Fixed Point Theory Analysis of a Lambda Policy Iteration with Randomization for the \'Ciri\'c Contraction Operator

Abstract

We apply methods of the fixed point theory to a Lambda policy iteration with a randomization algorithm for weak contractions mappings. This type of mappings covers a broader range than the strong contractions typically considered in the literature, such as \'Ciri\'c contraction. Specifically, we explore the characteristics of reinforcement learning procedures developed for feedback control within the context of fixed point theory. Under relatively general assumptions, we identify the sufficient conditions for convergence with a probability of one in infinite-dimensional policy spaces.