Stochastic Conjugate Gradient Algorithm With Variance Reduction

• Published in: IEEE transaction on neural networks and learning systems Vol. 30; no. 5; pp. 1360 - 1369
• Main Authors: Jin, Xiao-Bo, Zhang, Xu-Yao, Huang, Kaizhu, Geng, Guang-Gang
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.05.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Approximation algorithms; Computational efficiency; Computational modeling; Computer applications; Computing time; Conjugates; Convergence; covariance reduction; empirical risk minimization (ERM); Learning systems; linear convergence; Linear equations; Machine learning; Nonlinear equations; Optimization; Reduction; stochastic conjugate gradient (CG); Stochastic processes; Stochasticity
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2018.2868835

Conjugate gradient (CG) methods are a class of important methods for solving linear equations and nonlinear optimization problems. In this paper, we propose a new stochastic CG algorithm with variance reduction<xref rid="fn1" ref-type="fn"> 1 and we prove its linear convergence with the Fletcher and Reeves method for strongly convex and smooth functions. We experimentally demonstrate that the CG with variance reduction algorithm converges faster than its counterparts for four learning models, which may be convex, nonconvex or nonsmooth. In addition, its area under the curve performance on six large-scale data sets is comparable to that of the LIBLINEAR solver for the <inline-formula> <tex-math notation="LaTeX">L2 </tex-math></inline-formula>-regularized <inline-formula> <tex-math notation="LaTeX">L2 </tex-math></inline-formula>-loss but with a significant improvement in computational efficiency. 1 CGVR algorithm is available on github: https://github.com/xbjin/cgvr