On quadratic convergence of DC proximal Newton algorithm in nonconvex sparse learning

Xingguo Li, Lin F. Yang, Jason Ge, Jarvis D Haupt, Tong Zhang, Tuo Zhao

Research output: Contribution to journalConference articlepeer-review

5 Scopus citations

Abstract

We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the difference of convex (DC) programming, and enjoys both strong computational and statistical guarantees. Specifically, by leveraging a sophisticated characterization of sparse modeling structures (i.e., local restricted strong convexity and Hessian smoothness), we prove that within each stage of convex relaxation, our proposed algorithm achieves (local) quadratic convergence, and eventually obtains a sparse approximate local optimum with optimal statistical properties after only a few convex relaxations. Numerical experiments are provided to support our theory.

Original languageEnglish (US)
Pages (from-to)2743-2753
Number of pages11
JournalAdvances in Neural Information Processing Systems
Volume2017-December
StatePublished - Jan 1 2017
Event31st Annual Conference on Neural Information Processing Systems, NIPS 2017 - Long Beach, United States
Duration: Dec 4 2017Dec 9 2017

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