We investigate robust federated learning, where a group of workers collaboratively train a shared model under the orchestration of a central server in the presence of Byzantine adversaries capable of arbitrary and potentially malicious behaviors. To simultaneously enhance communication efficiency and resilience against such adversaries, we propose a Byzantine-resilient Nesterov-accelerated federated learning (Byrd-NAFL) algorithm. Byrd-NAFL seamlessly integrates Nesterov's momentum into the federated learning process alongside Byzantine-resilient aggregation rules to achieve fast and safe convergence against gradient corruption. We establish a finite-time convergence guarantee for Byrd-NAFL under non-convex and smooth loss functions with relaxed assumptions on the aggregated gradients. Extensive numerical experiments validate the effectiveness of Byrd-NAFL and demonstrate the superiority over existing benchmarks in terms of convergence speed, accuracy, and resilience to diverse malicious attacks.

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