Coordinate descent algorithms

• 成果类型: Article; Proceedings Paper
• 署名作者: Wright, Stephen J.
• 署名单位: University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0892-3
• 发表日期: 2015
• 页码: 3-34
• 关键词: convergence; optimization; minimization; tomography; regression; shrinkage

摘要

Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity continues to grow because of their usefulness in data analysis, machine learning, and other areas of current interest. This paper describes the fundamentals of the coordinate descent approach, together with variants and extensions and their convergence properties, mostly with reference to convex objectives. We pay particular attention to a certain problem structure that arises frequently in machine learning applications, showing that efficient implementations of accelerated coordinate descent algorithms are possible for problems of this type. We also present some parallel variants and discuss their convergence properties under several models of parallel execution.