Acceleration for Compressed Gradient Descent in Distributed Optimization

Jul 12, 2020

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Due to the high communication cost in distributed and federated learning problems, methods relying on sparsification or quantization of communicated messages are becoming increasingly popular. While in other contexts the best performing gradient-type methods invariably rely on some form of acceleration to reduce the number of iterations, there are no methods which combine the benefits of both gradient compression and acceleration. In this paper, we remedy this situation and propose the first accelerated compressed gradient descent (ACGD) methods. In the single machine regime, we prove that ACGD enjoys the rate O((1+ω)√(L/μ)log1/ϵ) for μ-strongly convex problems and O((1+ω)√(L/ϵ)) for convex problems, respectively, where L is the smoothness constant and ω is the variance parameter of an unbiased compression operator. Our results improve upon the existing non-accelerated rates O((1+ω)L/μlog1/ϵ) and O((1+ω)L/ϵ), respectively, and recover the best known rates of accelerated gradient descent as a special case when no compression (ω=0) is applied. We further propose a distributed variant of ACGD and establish the rate Õ(ω+√(L/μ) +√((ω/n+√(ω/n))ω L/μ)), where n is the number of machines and Õ hides the logarithmic factor log1/ϵ . This improves upon the previous best result Õ(ω + L/μ+ω L/nμ) achieved by the DIANA method. Finally, we conduct several experiments on real-world datasets which corroborate our theoretical results and confirm the practical superiority of our methods.

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The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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