The First Optimal Acceleration of High-Order Methods in Smooth Convex Optimization

arXiv2205.09647MaRDI QIDQ6399622

Author name not available (Why is that?)

Publication date: 19 May 2022

Abstract: In this paper, we study the fundamental open question of finding the optimal high-order algorithm for solving smooth convex minimization problems. Arjevani et al. (2019) established the lower bound $Omegaleft(epsilo{n}^{-2/(3p+1)}ight)$ on the number of the $p$-th order oracle calls required by an algorithm to find an $epsilon$-accurate solution to the problem, where the $p$-th order oracle stands for the computation of the objective function value and the derivatives up to the order $p$. However, the existing state-of-the-art high-order methods of Gasnikov et al. (2019b); Bubeck et al. (2019); Jiang et al. (2019) achieve the oracle complexity $mathcalOleft(epsilo{n}^{-2/(3p+1)}log(1/epsilon)ight)$, which does not match the lower bound. The reason for this is that these algorithms require performing a complex binary search procedure, which makes them neither optimal nor practical. We fix this fundamental issue by providing the first algorithm with $mathcalOleft(epsilo{n}^{-2/(3p+1)}ight)$ $p$-th order oracle complexity.

Has companion code repository: https://github.com/OPTAMI/OPTAMI

This page was built for publication: The First Optimal Acceleration of High-Order Methods in Smooth Convex Optimization

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6399622)