Comments on "Federated Learning with Differential Privacy: Algorithms and Performance Analysis"

TL;DR

The comment targets the convergence guarantee of the NbAFL algorithm under differential privacy and identifies an incorrect upper bound caused by a misapplication of the Polyak-Lojasiewicz inequality. It provides a corrected convergence bound: $\mathbb{E}\{F(\tilde{w}^{(T)}) - F(w^{*})\} \leq \Theta + k_2 T + \frac{k_1 T^{2}}{\epsilon} + \frac{k_0 T^{3}}{\epsilon^{2}}$, where $k_2 = \lambda_2 \beta^{2}$, $k_1 = \frac{2 \lambda_1 \beta C c}{m} \sqrt{\frac{2}{N\pi}}$, and $k_0 = \frac{4 \lambda_0 C^{2} c^{2}}{m^{2} N}$, with $\lambda_0 = \frac{\rho}{2}$ and $\lambda_1 = 1 + \frac{\rho B}{\mu}$ (and the corrected form for the remaining constants). The authors present two equivalent derivations from the key recursive relation that corroborate the corrected bound. This clarifies the theoretical guarantees for NbAFL under differential privacy and corrects the prior bound used in the literature.

Abstract

In the paper by Wei et al. ("Federated Learning with Differential Privacy: Algorithms and Performance Analysis"), the convergence performance of the proposed differential privacy algorithm in federated learning (FL), known as Noising before Model Aggregation FL (NbAFL), was studied. However, the presented convergence upper bound of NbAFL (Theorem 2) is incorrect. This comment aims to present the correct form of the convergence upper bound for NbAFL.