New TD(0) Algorithm Achieves Robust and Fast Rates with Single Stepsize.

This paper presents an advancement in reinforcement learning, specifically for the linear TD(0) algorithm, which is a fundamental method for value function estimation. The key innovation is the use of a single, carefully chosen stepsize schedule in conjunction with Polyak-Ruppert averaging. This approach eliminates the need for complex projections or prior knowledge of curvature parameters, which are often required to ensure stability and convergence in traditional TD(0) implementations. The researchers demonstrate that this single stepsize not only guarantees that the algorithm's iterates remain bounded with high probability but also achieves a dual convergence benefit. It simultaneously provides a robust convergence rate that is independent of the curvature and a faster rate that leverages curvature information, effectively taking the best of both worlds. This is achieved through a novel technical framework involving Poisson-equation toolkits for Markov chains, which helps decompose noise and establish pathwise stability.