This paper considers the decentralized optimization problem, which has applications in large scale machine learning, sensor networks, and control theory. We propose a novel algorithm that can achieve near optimal communication complexity, matching the known lower bound up to a logarithmic factor of the condition number of the problem. Our theoretical results give affirmative answers to the open problem on whether there exists an algorithm that can achieve a communication complexity (nearly) matching the lower bound depending on the global condition number instead of the local one. Moreover, the proposed algorithm achieves the optimal computation complexity matching the lower bound up to universal constants. Furthermore, to achieve a linear convergence rate, our algorithm doesn't require the individual functions to be (strongly) convex. Our method relies on a novel combination of known techniques including Nesterov's accelerated gradient descent, multi-consensus and gradient-tracking. The analysis is new, and may be applied to other related problems. Empirical studies demonstrate the effectiveness of our method for machine learning applications.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2025 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.