Inaccuracy rates for distributed inference over random networks with applications to social learning

TL;DR

This paper derives probabilistic convergence rates for distributed algorithms over random networks, with applications to social learning, hypothesis testing, and estimation, providing the first large deviations analysis in this context.

Contribution

It introduces bounds on large deviations rate functions for consensus+innovations algorithms in random networks, establishing the first large deviations principle for these methods.

Findings

Derived bounds on large deviations rate functions for nodes

Established tightness of bounds in specific network cases

First proof of large deviations principle for social learning in random networks

Abstract

This paper studies probabilistic rates of convergence for consensus+innovations type of algorithms in random, generic networks. For each node, we find a lower and also a family of upper bounds on the large deviations rate function, thus enabling the computation of the exponential convergence rates for the events of interest on the iterates. Relevant applications include error exponents in distributed hypothesis testing, rates of convergence of beliefs in social learning, and inaccuracy rates in distributed estimation. The bounds on the rate function have a very particular form at each node: they are constructed as the convex envelope between the rate function of the hypothetical fusion center and the rate function corresponding to a certain topological mode of the node's presence. We further show tightness of the discovered bounds for several cases, such as pendant nodes and regular networks, thus establishing the first proof of the large deviations principle for consensus+innovations and social learning in random networks.