Near-optimal method for highly smooth convex optimization

Sebastien Bubeck, Qijia Jiang, Yin Tat Lee, Yuanzhi Li, Aaron Sidford

Abstract: 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 $O(1/k^{3p+1/2} )$ after k queries to the oracle for any convex function whose pth order derivative is Lipschitz.