Finite Sample Analysis of Two-Timescale Stochastic Approximation with Applications to Reinforcement Learning

Two-timescale Stochastic Approximation (SA) algorithms are widely used in Reinforcement Learning (RL). Their iterates have two parts that are updated with distinct stepsizes. In this work we provide a recipe for analyzing two-timescale SA. Using it, we develop the first convergence rate result for them. From this result we extract key insights on stepsize selection. As an application, we obtain convergence rates for two-timescale RL algorithms such as GTD(0), GTD2, and TDC.