A Finite Time Analysis of Temporal Difference Learning With Linear Function Approximation
This work addresses a fundamental theoretical gap in reinforcement learning for researchers and practitioners, though it is incremental as it builds on existing stochastic gradient descent techniques.
The paper tackles the challenge of providing theoretical guarantees for temporal difference (TD) learning by offering a simple and explicit finite-time analysis with linear function approximation, extending results to TD(λ) and Q-learning in high-dimensional optimal stopping problems.
Temporal difference learning (TD) is a simple iterative algorithm used to estimate the value function corresponding to a given policy in a Markov decision process. Although TD is one of the most widely used algorithms in reinforcement learning, its theoretical analysis has proved challenging and few guarantees on its statistical efficiency are available. In this work, we provide a simple and explicit finite time analysis of temporal difference learning with linear function approximation. Except for a few key insights, our analysis mirrors standard techniques for analyzing stochastic gradient descent algorithms, and therefore inherits the simplicity and elegance of that literature. Final sections of the paper show how all of our main results extend to the study of TD learning with eligibility traces, known as TD($λ$), and to Q-learning applied in high-dimensional optimal stopping problems.