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.

翻译：本文旨在对时序差分（TD）学习算法进行控制理论分析。TD学习在强化学习领域具有基石地位，为马尔可夫决策过程中特定策略的价值函数逼近提供了方法论。尽管已有若干工作为TD学习的理论理解做出贡献，但直到近年，研究者才得以建立其统计效率的具体保证。本文引入了一个基于有限时间、控制理论的分析框架，用于解析TD学习，该框架借鉴了线性系统控制领域的成熟概念。由此，本文借助源自控制理论的简洁分析工具，为理解TD学习的内在机制及强化学习的更广阔图景提供了新见解。