SQuARM-SGD: Communication-Efficient Momentum SGD for Decentralized Optimization

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 smooth objectives, which, to the best of our knowledge, is the first theoretical analysis for compressed decentralized SGD with momentum updates. We show that SQuARM-SGD converges at rate $\mathcal{O}({{}^{1}}\!/\!_{\sqrt{nT}})$, matching that of vanilla distributed SGD. We empirically show that SQuARM-SGD saves significantly in total communicated bits over state-of-the-art without sacrificing much on accuracy.