A Decentralized Approach to Bayesian Learning

TL;DR

This paper introduces a decentralized Bayesian learning algorithm using Langevin dynamics, demonstrating exponential convergence of divergence and improved convergence rates with multiple agents, applicable to various machine learning tasks.

Contribution

It proposes a novel decentralized Langevin dynamics algorithm for Bayesian learning in non-convex settings, with theoretical convergence guarantees and empirical validation.

Findings

Exponential decrease in KL-divergence from initial state.

Polynomial-time decrease in error contributions from noise.

Performance comparable to centralized methods with faster convergence.

Abstract

Motivated by decentralized approaches to machine learning, we propose a collaborative Bayesian learning algorithm taking the form of decentralized Langevin dynamics in a non-convex setting. Our analysis show that the initial KL-divergence between the Markov Chain and the target posterior distribution is exponentially decreasing while the error contributions to the overall KL-divergence from the additive noise is decreasing in polynomial time. We further show that the polynomial-term experiences speed-up with number of agents and provide sufficient conditions on the time-varying step-sizes to guarantee convergence to the desired distribution. The performance of the proposed algorithm is evaluated on a wide variety of machine learning tasks. The empirical results show that the performance of individual agents with locally available data is on par with the centralized setting with considerable improvement in the convergence rate.