Distributed Learning for Cooperative Inference

TL;DR

This paper introduces a new distributed learning algorithm for cooperative inference in networks, leveraging variational Bayesian methods and stochastic mirror descent, with proven exponential convergence under certain conditions.

Contribution

It proposes a novel distributed inference algorithm based on variational Bayesian interpretation and stochastic mirror descent, with explicit convergence bounds and efficient algorithms for exponential family models.

Findings

Beliefs concentrate around the true parameter exponentially fast.

Explicit non-asymptotic convergence bounds are provided.

Algorithms are computationally efficient for exponential family models.

Abstract

We study the problem of cooperative inference where a group of agents interact over a network and seek to estimate a joint parameter that best explains a set of observations. Agents do not know the network topology or the observations of other agents. We explore a variational interpretation of the Bayesian posterior density, and its relation to the stochastic mirror descent algorithm, to propose a new distributed learning algorithm. We show that, under appropriate assumptions, the beliefs generated by the proposed algorithm concentrate around the true parameter exponentially fast. We provide explicit non-asymptotic bounds for the convergence rate. Moreover, we develop explicit and computationally efficient algorithms for observation models belonging to exponential families.