An accelerated communication-efficient primal-dual optimization framework for structured machine learning. (2nd January 2021)

• Record Type: Journal Article
• Authors: Ma, Chenxin; Jaggi, Martin; Curtis, Frank E.; Srebro, Nathan; Takáč, Martin
• Is Part Of: Optimization methods and software. Volume 36:Number 1(2021)
• Page Start: 20
• Page End: 44
• Publication Date: 2021-01-02
• Subjects: Nonlinear optimization -- nonsmooth optimization -- distributed optimization -- machine learning -- accelerated methods; 90C25; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2019.1650361
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : Distributed optimization algorithms are essential for training machine learning models on very large-scale datasets. However, they often suffer from communication bottlenecks. Confronting this issue, a communication-efficient primal-dual coordinate ascent framework (CoCoA) and its improved variant CoCoA+ have been proposed, achieving a convergence rate of O ( 1 / t ) for solving empirical risk minimization problems with Lipschitz continuous losses. In this paper, an accelerated variant of CoCoA+ is proposed and shown to possess a convergence rate of O ( 1 / t 2 ) in terms of reducing suboptimality. The analysis of this rate is also notable in that the convergence rate bounds involve constants that, except in extreme cases, are significantly reduced compared to those previously provided for CoCoA+. The results of numerical experiments are provided to show that acceleration can lead to significant performance gains.