IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method
Optimization and Control
2020-06-15 v1 Machine Learning
Abstract
We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by the accelerated augmented Lagrangian method, thereby providing a systematic way for deriving several well-known decentralized algorithms including EXTRA arXiv:1404.6264 and SSDA arXiv:1702.08704. When coupled with accelerated gradient descent, our framework yields a novel primal algorithm whose convergence rate is optimal and matched by recently derived lower bounds. We provide experimental results that demonstrate the effectiveness of the proposed algorithm on highly ill-conditioned problems.
Cite
@article{arxiv.2006.06733,
title = {IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method},
author = {Yossi Arjevani and Joan Bruna and Bugra Can and Mert Gürbüzbalaban and Stefanie Jegelka and Hongzhou Lin},
journal= {arXiv preprint arXiv:2006.06733},
year = {2020}
}