On TD(0) with function approximation: Concentration bounds and a centered variant with exponential convergence
This work addresses convergence guarantees for reinforcement learning algorithms, offering incremental improvements in analysis and algorithm design for researchers in the field.
The paper tackles the problem of analyzing the convergence of TD(0) with linear function approximation, providing non-asymptotic bounds and proposing a centered variant that achieves exponential convergence in expectation.
We provide non-asymptotic bounds for the well-known temporal difference learning algorithm TD(0) with linear function approximators. These include high-probability bounds as well as bounds in expectation. Our analysis suggests that a step-size inversely proportional to the number of iterations cannot guarantee optimal rate of convergence unless we assume (partial) knowledge of the stationary distribution for the Markov chain underlying the policy considered. We also provide bounds for the iterate averaged TD(0) variant, which gets rid of the step-size dependency while exhibiting the optimal rate of convergence. Furthermore, we propose a variant of TD(0) with linear approximators that incorporates a centering sequence, and establish that it exhibits an exponential rate of convergence in expectation. We demonstrate the usefulness of our bounds on two synthetic experimental settings.