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The First Optimal Acceleration of High-Order Methods in Smooth Convex Optimization. (arXiv:2205.09647v1 [math.OC])
May 20, 2022, 1:12 a.m. | Dmitry Kovalev, Alexander Gasnikov
cs.LG updates on arXiv.org arxiv.org
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
$\Omega\left(\epsilon^{-2/(3p+1)}\right)$ 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 …
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