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Lower Bounds For Finding Stationary Points Ii: First-Order Methods

MATHEMATICAL PROGRAMMING, no. 1-2 (2021): 315-355

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academic.microsoft.com arxiv.org dblp.uni-trier.de

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Non-convex optimization Information-based complexity Dimension-free rates Gradient methods Accelerated gradient descent

Abstract

We establish lower bounds on the complexity of finding similar to-stationary points of smooth, non-convex high-dimensional functions using first-order methods. We prove that deterministic first-order methods, even applied to arbitrarily smooth functions, cannot achieve convergence rates in similar to better than similar to -8/5, which is ...More

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