Alexander Westberg: Bang-Bang control in Reinforcement Learningand System Identification

Abstract.

From numerical results it is observed that a Bang-Bang controller has competitive performance against a continuous controller on different tasks in Re- inforcement learning problems. The performance of a Bang-Bang controller in Reinforcement learning problems is yet not fully understood yet, and is thus and open research question. In this paper we explore this open question and provide an partial explanation with mathematical proof why this phenomena exist. We start by understanding the foundations of control theory and the Bang-bang controller. With an existing mathematical foundation of System Identification we derive errors for approximating dynamical systems. Using the error terms, we prove that the Bang-Bang controller yields a better approximation then a continuous controller in Reinforcement learning problems