Federated Online Prediction from Experts with Differential Privacy: Separations and Regret Speed-ups

TL;DR

This paper introduces federated algorithms for online expert prediction with differential privacy, achieving regret speed-ups in stochastic settings and near-optimal performance in special oblivious adversary cases, with theoretical guarantees and experiments.

Contribution

It presents the first study of differentially private federated online prediction from experts, proposing algorithms that attain regret speed-ups and establishing lower bounds for various adversary models.

Findings

Fed-DP-OPE-Stoch achieves √m regret speed-up with stochastic adversaries.

Fed-SVT attains m-fold regret speed-up with low-loss experts in oblivious adversaries.

Algorithms maintain logarithmic communication costs and are nearly optimal.

Abstract

We study the problems of differentially private federated online prediction from experts against both stochastic adversaries and oblivious adversaries. We aim to minimize the average regret on $m$ clients working in parallel over time horizon $T$ with explicit differential privacy (DP) guarantees. With stochastic adversaries, we propose a Fed-DP-OPE-Stoch algorithm that achieves $\sqrt{m}$-fold speed-up of the per-client regret compared to the single-player counterparts under both pure DP and approximate DP constraints, while maintaining logarithmic communication costs. With oblivious adversaries, we establish non-trivial lower bounds indicating that collaboration among clients does not lead to regret speed-up with general oblivious adversaries. We then consider a special case of the oblivious adversaries setting, where there exists a low-loss expert. We design a new algorithm Fed-SVT and show that it achieves an $m$-fold regret speed-up under both pure DP and approximate DP constraints over the single-player counterparts. Our lower bound indicates that Fed-SVT is nearly optimal up to logarithmic factors. Experiments demonstrate the effectiveness of our proposed algorithms. To the best of our knowledge, this is the first work examining the differentially private online prediction from experts in the federated setting.