Convergence Analysis for Differentially Private Federated Averaging in Heterogeneous Settings

Federated learning (FL) has emerged as a prominent approach for distributed machine learning, enabling collaborative model training while preserving data privacy. However, the presence of non-i.i.d. data and the need for robust privacy protection introduce significant challenges in theoretically analyzing the performance of FL algorithms. In this paper, we present novel theoretical analysis on typical differentially private federated averaging (DP-FedAvg) by judiciously considering the impact of non-i.i.d. data on convergence and privacy guarantees. Our contributions are threefold: (i) We introduce a theoretical framework for analyzing the convergence of DP-FedAvg algorithm by considering different client sampling and data sampling strategies, privacy amplification and non-i.i.d. data. (ii) We explore the privacy–utility tradeoff and demonstrate how client strategies interact with differential privacy to affect learning performance. (iii) We provide extensive experimental validation using real-world datasets to verify our theoretical findings.