The Complexity of Nonconvex-Strongly-Concave Minimax Optimization


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Date

2021

Publication Type

Conference Paper

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yes

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Abstract

This paper studies the complexity for finding approximate stationary points of nonconvex-strongly-concave (NC-SC) smooth minimax problems, in both general and averaged smooth finite-sum settings. We establish nontrivial lower complexity bounds for the two settings, respectively. Our result reveals substantial gaps between these limits and best-known upper bounds in the literature. To close these gaps, we introduce a generic acceleration scheme that deploys existing gradient-based methods to solve a sequence of crafted strongly-convex-strongly-concave subproblems. In the general setting, the complexity of our proposed algorithm nearly matches the lower bound; in particular, it removes an additional poly-logarithmic dependence on accuracy present in previous works. In the averaged smooth finite-sum setting, our proposed algorithm improves over previous algorithms by providing a nearly-tight dependence on the condition number.

Publication status

published

Book title

Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence

Volume

161

Pages / Article No.

482 - 492

Publisher

PMLR

Event

37th Conference on Uncertainty in Artificial Intelligence (UAI 2021)

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Organisational unit

09729 - He, Niao / He, Niao check_circle

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