Near-optimal method for highly smooth convex optimization

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

arXiv comment15 pages

Cited by in corpus (9)

• A Control-Theoretic Perspective on Optimal High-Order Optimization
• Near-Optimal Methods for Minimizing Star-Convex Functions and Beyond
• Optimization with Momentum: Dynamical, Control-Theoretic, and Symplectic Perspectives
• A Unified Adaptive Tensor Approximation Scheme to Accelerate Composite Convex Optimization
• Acceleration via Fractal Learning Rate Schedules
• High-Order Oracle Complexity of Smooth and Strongly Convex Optimization
• Convex optimization
• Monotone Inclusions, Acceleration and Closed-Loop Control
• Accelerated Proximal Envelopes: Application to the Coordinate Descent Method