On the Convergence of Decentralized Adaptive Gradient Methods

TL;DR

This paper introduces a general framework for converting adaptive gradient methods into decentralized algorithms, providing convergence guarantees and demonstrating benefits through theoretical analysis and numerical experiments.

Contribution

It presents a novel, rigorous framework for decentralized adaptive gradient methods, extending existing algorithms with proven convergence properties.

Findings

Decentralized AMSGrad converges under certain conditions.

The framework applies to various adaptive methods, ensuring their decentralized versions are convergent.

Numerical results show improved performance in distributed settings.

Abstract

Adaptive gradient methods including Adam, AdaGrad, and their variants have been very successful for training deep learning models, such as neural networks. Meanwhile, given the need for distributed computing, distributed optimization algorithms are rapidly becoming a focal point. With the growth of computing power and the need for using machine learning models on mobile devices, the communication cost of distributed training algorithms needs careful consideration. In this paper, we introduce novel convergent decentralized adaptive gradient methods and rigorously incorporate adaptive gradient methods into decentralized training procedures. Specifically, we propose a general algorithmic framework that can convert existing adaptive gradient methods to their decentralized counterparts. In addition, we thoroughly analyze the convergence behavior of the proposed algorithmic framework and show that if a given adaptive gradient method converges, under some specific conditions, then its decentralized counterpart is also convergent. We illustrate the benefit of our generic decentralized framework on a prototype method, i.e., AMSGrad, both theoretically and numerically.