Local Methods with Adaptivity via Scaling
Savelii Chezhegov, Sergey Skorik, Nikolas Khachaturov, Danil Shalagin, Aram Avetisyan, Martin Takáč, Yaroslav Kholodov, Aleksandr Beznosikov
TL;DR
The paper tackles distributed optimization under communication constraints by merging Local SGD with adaptive scaling through a diagonal preconditioner $\hat{D}^{t_p}$ that can represent schemes such as $Adam$, $RMSProp$, and $OASIS$. It proposes the SAVIC framework, provides a unified convergence analysis under generalized preconditioning for both identical and heterogeneous data, and validates the approach with neural network experiments showing faster convergence with scaling. The key contributions include embedding preconditioning into local updates, a broad theoretical analysis that does not rely on gradient boundedness or similarity, and empirical evidence of practical speedups in federated/distributed settings. This work demonstrates that integrating adaptive scaling into local methods can maintain convergence guarantees while reducing communication, with implications for scalable training in distributed and federated systems.
Abstract
The rapid development of machine learning and deep learning has introduced increasingly complex optimization challenges that must be addressed. Indeed, training modern, advanced models has become difficult to implement without leveraging multiple computing nodes in a distributed environment. Distributed optimization is also fundamental to emerging fields such as federated learning. Specifically, there is a need to organize the training process to minimize the time lost due to communication. A widely used and extensively researched technique to mitigate the communication bottleneck involves performing local training before communication. This approach is the focus of our paper. Concurrently, adaptive methods that incorporate scaling, notably led by Adam, have gained significant popularity in recent years. Therefore, this paper aims to merge the local training technique with the adaptive approach to develop efficient distributed learning methods. We consider the classical Local SGD method and enhance it with a scaling feature. A crucial aspect is that the scaling is described generically, allowing us to analyze various approaches, including Adam, RMSProp, and OASIS, in a unified manner. In addition to theoretical analysis, we validate the performance of our methods in practice by training a neural network.