While machine learning is going through an era of celebrated success, concerns have been raised about the vulnerability of its backbone: stochastic gradient descent (SGD). Recent approaches have been proposed to ensure the robustness of distributed SGD against adversarial (Byzantine) workers sending poisoned gradients during the training phase. Some of these approaches have been proven Byzantine-resilient: they ensure the convergence of SGD despite the presence of a minority of adversarial workers. We show in this paper that convergence is not enough. In high dimension $d \gg 1$, an adver\-sary can build on the loss function's non--convexity to make SGD converge to ineffective models. More precisely, we bring to light that existing Byzantine--resilient schemes leave a margin of poisoning of $\Omega\left(f(d)\right)$, where $f(d)$ increases at least like $\sqrt[p]{d~}$. Based on this leeway, we build a simple attack, and experimentally show its strong to utmost effectivity on CIFAR--10 and MNIST. We introduce Bulyan, and prove it significantly reduces the attackers leeway to a narrow $O( \frac{1}{\sqrt{d~}})$ bound. We empirically show that Bulyan does not suffer the fragility of existing aggregation rules and, at a reasonable cost in terms of required batch size, achieves convergence as if only non--Byzantine gradients had been used to update the model.

本文提出了一种新的聚合规则Bulyan，可以有效地保护分布式随机梯度下降算法免受对抗攻击，缩小攻击者留下的空间，并提高算法的收敛性能。

拜占庭分布式学习的隐形漏洞