Concentration Bounds for Two Timescale Stochastic Approximation with Applications to Reinforcement Learning

Two-timescale Stochastic Approximation (SA) algorithms are widely used in Reinforcement Learning (RL). In such methods, the iterates consist of two parts that are updated using different stepsizes. We develop the first convergence rate result for these algorithms; in particular, we provide a general methodology for analyzing two-timescale linear SA. We apply our methodology to two-timescale RL algorithms such as GTD(0), GTD2, and TDC.