  In this paper, we propose and analyze SQuARM-SGD, a communication-efficient
algorithm for decentralized training of large-scale machine learning models
over a network. In SQuARM-SGD, each node performs a fixed number of local SGD
steps using Nesterov's momentum and then sends sparsified and quantized updates
to its neighbors regulated by a locally computable triggering criterion. We
provide convergence guarantees of our algorithm for general (non-convex) and
convex smooth objectives, which, to the best of our knowledge, is the first
theoretical analysis for compressed decentralized SGD with momentum updates. We
show that the convergence rate of SQuARM-SGD matches that of vanilla SGD. We
empirically show that including momentum updates in SQuARM-SGD can lead to
better test performance than the current state-of-the-art which does not
consider momentum updates.
