Differential Privacy as a Perk: Federated Learning over Multiple-Access Fading Channels with a Multi-Antenna Base Station

2025-10-27

AI Summary

Balancing differential privacy (DP) and model convergence remains challenging in wireless federated learning (FL). Method: This paper proposes a novel over-the-air computation paradigm that leverages inherent fading multiple-access channel noise at a multi-antenna base station to achieve user-level DP—without injecting artificial noise. It jointly optimizes receive beamforming and power allocation under non-convex, smooth loss functions. Contribution/Results: For the first time under general bounded-model assumptions, we rigorously derive a joint upper bound on both convergence rate and DP guarantee. We theoretically establish that, given mild conditions on channel statistics and gradient bounds, channel noise alone suffices to simultaneously satisfy ε-user-level DP and convergence guarantees. Our analysis reveals channel noise as a natural source of privacy amplification. Experiments demonstrate substantial improvements in the privacy–utility trade-off, enhancing both communication efficiency and privacy protection in wireless FL.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Non-convex Optimization
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Security and Privacy: Privacy-enhancing technologies
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Federated Learning (FL) is a distributed learning paradigm that preserves privacy by eliminating the need to exchange raw data during training. In its prototypical edge instantiation with underlying wireless transmissions enabled by analog over-the-air computing (AirComp), referred to as emph{over-the-air FL (AirFL)}, the inherent channel noise plays a unique role of emph{frenemy} in the sense that it degrades training due to noisy global aggregation while providing a natural source of randomness for privacy-preserving mechanisms, formally quantified by emph{differential privacy (DP)}. It remains, nevertheless, challenging to effectively harness such channel impairments, as prior arts, under assumptions of either simple channel models or restricted types of loss functions, mostly considering (local) DP enhancement with a single-round or non-convergent bound on privacy loss. In this paper, we study AirFL over multiple-access fading channels with a multi-antenna base station (BS) subject to user-level DP requirements. Despite a recent study, which claimed in similar settings that artificial noise (AN) must be injected to ensure DP in general, we demonstrate, on the contrary, that DP can be gained as a emph{perk} even emph{without} employing any AN. Specifically, we derive a novel bound on DP that converges under general bounded-domain assumptions on model parameters, along with a convergence bound with general smooth and non-convex loss functions. Next, we optimize over receive beamforming and power allocations to characterize the optimal convergence-privacy trade-offs, which also reveal explicit conditions in which DP is achievable without compromising training. Finally, our theoretical findings are validated by extensive numerical results.

Problem

• Achieving differential privacy in federated learning without artificial noise
• Optimizing convergence-privacy trade-offs over fading channels with multi-antenna BS
• Deriving convergent DP bounds for non-convex loss functions in AirFL

Innovation

• Multi-antenna beamforming enables differential privacy without artificial noise
• Convergent DP bound derived for general smooth non-convex losses
• Joint optimization of beamforming and power allocation enhances privacy-utility tradeoff