Distributed Gaussian Learning over Time-varying Directed Graphs

TL;DR

This paper introduces a distributed Gaussian learning algorithm for parameter estimation in networks with Gaussian noise, demonstrating convergence rates and robustness to time-varying directed graphs.

Contribution

It proposes a novel explicit update method for Gaussian beliefs in distributed settings and proves convergence under dynamic network topologies.

Findings

Convergence rate of O(1/k) for the proposed algorithm.

Almost sure convergence to the optimal solution.

Effective performance on time-varying directed graphs.

Abstract

We present a distributed (non-Bayesian) learning algorithm for the problem of parameter estimation with Gaussian noise. The algorithm is expressed as explicit updates on the parameters of the Gaussian beliefs (i.e. means and precision). We show a convergence rate of $O(1/k)$ with the constant term depending on the number of agents and the topology of the network. Moreover, we show almost sure convergence to the optimal solution of the estimation problem for the general case of time-varying directed graphs.