The Hidden Vulnerability of Distributed Learning in Byzantium

TL;DR

This paper reveals that existing Byzantine-resilient distributed learning methods are vulnerable in high dimensions, allowing attackers to significantly influence model convergence, and proposes Bulyan to mitigate this issue effectively.

Contribution

The paper demonstrates the limitations of current Byzantine-resilient schemes in high-dimensional settings and introduces Bulyan, a new aggregation rule that substantially reduces attacker's leverage.

Findings

Existing schemes leave a poisoning margin growing with dimension

Bulyan reduces attacker leverage to a narrow bound

Bulyan achieves robust convergence comparable to non-Byzantine training

Abstract

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 $\sqrt{d~}$. 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.