This paper revisits the Polyak step size schedule for convex optimization problems, proving that a simple variant of it simultaneously attains near optimal convergence rates for the gradient descent algorithm, for all ranges of strong convexity, smoothness, and Lipschitz parameters, without a-priory knowledge of these parameters.
@article{arxiv.1905.00313,
title = {Revisiting the Polyak step size},
author = {Elad Hazan and Sham Kakade},
journal= {arXiv preprint arXiv:1905.00313},
year = {2022}
}