We propose a near-optimal method for highly smooth convex optimization. More precisely, in the oracle model where one obtains the pth order Taylor expansion of a function at the query point, we propose a method with rate of convergence O~(1/k23p+1) after k queries to the oracle for any convex function whose pth order derivative is Lipschitz.
@article{arxiv.1812.08026,
title = {Near-optimal method for highly smooth convex optimization},
author = {Sébastien Bubeck and Qijia Jiang and Yin Tat Lee and Yuanzhi Li and Aaron Sidford},
journal= {arXiv preprint arXiv:1812.08026},
year = {2019}
}