Lower Bounds for Higher-Order Convex Optimization
Optimization and Control
2017-10-31 v1 Machine Learning
Machine Learning
Abstract
State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization, a polynomial dependence on the approximation guarantee and higher-order smoothness parameters is necessary. As a special case, we show Nesterov's accelerated cubic regularization method to be nearly tight.
Cite
@article{arxiv.1710.10329,
title = {Lower Bounds for Higher-Order Convex Optimization},
author = {Naman Agarwal and Elad Hazan},
journal= {arXiv preprint arXiv:1710.10329},
year = {2017}
}