IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method

Part of Advances in Neural Information Processing Systems 33 (NeurIPS 2020)

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Authors

Yossi Arjevani, Joan Bruna, Bugra Can, Mert Gurbuzbalaban, Stefanie Jegelka, Hongzhou Lin

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 and SSDA. 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.