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Two-time-scale stochastic approximation is a popular iterative method forfinding the solution of a system of two equations. Such methods have foundbroad applications in many areas, especially in machine learning andreinforcement learning. In this paper, we propose a distributed variant of thismethod over a network of agents, where the agents use two graphs representingtheir communication at different speeds due to the nature of theirtwo-time-scale updates. Our main contribution is to provide a finite-timeanalysis for the performance of the proposed method. In particular, weestablish an upper bound for the convergence rates of the mean square errors atthe agents to zero as a function of the step sizes and the network topology.

Finite-Time Performance of Distributed Two-Time-Scale Stochastic Approximation