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We propose two novel stochastic gradient descent algorithms, ByGARS andByGARS++, for distributed machine learning in the presence of any number ofByzantine adversaries. In these algorithms, reputation scores of workers arecomputed using an auxiliary dataset at the server. This reputation score isthen used for aggregating the gradients for stochastic gradient descent. Thecomputational complexity of ByGARS++ is the same as the usual distributedstochastic gradient descent method with only an additional inner productcomputation in every iteration. We show that using these reputation scores forgradient aggregation is robust to any number of multiplicative noise Byzantineadversaries and use two-timescale stochastic approximation theory to proveconvergence for strongly convex loss functions. We demonstrate theeffectiveness of the algorithms for non-convex learning problems using MNISTand CIFAR-10 datasets against almost all state-of-the-art Byzantine attacks. Wealso show that the proposed algorithms are robust to multiple different typesof attacks at the same time.

ByGARS: Byzantine SGD with Arbitrary Number of Attackers