Network Independent Rates in Distributed Learning

We propose a new belief update rule for Distributed Non-Bayesian learning in time-varying directed graphs, where a group of agents tries to collectively identify a hypothesis that best describes a sequence of observed data. We show that the proposed update rule, inspired by the Push-Sum algorithm, is consistent, moreover we provide an explicit characterization of its convergence rate. Our main result states that, after a transient time, all agents will concentrate their beliefs at a network independent rate. Network independent rates were not available for other consensus based distributed learning algorithms.