Smooth Primal-Dual Coordinate Descent Algorithms for Nonsmooth Convex Optimization
This work addresses optimization problems in machine learning and data science, offering incremental improvements in efficiency for a broad class of applications.
The authors tackled nonsmooth convex optimization by proposing a new randomized coordinate descent method that combines smoothing, acceleration, homotopy, and non-uniform sampling, achieving best-known convergence rates under various structure assumptions.
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.