In this paper, we investigate the problem of distributed learning (DL) in the presence of Byzantine attacks. For this problem, various robust bounded aggregation (RBA) rules have been proposed at the central server to mitigate the impact of Byzantine attacks. However, current DL methods apply RBA rules for the local gradients from the honest devices and the disruptive information from Byzantine devices, and the learning performance degrades significantly when the local gradients of different devices vary considerably from each other. To overcome this limitation, we propose a new DL method to cope with Byzantine attacks based on coded robust aggregation (CRA-DL). Before training begins, the training data are allocated to the devices redundantly. During training, in each iteration, the honest devices transmit coded gradients to the server computed from the allocated training data, and the server then aggregates the information received from both honest and Byzantine devices using RBA rules. In this way, the global gradient can be approximately recovered at the server to update the global model. Compared with current DL methods applying RBA rules, the improvement of CRA-DL is attributed to the fact that the coded gradients sent by the honest devices are closer to each other. This closeness enhances the robustness of the aggregation against Byzantine attacks, since Byzantine messages tend to be significantly different from those of honest devices in this case. We theoretically analyze the convergence performance of CRA-DL. Finally, we present numerical results to verify the superiority of the proposed method over existing baselines, showing its enhanced learning performance under Byzantine attacks.

Over-the-air computation (AirComp) has emerged as an essential approach for enabling communication-efficient federated learning (FL) over wireless networks. Nonetheless, the inherent analog transmission mechanism in AirComp-based FL (AirFL) intensifies challenges posed by potential Byzantine attacks. In this paper, we propose a novel Byzantine-robust FL paradigm for over-the-air transmissions, referred to as federated learning with secure adaptive clustering (FedSAC). FedSAC aims to protect a portion of the devices from attacks through zero trust architecture (ZTA) based Byzantine identification and adaptive device clustering. By conducting a one-step convergence analysis, we theoretically characterize the convergence behavior with different device clustering mechanisms and uneven aggregation weighting factors for each device. Building upon our analytical results, we formulate a joint optimization problem for the clustering and weighting factors in each communication round. To facilitate the targeted optimization, we propose a dynamic Byzantine identification method using historical reputation based on ZTA. Furthermore, we introduce a sequential clustering method, transforming the joint optimization into a weighting optimization problem without sacrificing the optimality. To optimize the weighting, we capitalize on the penalty convex-concave procedure (P-CCP) to obtain a stationary solution. Numerical results substantiate the superiority of the proposed FedSAC over existing methods in terms of both test accuracy and convergence rate.

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.