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Federated learning has exhibited vulnerabilities to Byzantine attacks, wherethe Byzantine attackers can send arbitrary gradients to a central server todestroy the convergence and performance of the global model. A wealth of robustAGgregation Rules (AGRs) have been proposed to defend against Byzantineattacks. However, Byzantine clients can still circumvent robust AGRs when datais non-Identically and Independently Distributed (non-IID). In this paper, wefirst reveal the root causes of performance degradation of current robust AGRsin non-IID settings: the curse of dimensionality and gradient heterogeneity. Inorder to address this issue, we propose GAS, a \shorten approach that cansuccessfully adapt existing robust AGRs to non-IID settings. We also provide adetailed convergence analysis when the existing robust AGRs are combined withGAS. Experiments on various real-world datasets verify the efficacy of ourproposed GAS. The implementation code is provided inhttps://github.com/YuchenLiu-a/byzantine-gas.

Byzantine-Robust Learning on Heterogeneous Data via Gradient Splitting