Privacy and security concerns in real-world applications have led to the development of adversarially robust federated models. However, the straightforward combination between adversarial training and federated learning in one framework can lead to the undesired robustness deterioration. We discover that the attribution behind this phenomenon is that the generated adversarial data could exacerbate the data heterogeneity among local clients, making the wrapped federated learning perform poorly. To deal with this problem, we propose a novel framework called Slack Federated Adversarial Training (SFAT), assigning the client-wise slack during aggregation to combat the intensified heterogeneity. Theoretically, we analyze the convergence of the proposed method to properly relax the objective when combining federated learning and adversarial training. Experimentally, we verify the rationality and effectiveness of SFAT on various benchmarked and real-world datasets with different adversarial training and federated optimization methods. The code is publicly available at https://github.com/ZFancy/SFAT.
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