes (MDPs), we study the effect of parameter uncertainty on BeLLMan operator-based methods. Specifically, we consider a family of MDPs where the cost parameters are from a given compact set. We then define a BeLLMan operator acting on an input set of value functions to produce a new set of value functions as the output under all possible variations in the cost parameters. Finally we prove the existence of a fixed point of this set-based BeLLMan operator by showing that it is a contractive operator on a complete metric space.