Decentralized Bayesian Learning with Metropolis-Adjusted Hamiltonian Monte Carlo

TL;DR

This paper introduces a novel decentralized Bayesian sampling method using Metropolis-adjusted Hamiltonian Monte Carlo with constant stepsize, providing theoretical guarantees and demonstrating effectiveness on complex real-world problems.

Contribution

It is the first to incorporate constant stepsize Metropolis-adjusted HMC in decentralized sampling, with proven theoretical guarantees and practical validation.

Findings

Achieves consensus and accurate posterior sampling in decentralized networks.

Effective on non-convex neural network learning tasks.

Outperforms existing stochastic gradient methods in uncertainty quantification.

Abstract

Federated learning performed by a decentralized networks of agents is becoming increasingly important with the prevalence of embedded software on autonomous devices. Bayesian approaches to learning benefit from offering more information as to the uncertainty of a random quantity, and Langevin and Hamiltonian methods are effective at realizing sampling from an uncertain distribution with large parameter dimensions. Such methods have only recently appeared in the decentralized setting, and either exclusively use stochastic gradient Langevin and Hamiltonian Monte Carlo approaches that require a diminishing stepsize to asymptotically sample from the posterior and are known in practice to characterize uncertainty less faithfully than constant step-size methods with a Metropolis adjustment, or assume strong convexity properties of the potential function. We present the first approach to incorporating constant stepsize Metropolis-adjusted HMC in the decentralized sampling framework, show theoretical guarantees for consensus and probability distance to the posterior stationary distribution, and demonstrate their effectiveness numerically on standard real world problems, including decentralized learning of neural networks which is known to be highly non-convex.