  Byzantine attacks hinder the deployment of federated learning algorithms.
Although we know that the benign gradients and Byzantine attacked gradients are
distributed differently, to detect the malicious gradients is challenging due
to (1) the gradient is high-dimensional and each dimension has its unique
distribution and (2) the benign gradients and the attacked gradients are always
mixed (two-sample test methods cannot apply directly). To address the above,
for the first time, we propose MANDERA which is theoretically guaranteed to
efficiently detect all malicious gradients under Byzantine attacks with no
prior knowledge or history about the number of attacked nodes. More
specifically, we transfer the original updating gradient space into a ranking
matrix. By such an operation, the scales of different dimensions of the
gradients in the ranking space become identical. The high-dimensional benign
gradients and the malicious gradients can be easily separated. The
effectiveness of MANDERA is further confirmed by experimentation on four
Byzantine attack implementations (Gaussian, Zero Gradient, Sign Flipping,
Shifted Mean), comparing with state-of-the-art defenses. The experiments cover
both IID and Non-IID datasets.

Machine Learning