GT-STORM: Taming Sample, Communication, and Memory Complexities in Decentralized Non-Convex Learning

Abstract: Decentralized nonconvex optimization has received increasing attention in recent years in machine learning due to its advantages in system robustness, data privacy, and implementation simplicity. However, three fundamental challenges in designing decentralized optimization algorithms are how to reduce their sample, communication, and memory complexities. In this paper, we propose a \underline{g}radient-\underline{t}racking-based \underline{sto}chastic \underline{r}ecursive \underline{m}omentum (GT-STORM) algorithm for efficiently solving nonconvex optimization problems. We show that to reach an $\epsilon^2$-stationary solution, the total number of sample evaluations of our algorithm is $\tilde{O}(m^{1/2}\epsilon^{-3})$ and the number of communication rounds is $\tilde{O}(m^{-1/2}\epsilon^{-3})$, which improve the $O(\epsilon^{-4})$ costs of sample evaluations and communications for the existing decentralized stochastic gradient algorithms. We conduct extensive experiments with a variety of learning models, including non-convex logistical regression and convolutional neural networks, to verify our theoretical findings. Collectively, our results contribute to the state of the art of theories and algorithms for decentralized network optimization.