On the Complexity of a Practical Primal-Dual Coordinate Method

TL;DR

This paper establishes complexity bounds for the PURE-CD primal-dual coordinate method, demonstrating its efficiency and theoretical guarantees in solving convex-concave min-max problems with bilinear coupling.

Contribution

It provides the first comprehensive complexity analysis of PURE-CD, matching or surpassing existing results for dense and sparse convex-concave problems.

Findings

Complexity bounds match or improve existing results.

PURE-CD performs well on dense and sparse problems.

Theoretical guarantees support practical efficiency.

Abstract

We prove complexity bounds for the primal-dual algorithm with random extrapolation and coordinate descent (PURE-CD), which has been shown to obtain good practical performance for solving convex-concave min-max problems with bilinear coupling. Our complexity bounds either match or improve the best-known results in the literature for both dense and sparse (strongly)-convex-(strongly)-concave problems.