Smooth Primal-Dual Coordinate Descent Algorithms for Nonsmooth Convex Optimization

Part of Advances in Neural Information Processing Systems 30 (NIPS 2017)

Bibtex »Metadata »Paper »Reviews »Supplemental »

Authors

Ahmet Alacaoglu, Quoc Tran Dinh, Olivier Fercoq, Volkan Cevher

Abstract

<p>We propose a new randomized coordinate descent method for a convex optimization template with broad applications. Our analysis relies on a novel combination of four ideas applied to the primal-dual gap function: smoothing, acceleration, homotopy, and coordinate descent with non-uniform sampling. As a result, our method features the first convergence rate guarantees among the coordinate descent methods, that are the best-known under a variety of common structure assumptions on the template. We provide numerical evidence to support the theoretical results with a comparison to state-of-the-art algorithms.</p>