IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method
This work provides an incremental improvement in decentralized optimization methods, offering a systematic framework for researchers and practitioners in distributed computing.
The authors tackled the problem of decentralized optimization for smooth, strongly convex local functions by introducing a framework that systematically derives known algorithms and yields a novel primal algorithm with optimal convergence rate, matching lower bounds and demonstrating effectiveness on highly ill-conditioned problems.
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.