  Federated learning has exhibited vulnerabilities to Byzantine attacks, where
the Byzantine attackers can send arbitrary gradients to a central server to
destroy the convergence and performance of the global model. A wealth of robust
AGgregation Rules (AGRs) have been proposed to defend against Byzantine
attacks. However, Byzantine clients can still circumvent robust AGRs when data
is non-Identically and Independently Distributed (non-IID). In this paper, we
first reveal the root causes of performance degradation of current robust AGRs
in non-IID settings: the curse of dimensionality and gradient heterogeneity. In
order to address this issue, we propose GAS, a \shorten approach that can
successfully adapt existing robust AGRs to non-IID settings. We also provide a
detailed convergence analysis when the existing robust AGRs are combined with
GAS. Experiments on various real-world datasets verify the efficacy of our
proposed GAS. The implementation code is provided in
https://github.com/YuchenLiu-a/byzantine-gas.
