Privacy Amplification for Federated Learning via User Sampling and Wireless Aggregation

TL;DR

This paper introduces a novel wireless federated learning scheme that combines user sampling and wireless aggregation to significantly improve privacy guarantees while maintaining convergence efficiency.

Contribution

It proposes a new private wireless gradient aggregation method that enhances differential privacy by integrating user sampling with wireless channel properties.

Findings

Central DP leakage scales as O(1/K^{3/4}) with the new scheme.

User sampling boosts both DP and LDP privacy guarantees.

The scheme achieves favorable convergence rates under different sampling knowledge scenarios.

Abstract

In this paper, we study the problem of federated learning over a wireless channel with user sampling, modeled by a Gaussian multiple access channel, subject to central and local differential privacy (DP/LDP) constraints. It has been shown that the superposition nature of the wireless channel provides a dual benefit of bandwidth efficient gradient aggregation, in conjunction with strong DP guarantees for the users. Specifically, the central DP privacy leakage has been shown to scale as $\mathcal{O}(1/K^{1/2})$, where $K$ is the number of users. It has also been shown that user sampling coupled with orthogonal transmission can enhance the central DP privacy leakage with the same scaling behavior. In this work, we show that, by join incorporating both wireless aggregation and user sampling, one can obtain even stronger privacy guarantees. We propose a private wireless gradient aggregation scheme, which relies on independently randomized participation decisions by each user. The central DP leakage of our proposed scheme scales as $\mathcal{O}(1/K^{3/4})$. In addition, we show that LDP is also boosted by user sampling. We also present analysis for the convergence rate of the proposed scheme and study the tradeoffs between wireless resources, convergence, and privacy theoretically and empirically for two scenarios when the number of sampled participants are $(a)$ known, or $(b)$ unknown at the parameter server.