The success of machine learning (ML) has been intimately linked with the availability of large amounts of data, typically collected from heterogeneous sources and processed on vast networks of computing devices (also called {\em workers}). Beyond accuracy, the use of ML in critical domains such as healthcare and autonomous driving calls for robustness against {\em data poisoning}and some {\em faulty workers}. The problem of {\em Byzantine ML} formalizes these robustness issues by considering a distributed ML environment in which workers (storing a portion of the global dataset) can deviate arbitrarily from the prescribed algorithm. Although the problem has attracted a lot of attention from a theoretical point of view, its practical importance for addressing realistic faults (where the behavior of any worker is locally constrained) remains unclear. It has been argued that the seemingly weaker threat model where only workers' local datasets get poisoned is more reasonable. We prove that, while tolerating a wider range of faulty behaviors, Byzantine ML yields solutions that are, in a precise sense, optimal even under the weaker data poisoning threat model. Then, we study a generic data poisoning model wherein some workers have {\em fully-poisonous local data}, i.e., their datasets are entirely corruptible, and the remainders have {\em partially-poisonous local data}, i.e., only a fraction of their local datasets is corruptible. We prove that Byzantine-robust schemes yield optimal solutions against both these forms of data poisoning, and that the former is more harmful when workers have {\em heterogeneous} local data.

机器学习中的数据污染和故障工作者问题对鲁棒性的重要性进行了研究，通过考虑具有分布式特征的机器学习环境中的Byzantine ML问题，证明了解决方法在更弱的数据污染威胁模型下依然是最优的。同时，研究了一种一般的数据污染模型，其中一些工作者具有完全污染的本地数据，而其他工作者只有部分污染的本地数据。

论拜占庭鲁棒优化抗数据污染的相关性