Exponentially Fast Parameter Estimation in Networks Using Distributed Dual Averaging

TL;DR

This paper introduces a distributed dual averaging algorithm for networked agents to efficiently estimate parameters and learn the true state exponentially fast, even with local information and continuous network adaptation.

Contribution

It presents a novel optimization-based framework using distributed dual averaging for rapid parameter estimation and social learning in networks.

Findings

Agents learn the true parameter exponentially fast with high probability.

Convergence rate depends on the KL divergence between true and second likeliest states.

Learning is possible under continuous network adaptation with constant stepsize.

Abstract

In this paper we present an optimization-based view of distributed parameter estimation and observational social learning in networks. Agents receive a sequence of random, independent and identically distributed (i.i.d.) signals, each of which individually may not be informative about the underlying true state, but the signals together are globally informative enough to make the true state identifiable. Using an optimization-based characterization of Bayesian learning as proximal stochastic gradient descent (with Kullback-Leibler divergence from a prior as a proximal function), we show how to efficiently use a distributed, online variant of Nesterov's dual averaging method to solve the estimation with purely local information. When the true state is globally identifiable, and the network is connected, we prove that agents eventually learn the true parameter using a randomized gossip scheme. We demonstrate that with high probability the convergence is exponentially fast with a rate dependent on the KL divergence of observations under the true state from observations under the second likeliest state. Furthermore, our work also highlights the possibility of learning under continuous adaptation of network which is a consequence of employing constant, unit stepsize for the algorithm.