Both Byzantine resilience and communication efficiency have attracted tremendous attention recently for their significance in edge federated learning. However, most existing algorithms may fail when dealing with real-world irregular data that behaves in a heavy-tailed manner. To address this issue, we study the stochastic convex and non-convex optimization problem for federated learning at edge and show how to handle heavy-tailed data while retaining the Byzantine resilience, communication efficiency and the optimal statistical error rates simultaneously. Specifically, we first present a Byzantine-resilient distributed gradient descent algorithm that can handle the heavy-tailed data and meanwhile converge under the standard assumptions. To reduce the communication overhead, we further propose another algorithm that incorporates gradient compression techniques to save communication costs during the learning process. Theoretical analysis shows that our algorithms achieve order-optimal statistical error rate in presence of Byzantine devices. Finally, we conduct extensive experiments on both synthetic and real-world datasets to verify the efficacy of our algorithms.

本文研究边缘联邦学习中的随机凸和非凸优化问题，以解决处理重尾数据时现有算法的不足，并同时保持拜占庭鲁棒性，通信效率和最佳统计误差率。我们提出了两种算法，分别是具有拜占庭鲁棒性的分布式梯度下降算法，以及结合梯度压缩技术的通信开销较小的算法。理论分析表明，我们的算法在存在拜占庭设备的情况下实现了最优的统计误差率。最后，我们在合成和现实世界数据集上进行了广泛的实验，以验证算法的有效性。

边缘拜占庭容错联邦学习