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TD-learning is a fundamental algorithm in the field of reinforcement learning(RL), that is employed to evaluate a given policy by estimating thecorresponding value function for a Markov decision process. While significantprogress has been made in the theoretical analysis of TD-learning, recentresearch has uncovered guarantees concerning its statistical efficiency bydeveloping finite-time error bounds. This paper aims to contribute to theexisting body of knowledge by presenting a novel finite-time analysis oftabular temporal difference (TD) learning, which makes direct and effective useof discrete-time stochastic linear system models and leverages Schur matrixproperties. The proposed analysis can cover both on-policy and off-policysettings in a unified manner. By adopting this approach, we hope to offer newand straightforward templates that not only shed further light on the analysisof TD-learning and related RL algorithms but also provide valuable insights forfuture research in this domain.

Finite-Time Analysis of Temporal Difference Learning: Discrete-Time Linear System Perspective