An accelerated gradient method for trace norm minimization

Shuiwang Ji, Jieping Ye

Research output: Chapter in Book/Report/Conference proceedingConference contribution

325 Scopus citations

Abstract

We consider the minimization of a smooth loss function regularized by the trace norm of the matrix variable. Such formulation finds applications in many machine learning tasks including multi-task learning, matrix classification, and matrix completion. The standard semidefinite programming formulation for this problem is computationally expensive. In addition, due to the non-smooth nature of the trace norm, the optimal first-order black-box method for solving such class of problems converges as O(1/√k), where k is the iteration counter. In this paper, we exploit the special structure of the trace norm, based on which we propose an extended gradient algorithm that converges as O(1/k). We further propose an accelerated gradient algorithm, which achieves the optimal convergence rate of O(1/k2) for smooth problems. Experiments on multi-task learning problems demonstrate the efficiency of the proposed algorithms.

Original languageEnglish (US)
Title of host publicationProceedings of the 26th International Conference On Machine Learning, ICML 2009
Pages457-464
Number of pages8
Publication statusPublished - 2009
Event26th International Conference On Machine Learning, ICML 2009 - Montreal, QC, Canada
Duration: Jun 14 2009Jun 18 2009

Other

Other26th International Conference On Machine Learning, ICML 2009
CountryCanada
CityMontreal, QC
Period6/14/096/18/09

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ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Networks and Communications
  • Software

Cite this

Ji, S., & Ye, J. (2009). An accelerated gradient method for trace norm minimization. In Proceedings of the 26th International Conference On Machine Learning, ICML 2009 (pp. 457-464)