Distributed learning is central for large-scale training of deep-learning models. However, they are exposed to a security threat in which Byzantine participants can interrupt or control the learning process. Previous attack models and their corresponding defenses assume that the rogue participants are (a) omniscient (know the data of all other participants), and (b) introduce large change to the parameters. We show that small but well-crafted changes are sufficient, leading to a novel non-omniscient attack on distributed learning that go undetected by all existing defenses. We demonstrate our attack method works not only for preventing convergence but also for repurposing of the model behavior (backdooring). We show that 20% of corrupt workers are sufficient to degrade a CIFAR10 model accuracy by 50%, as well as to introduce backdoors into MNIST and CIFAR10 models without hurting their accuracy

We consider the problem of distributed statistical machine learning in adversarial settings, where some unknown and time-varying subset of working machines may be compromised and behave arbitrarily to prevent an accurate model from being learned. This setting captures the potential adversarial attacks faced by Federated Learning -- a modern machine learning paradigm that is proposed by Google researchers and has been intensively studied for ensuring user privacy. Formally, we focus on a distributed system consisting of a parameter server and $m$ working machines. Each working machine keeps $N/m$ data samples, where $N$ is the total number of samples. The goal is to collectively learn the underlying true model parameter of dimension $d$. In classical batch gradient descent methods, the gradients reported to the server by the working machines are aggregated via simple averaging, which is vulnerable to a single Byzantine failure. In this paper, we propose a Byzantine gradient descent method based on the geometric median of means of the gradients. We show that our method can tolerate $q \le (m-1)/2$ Byzantine failures, and the parameter estimate converges in $O(\log N)$ rounds with an estimation error of $\sqrt{d(2q+1)/N}$, hence approaching the optimal error rate $\sqrt{d/N}$ in the centralized and failure-free setting. The total computational complexity of our algorithm is of $O((Nd/m) \log N)$ at each working machine and $O(md + kd \log^3 N)$ at the central server, and the total communication cost is of $O(m d \log N)$. We further provide an application of our general results to the linear regression problem. A key challenge arises in the above problem is that Byzantine failures create arbitrary and unspecified dependency among the iterations and the aggregated gradients. We prove that the aggregated gradient converges uniformly to the true gradient function.