Lower Bounds for Higher-Order Convex Optimization

Naman Agarwal; Elad Hazan

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arXiv · 1710.10329

Lower Bounds for Higher-Order Convex Optimization

Naman Agarwal·Elad Hazan

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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.

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Naman Agarwal, Elad Hazan. 2017-10-27. Lower Bounds for Higher-Order Convex Optimization. https://arxiv.org/abs/1710.10329

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