Linear convergence of SDCA in statistical estimation
Machine Learning
2017-04-04 v4 Machine Learning
Abstract
In this paper, we consider stochastic dual coordinate (SDCA) {\em without} strongly convex assumption or convex assumption. We show that SDCA converges linearly under mild conditions termed restricted strong convexity. This covers a wide array of popular statistical models including Lasso, group Lasso, and logistic regression with regularization, corrected Lasso and linear regression with SCAD regularizer. This significantly improves previous convergence results on SDCA for problems that are not strongly convex. As a by product, we derive a dual free form of SDCA that can handle general regularization term, which is of interest by itself.
Keywords
Cite
@article{arxiv.1701.07808,
title = {Linear convergence of SDCA in statistical estimation},
author = {Chao Qu and Huan Xu},
journal= {arXiv preprint arXiv:1701.07808},
year = {2017}
}