BEER: Fast $O(1/T)$ Rate for Decentralized Nonconvex Optimization with Communication Compression
Year: 2022
Type: preprint
Abstract: Communication efficiency has been widely recognized as the bottleneck for large-scale decentralized machine learning applications in multi-agent or federated environments. To tackle the communication bottleneck, there have been many efforts to design communication-compressed algorithms for decentralized nonconvex optimization, where the clients are only allowed to communicate a small amount of quantized information (aka bits) with their neighbors over a predefined graph topology. Despite significant efforts, the state-of-the-art algorithm in the nonconvex setting still suffers from a slower rate of convergence $O((G/T)^{2/3})$ compared with their uncompressed counterpart, where $G$ measures the data heterogeneity across different clients, and $T$ is the number of communication rounds. This paper proposes BEER, which adopts communication compression with gradient tracking, and shows it converges at a faster rate of $O(1/T)$. This significantly improves over the state-of-the-art rate, by matching the rate without compression even under arbitrary data heterogeneity. Numerical experiments are also provided to corroborate our theory and confirm the practical superiority of BEER in the data heterogeneous regime.
Source: arXiv (Cornell University)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1469985387, RINGS: Learning-Enabled Ground and Air Integrated Networks (GAINs), CIF: Medium: Collaborative Research: Theory of Optimization Geometry and Algorithms for Neural Networks, G4713059963, G5972442391, CIF: Small: Resource-Efficient Statistical Inference in Networked Environments, G823371236, G8876996369
OpenAlex ID: W4221142145