When Differential Privacy Meets Wireless Federated Learning: An Improved Analysis for Privacy and Convergence

TL;DR

This paper provides a comprehensive analysis of privacy and convergence in wireless federated learning with differential privacy, addressing limitations of prior work and deriving explicit privacy-utility trade-offs.

Contribution

It introduces a novel analysis framework for DPWFL that accounts for device selection, mini-batch sampling, and gradient clipping, improving understanding of privacy loss and convergence.

Findings

Privacy loss converges to a constant with iterations.

Convergence guarantees are established with gradient clipping.

Numerical results validate theoretical privacy-utility trade-offs.

Abstract

Differentially private wireless federated learning (DPWFL) is a promising framework for protecting sensitive user data. However, foundational questions on how to precisely characterize privacy loss remain open, and existing work is further limited by convergence analyses that rely on restrictive convexity assumptions or ignore the effect of gradient clipping. To overcome these issues, we present a comprehensive analysis of privacy and convergence for DPWFL with general smooth non-convex loss objectives. Our analysis explicitly incorporates both device selection and mini-batch sampling, and shows that the privacy loss can converge to a constant rather than diverge with the number of iterations. Moreover, we establish convergence guarantees with gradient clipping and derive an explicit privacy-utility trade-off. Numerical results validate our theoretical findings.