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arXiv · 2006.06733

IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method

Yossi Arjevani·Joan Bruna·Bugra Can·Mert Gürbüzbalaban·Stefanie Jegelka·Hongzhou Lin
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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.

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Yossi Arjevani, Joan Bruna, Bugra Can, Mert Gürbüzbalaban, Stefanie Jegelka, Hongzhou Lin. 2020-06-11. IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method. https://arxiv.org/abs/2006.06733

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