In this short note, I show how to adapt to H\"{o}lder smoothness using normalized gradients in a black-box way. Moreover, the bound will depend on a novel notion of local H\"{o}lder smoothness. The main idea directly comes from Levy [2017].
Cite
@article{arxiv.2308.05621,
title = {Normalized Gradients for All},
author = {Francesco Orabona},
journal= {arXiv preprint arXiv:2308.05621},
year = {2023}
}