Coordinate Descent with Arbitrary Sampling I: Algorithms and Complexity

Zheng Qu; Peter Richtárik

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arXiv · 1412.8060

Coordinate Descent with Arbitrary Sampling I: Algorithms and Complexity

Zheng Qu·Peter Richtárik

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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 remarkably 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.

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BibTeX RIS

Zheng Qu, Peter Richtárik. 2014-12-27. Coordinate Descent with Arbitrary Sampling I: Algorithms and Complexity. https://arxiv.org/abs/1412.8060

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