To defend against Byzantine attacks in decentralized learning, most existing methods rely on robust aggregation rules to mitigate the influence of malicious machines. However, these strategies inherently introduce bias, leading to inexact convergence with non-vanishing steady-state errors. In this paper, we propose a strategic shift from passive aggregation to active identification by introducing the Decentralized Rescaled Stochastic Gradient Descent with Byzantine Machine Identification (DRSGD-ByMI) framework. The core of our approach is an identification-based ``detect-then-optimize'' pipeline, where a p-value-free detection procedure is developed to accurately prune malicious nodes from the network. By leveraging sample-splitting score statistics, this identification mechanism achieves false discovery rate control without requiring restrictive distributional assumptions. We theoretically demonstrate that this precise identification allows the decentralized network to recover sufficient connectivity among the normal nodes, thereby enabling DRSGD-ByMI to match, even in the presence of Byzantine machines, the same order-optimal convergence rate as standard decentralized stochastic first-order methods. Numerical experiments validate our theoretical results and demonstrate the effectiveness of DRSGD-ByMI for decentralized robust learning problems.

翻译：为了防御分布式学习中的拜占庭攻击，现有方法大多依赖鲁棒聚合规则来降低恶意机器的影响。然而，这些策略本质上会引入偏差，导致稳态误差无法消除而难以实现精确收敛。本文提出从被动聚合转向主动识别，引入了一种带拜占庭机识别的分布式重缩放随机梯度下降框架（DRSGD-ByMI）。该方法的核心是基于识别的“检测-优化”流水线：通过开发无p值的检测过程，精准剔除网络中的恶意节点。该识别机制利用样本分割评分统计量，在无需严格分布假设的条件下实现了错误发现率控制。我们从理论上证明，这种精准识别能使分布式网络恢复正常节点间的充分连通性，从而使DRSGD-ByMI在存在拜占庭机时仍能达到与标准分布式随机一阶方法相同阶最优的收敛速率。数值实验验证了理论结果，并展示了DRSGD-ByMI在分布式鲁棒学习问题中的有效性。