El Mhamdi, El Mahdi
Guerraoui, Rachid
Rouault, Sébastien Louis Alexandre
The Hidden Vulnerability of Distributed Learning in Byzantium
13
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 \emph{poisoned} gradients during the training phase. Some of these approaches have been proven \emph{Byzantine--resilient}: they ensure the \emph{convergence} of SGD despite the presence of a minority of adversarial workers. We show in this paper that \emph{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 \emph{ineffective} models. More precisely, we bring to light that existing Byzantine--resilient schemes leave a \emph{margin of poisoning} of $\bigOmega\left(f(d)\right)$, where $f(d)$ increases at least like $\sqrt{d}$. Based on this \emph{leeway}, we build a simple attack, and experimentally show its strong to utmost effectivity on CIFAR--10 and MNIST. We introduce \emph{Bulyan}, and prove it significantly reduces the attacker's leeway to a narrow $\bigO\,( \sfrac{1}{\sqrt{d~}})$ 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 \emph{as if} only non--Byzantine gradients had been used to update the model.
Machine Learning;
Distributed Algorithms;
Byzantine fault tolerance;
Robustness;
stochastic gradient descent;
SGD;
Poisoning attack;
adversarial machine learning;
2018
http://infoscience.epfl.ch/record/256124/files/bulyan.pdf;