An optimal gradient method for smooth strongly convex minimization

TL;DR

This paper introduces an optimal gradient method for smooth strongly convex problems that achieves the best possible worst-case performance, matching theoretical lower bounds, and provides a systematic way to determine its parameters.

Contribution

The paper proposes a new optimal gradient method with a constructive approach for parameter selection, applicable to various optimality criteria.

Findings

Method achieves worst-case bounds matching lower bounds.

Constructive recipe for algorithmic parameters.

Applicable to different optimality criteria.

Abstract

We present an optimal gradient method for smooth strongly convex optimization. The method is optimal in the sense that its worst-case bound on the distance to an optimal point exactly matches the lower bound on the oracle complexity for the class of problems, meaning that no black-box first-order method can have a better worst-case guarantee without further assumptions on the class of problems at hand. In addition, we provide a constructive recipe for obtaining the algorithmic parameters of the method and illustrate that it can be used for deriving methods for other optimality criteria as well.