Conference proceeding
An Adaptive Accelerated Proximal Gradient Method and its Homotopy Continuation for Sparse Optimization
INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 32 (CYCLE 1), Vol.32
Proceedings of Machine Learning Research
01/01/2014
Abstract
We first propose an adaptive accelerated proximal gradient (APG) method for minimizing strongly convex composite functions with unknown convexity parameters. This method incorporates a restarting scheme to automatically estimate the strong convexity parameter and achieves a nearly optimal iteration complexity. Then we consider the l(1)-regularized least-squares (l(1)-LS) problem in the high-dimensional setting. Although such an objective function is not strongly convex, it has restricted strong convexity over sparse vectors. We exploit this property by combining the adaptive APG method with a homotopy continuation scheme, which generates a sparse solution path towards optimality. This method obtains a global linear rate of convergence and its overall iteration complexity has a weaker dependency on the restricted condition number than previous work.
Details
- Title: Subtitle
- An Adaptive Accelerated Proximal Gradient Method and its Homotopy Continuation for Sparse Optimization
- Creators
- Qihang Lin - Univ Iowa, Iowa City, IA 52245 USALin Xiao - Microsoft Research
- Contributors
- E P Xing (Editor)T Jebara (Editor)
- Resource Type
- Conference proceeding
- Publication Details
- INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 32 (CYCLE 1), Vol.32
- Publisher
- JMLR-JOURNAL MACHINE LEARNING RESEARCH
- Series
- Proceedings of Machine Learning Research
- ISSN
- 2640-3498
- Number of pages
- 9
- Language
- English
- Date published
- 01/01/2014
- Academic Unit
- Business Analytics
- Record Identifier
- 9984380496902771
Metrics
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