Fast Convergence Rates for Distributed Non-Bayesian Learning

TL;DR

This paper introduces a distributed learning algorithm with proven fast convergence rates for agents collectively identifying the best hypothesis from distributed data, improving scalability over static networks.

Contribution

It presents a new distributed learning algorithm with explicit convergence rates and enhanced scalability for static network topologies.

Findings

Proven geometric convergence rate for belief concentration.

Algorithm achieves consistency in distributed hypothesis testing.

Improved protocol for static networks with better scalability.

Abstract

We consider the problem of distributed learning, where a network of agents collectively aim to agree on a hypothesis that best explains a set of distributed observations of conditionally independent random processes. We propose a distributed algorithm and establish consistency, as well as a non-asymptotic, explicit and geometric convergence rate for the concentration of the beliefs around the set of optimal hypotheses. Additionally, if the agents interact over static networks, we provide an improved learning protocol with better scalability with respect to the number of nodes in the network.