Federated Learning with a Sampling Algorithm under Isoperimetry

TL;DR

This paper introduces a Bayesian federated learning method using a sampling algorithm based on Langevin dynamics, which is communication-efficient and effective under nonconvex conditions with isoperimetric properties.

Contribution

It proposes a novel, communication-efficient Langevin sampling algorithm for federated learning that operates under weaker assumptions than strong convexity, specifically using isoperimetric inequalities.

Findings

Algorithm is robust under nonconvex conditions.

Provides theoretical analysis without strong log-concavity assumptions.

Achieves efficient sampling with reduced communication costs.

Abstract

Federated learning uses a set of techniques to efficiently distribute the training of a machine learning algorithm across several devices, who own the training data. These techniques critically rely on reducing the communication cost -- the main bottleneck -- between the devices and a central server. Federated learning algorithms usually take an optimization approach: they are algorithms for minimizing the training loss subject to communication (and other) constraints. In this work, we instead take a Bayesian approach for the training task, and propose a communication-efficient variant of the Langevin algorithm to sample a posteriori. The latter approach is more robust and provides more knowledge of the \textit{a posteriori} distribution than its optimization counterpart. We analyze our algorithm without assuming that the target distribution is strongly log-concave. Instead, we assume the weaker log Sobolev inequality, which allows for nonconvexity.