QLSD: Quantised Langevin stochastic dynamics for Bayesian federated learning.

Federated learning aims at conducting inference when data are decentralised and locally stored on several clients, under two main constraints: data ownership and communication overhead. In this paper, we address these issues under the Bayesian paradigm. To this end, we propose a novel Markov chain Monte Carlo algorithm coined \texttt{QLSD} built upon quantised versions of stochastic gradient Langevin dynamics. To improve performance in a big data regime, we introduce variance-reduced alternatives of our methodology referred to as \texttt{QLSD}$^\star$ and \texttt{QLSD}$^{++}$. We provide both non-asymptotic and asymptotic convergence guarantees for the proposed algorithms and illustrate their benefits on several federated learning benchmarks.