Robust distributed learning with Byzantine failures has attracted extensive research interests in recent years. However, most of existing methods suffer from curse of dimensionality, which is increasingly serious with the growing complexity of modern machine learning models. In this paper, we design a new method that is suitable for high dimensional problems, under arbitrary number of Byzantine attackers. The core of our design is a direct high dimensional semi-verified mean estimation method. Our idea is to identify a subspace first. The components of mean value perpendicular to this subspace can be estimated via gradient vectors uploaded from worker machines, while the components within this subspace are estimated using auxiliary dataset. We then use our new method as the aggregator of distributed learning problems. Our theoretical analysis shows that the new method has minimax optimal statistical rates. In particular, the dependence on dimensionality is significantly improved compared with previous works.

我们设计了一个适用于高维问题的新方法，可以在任意数量的拜占庭攻击者下进行高效分布式学习，并采用半验证的均值估计方法实现，通过从工作机上传的梯度向量估计均值值的分量以及通过辅助数据集估计子空间内的分量，最终以我们的新方法作为分布式学习聚合器。理论分析表明，该新方法具有极小极大统计速率，并且与之前的方法相比，在维度依赖性方面得到了显着改进。

高维度分布式梯度下降与任意数量的拜占庭攻击者