An online conjugate gradient algorithm for large-scale data analysis in machine learning

• Main Authors: Wei Xue, Pengcheng Wan, Qiao Li, Ping Zhong, Gaohang Yu, Tao Tao
• Format: Article
• Language: English
• Published: AIMS Press 2021-12-01
• Series: AIMS Mathematics
• Subjects: machine learning; online learning; stochastic optimization; conjugate gradient; variance reduction
• Online Access: http://awstest.aimspress.com/article/doi/10.3934/math.2021092?viewType=HTML

In recent years, the amount of available data is growing exponentially, and large-scale data is becoming ubiquitous. Machine learning is a key to deriving insight from this deluge of data. In this paper, we focus on the large-scale data analysis, especially classification data, and propose an online conjugate gradient (CG) descent algorithm. Our algorithm draws from a recent improved Fletcher-Reeves (IFR) CG method proposed in Jiang and Jian[13] as well as a recent approach to reduce variance for stochastic gradient descent from Johnson and Zhang [15]. In theory, we prove that the proposed online algorithm achieves a linear convergence rate under strong Wolfe line search when the objective function is smooth and strongly convex. Comparison results on several benchmark classification datasets demonstrate that our approach is promising in solving large-scale machine learning problems, viewed from the points of area under curve (AUC) value and convergence behavior.