Control Theoretic Analysis of Temporal Difference Learning

The goal of this manuscript is to conduct a controltheoretic analysis of Temporal Difference (TD) learning algorithms. TD-learning serves as a cornerstone in the realm of reinforcement learning, offering a methodology for approximating the value function associated with a given policy in a Markov Decision Process. Despite several existing works that have contributed to the theoretical understanding of TD-learning, it is only in recent years that researchers have been able to establish concrete guarantees on its statistical efficiency. In this paper, we introduce a finite-time, control-theoretic framework for analyzing TD-learning, leveraging established concepts from the field of linear systems control. Consequently, this paper provides additional insights into the mechanics of TD learning and the broader landscape of reinforcement learning, all while employing straightforward analytical tools derived from control theory.