Abstract
We study the problem of minimizing the sum of a smooth convex function and a convex block-separable regularizer and propose a new randomized coordinate descent method, which we call ALPHA. Our method at every iteration updates a random subset of coordinates, following an arbitrary distribution. No coordinate descent methods capable to handle an arbitrary sampling have been studied in the literature before for this problem. ALPHA is a very flexible algorithm: in special cases, it reduces to deterministic and randomized methods such as gradient descent, coordinate descent, parallel coordinate descent and distributed coordinate descent—both in nonaccelerated and accelerated variants. The variants with arbitrary (or importance) sampling are new. We provide a complexity analysis of ALPHA, from which we deduce as a direct corollary complexity bounds for its many variants, all matching or improving best known bounds.
Original language | English (US) |
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Pages (from-to) | 829-857 |
Number of pages | 29 |
Journal | Optimization Methods and Software |
Volume | 31 |
Issue number | 5 |
DOIs | |
State | Published - Sep 2 2016 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2016 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
Keywords
- accelerated coordinate descent
- arbitrary sampling
- complexity analysis
- coordinate descent
ASJC Scopus subject areas
- Software
- Control and Optimization
- Applied Mathematics