Communication Efficient and Byzantine Tolerant Distributed Learning

We develop a communication-efficient distributed learning algorithm that is robust against Byzantine worker machines. We propose and analyze a distributed gradient-descent algorithm that performs a simple thresholding based on gradient norms to mitigate Byzantine failures. We show the (statistical) error-rate of our algorithm matches that of Yin et al., 2018, which uses more complicated schemes (like coordinate-wise median or trimmed mean). Furthermore, for communication efficiency, we consider a generic class of delta-approximate compressors from Karimireddy et al., 2019, that encompasses sign-based compressors and top-k sparsification. Our algorithm uses compressed gradients and gradient norms for aggregation and Byzantine removal respectively. We establish the statistical error rate of the algorithm for arbitrary (convex or non-convex) smooth loss function. We show that, in certain regime of delta, the rate of convergence is not affected by the compression operation. We have experimentally validated our results and shown good performance in convergence for convex (least-square regression) and non-convex (neural network training) problems.