Convergence Rate of Discrete-Time Stochastic Approximation Type Consensus Algorithms∗

In this paper, we study the convergence rate of the distributed stochastic approximation (SA) type algorithm for the discrete-time multi-agent consensus with communication noises. Basic results of algebraic graph theory and probability limit theory are used to study the closed-form solution of the consensus error. Under mild conditions on the decreasing step size and the network topology, we give upper bounds for the mean square and almost sure convergence rates of the consensus errors. Furthermore, for the case with balanced graphs, the exact convergence rate is provided for the mean square of the consensus error.