Differentially Private Federated Frank-Wolfe

Abstract

In this paper, we propose DP-FedFW, a novel Frank-Wolfe based federated learning algorithm with local (ϵ,δ)-differential privacy (DP) guarantees in a constrained learning setting. In DP-FedFW, we perturb local models to ensure privacy while communicating with the server, and each client performs several Frank-Wolfe steps to arrive at a local model. The proposed method guarantees (ϵ,δ)-DP for each client and has a sublinear convergence of $\mathcal{O}$(1/k) for smooth convex objective functions, where k is the number of communication rounds and an asymptotic convergence for smooth non-convex objective functions. The theoretical analysis shows that given an (ϵ,δ)-DP requirement, the proposed algorithm’s performance improves with the number of clients and the batch size. We empirically validate the efficacy of the proposed method on several constrained machine learning tasks.