An Efficient Augmented Lagrangian-Based Method for Linear Equality-Constrained Lasso

Zengde Deng, Man Chung Yue, Anthony Man-Cho So

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review

Abstract

Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, various constrained Lasso models have been proposed in the literature. Compared with the classic (unconstrained) Lasso model, the algorithmic aspects of constrained Lasso models are much less explored. In
this paper, we demonstrate how the recently developed semismooth Newton based augmented Lagrangian framework can be extended to solve a linear equality-constrained Lasso model. A key technical challenge that is not present in prior works is the lack of strong convexity in our dual problem, which we
overcome by adopting a regularization strategy. We show that under mild assumptions, our proposed method will converge superlinearly. Moreover, extensive numerical experiments on both synthetic and real-world data show that our method can be substantially faster than existing first-order methods while achieving a better solution accuracy.
Original languageEnglish
Title of host publication2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings
Pages5760-5764
Number of pages5
ISBN (Electronic)978-1-5090-6631-5
DOIs
Publication statusPublished - May 2020

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2020-May
ISSN (Print)1520-6149

Keywords

  • augmented Lagrangian
  • constrained Lasso
  • semismooth Newton
  • superlinear convergence

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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