  This paper considers the Byzantine fault-tolerance problem in distributed
stochastic gradient descent (D-SGD) method - a popular algorithm for
distributed multi-agent machine learning. In this problem, each agent samples
data points independently from a certain data-generating distribution. In the
fault-free case, the D-SGD method allows all the agents to learn a mathematical
model best fitting the data collectively sampled by all agents. We consider the
case when a fraction of agents may be Byzantine faulty. Such faulty agents may
not follow a prescribed algorithm correctly, and may render traditional D-SGD
method ineffective by sharing arbitrary incorrect stochastic gradients. We
propose a norm-based gradient-filter, named comparative gradient elimination
(CGE), that robustifies the D-SGD method against Byzantine agents. We show that
the CGE gradient-filter guarantees fault-tolerance against a bounded fraction
of Byzantine agents under standard stochastic assumptions, and is
computationally simpler compared to many existing gradient-filters such as
multi-KRUM, geometric median-of-means, and the spectral filters. We empirically
show, by simulating distributed learning on neural networks, that the
fault-tolerance of CGE is comparable to that of existing gradient-filters. We
also empirically show that exponential averaging of stochastic gradients
improves the fault-tolerance of a generic gradient-filter.
