Lower bounds for non-convex stochastic optimization

We lower bound the complexity of finding ϵ -stationary points (with gradient norm at most ϵ ) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions through queries to an unbiased stochastic gradient oracle with bounded variance...

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Bibliographic Details
Published in:	Mathematical programming Vol. 199; no. 1-2; pp. 165 - 214
Main Authors:	Arjevani, Yossi, Carmon, Yair, Duchi, John C., Foster, Dylan J., Srebro, Nathan, Woodworth, Blake
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2023 Springer
Subjects:	Algorithms Analysis Calculus of Variations and Optimal Control; Optimization Combinatorics Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Theoretical 90C06 68Q25 90C15 90C26 90C30 90C60
ISSN:	0025-5610, 1436-4646
Online Access:	Get full text
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