Near-optimal method for highly smooth convex optimization

2018/12/19 by Sébastien Bubeck, Bubeck, Sébastien, Qijia Jiang +7 · 3 citations
Computer Science · Engineering · #Complexity and Algorithms in Graphs #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.1812.08026

openalex publication_date 2018/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a near-optimal method for highly smooth convex optimization. More precisely, in the oracle model where one obtains the p^th 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 p^th order derivative is Lipschitz.

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• Optimal Convex Optimization with Inexact Second-Order Oracles
• Solving Zero-Sum Games with Fewer Matrix-Vector Products
• Simple Stepsize for Quasi-Newton Methods with Global Convergence Guarantees

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