Federated Stochastic Gradient Langevin Dynamics

TL;DR

This paper introduces FSGLD, a federated sampling method that uses conducive gradients to improve convergence and accuracy in non-IID data settings, addressing issues of variance and communication delays.

Contribution

The paper proposes conducive gradients for federated SGLD, enabling better convergence and handling of delayed communication in non-IID data scenarios.

Findings

FSGLD converges to the true posterior even with delayed communication.

FSGLD outperforms DSGLD on non-IID federated data in experiments.

Conducive gradients are computationally efficient with negligible overhead.

Abstract

Stochastic gradient MCMC methods, such as stochastic gradient Langevin dynamics (SGLD), employ fast but noisy gradient estimates to enable large-scale posterior sampling. Although we can easily extend SGLD to distributed settings, it suffers from two issues when applied to federated non-IID data. First, the variance of these estimates increases significantly. Second, delaying communication causes the Markov chains to diverge from the true posterior even for very simple models. To alleviate both these problems, we propose conducive gradients, a simple mechanism that combines local likelihood approximations to correct gradient updates. Notably, conducive gradients are easy to compute, and since we only calculate the approximations once, they incur negligible overhead. We apply conducive gradients to distributed stochastic gradient Langevin dynamics (DSGLD) and call the resulting method federated stochastic gradient Langevin dynamics (FSGLD). We demonstrate that our approach can handle delayed communication rounds, converging to the target posterior in cases where DSGLD fails. We also show that FSGLD outperforms DSGLD for non-IID federated data with experiments on metric learning and neural networks.