Primal-dual Accelerated Mirror-Descent Method for Constrained Bilinear Saddle-Point Problems

TL;DR

This paper introduces an accelerated primal-dual mirror-descent algorithm for constrained bilinear saddle-point problems, achieving fast convergence and applicability to network systems, distributed optimization, and zero-sum games.

Contribution

It presents a novel accelerated primal-dual mirror-descent method with convergence rate $O(1/t^2)$ for constrained saddle-point problems, including distributed and game-theoretic applications.

Findings

Achieves $O(1/t^2)$ convergence rate.

Effectively handles simplex and convex set constraints.

Develops distributed accelerated algorithms for network systems.

Abstract

We develop a first-order accelerated algorithm for a class of constrained bilinear saddle-point problems with applications to network systems. The algorithm is a modified time-varying primal-dual version of an accelerated mirror-descent dynamics. It deals with constraints such as simplices and convex set constraints effectively, and converges with a rate of $O(1/t^2)$. Furthermore, we employ the acceleration scheme to constrained distributed optimization and bilinear zero-sum games, and obtain two variants of distributed accelerated algorithms.