Federated Learning Resilient to Byzantine Attacks and Data Heterogeneity

This paper addresses federated learning (FL) in the context of malicious Byzantine attacks and data heterogeneity. We introduce a novel Robust Average Gradient Algorithm (RAGA), which uses the geometric median for aggregation and allows flexible round number for local updates. Unlike most existing resilient approaches, which base their convergence analysis on strongly-convex loss functions or homogeneously distributed datasets, this work conducts convergence analysis for both strongly-convex and non-convex loss functions over heterogeneous datasets. The theoretical analysis indicates that as long as the fraction of the data from malicious users is less than half, RAGA can achieve convergence at a rate of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}({1}/{T^{2/3- \delta }})$</tex-math></inline-formula> for non-convex loss functions, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T$</tex-math></inline-formula> is the iteration number and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\delta \in (0, 2/3)$</tex-math></inline-formula>. For strongly-convex loss functions, the convergence rate is linear. Furthermore, the stationary point or global optimal solution is shown to be attainable as data heterogeneity diminishes. Experimental results validate the robustness of RAGA against Byzantine attacks and demonstrate its superior convergence performance compared to baselines under varying intensities of Byzantine attacks on heterogeneous datasets.