2014/08/13 by Tianbao Yang, Rong Jin, Yang, Tianbao +5
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1408.3115
openalex publication_date 2014/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we study data preconditioning, a well-known and long-existing technique, for boosting the convergence of first-order methods for regularized loss minimization. It is well understood that the condition number of the problem, i.e., the ratio of the Lipschitz constant to the strong convexity modulus, has a harsh effect on the convergence of the first-order optimization methods. Therefore, minimizing a small regularized loss for achieving good generalization performance, yielding an ill conditioned problem, becomes the bottleneck for big data problems. We provide a theory on data preconditioning for regularized loss minimization. In particular, our analysis exhibits an appropriate data preconditioner and characterizes the conditions on the loss function and on the data under which data preconditioning can reduce the condition number and therefore boost the convergence for minimizing the regularized loss. To make the data preconditioning practically useful, we endeavor to employ and analyze a random sampling approach to efficiently compute the preconditioned data. The preliminary experiments validate our theory.