An optimal gradient method for smooth strongly convex minimization

Adrien Taylor; Yoel Drori

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arXiv · 2101.09741

An optimal gradient method for smooth strongly convex minimization

Adrien Taylor·Yoel Drori

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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.

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Adrien Taylor, Yoel Drori. 2021-01-24. An optimal gradient method for smooth strongly convex minimization. https://arxiv.org/abs/2101.09741

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