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

Chen Yaoling, Liang Hao, Tu Xiaotong

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.

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

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.
Paper Structure (10 sections, 6 theorems, 10 equations, 1 figure)

This paper contains 10 sections, 6 theorems, 10 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. System Model
  4. Differential Privacy
  5. Assumptions
  6. Main Results
  7. Privacy Analysis
  8. Convergence Analysis
  9. Numerical Results
  10. Conclusion

Key Result

Lemma 2.1

If the above system model is an $(\alpha,\varepsilon)$-RDP protocol, it also satisfies $(\varepsilon+\frac{\log1/\delta}{\alpha-1},\delta)$-DP for any $0<\delta<1$.

Figures (1)

  • Figure 1: The evolution of the privacy level during DPWFL with different settings: (a) domain diameter, $D$, (b) device sampling rate, $p$, and mini-batch sampling rate, $q$.

Theorems & Definitions (8)

  • Definition 2.1: Differential Privacy dwork14algorithmicDP
  • Definition 2.2: Rényi Differential Privacy mironov2017renyi
  • Lemma 2.1: From RDP to Standard DP mironov2017renyi
  • Lemma 3.1: Wireless Noisy Reduction
  • Theorem 3.1: $(\alpha,\varepsilon)$-RDP Guarantee for DPWFL
  • Corollary 3.1: $(\epsilon,\delta)$-DP Guarantee for DPWFL
  • Theorem 3.2: Convergence Analysis for DPWFL
  • Proposition 3.2: Privacy-Utility Trade-off for DPWFL