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- W4306885929 abstract "Despite the established convergence theory of Optimistic Gradient Descent Ascent (OGDA) and Extragradient (EG) methods for the convex-concave minimax problems, little is known about the theoretical guarantees of these methods in nonconvex settings. To bridge this gap, for the first time, this paper establishes the convergence of OGDA and EG methods under the nonconvex-strongly-concave (NC-SC) and nonconvex-concave (NC-C) settings by providing a unified analysis through the lens of single-call extra-gradient methods. We further establish lower bounds on the convergence of GDA/OGDA/EG, shedding light on the tightness of our analysis. We also conduct experiments supporting our theoretical results. We believe our results will advance the theoretical understanding of OGDA and EG methods for solving complicated nonconvex minimax real-world problems, e.g., Generative Adversarial Networks (GANs) or robust neural networks training." @default.
- W4306885929 created "2022-10-21" @default.
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- W4306885929 date "2022-10-17" @default.
- W4306885929 modified "2023-09-29" @default.
- W4306885929 title "Tight Analysis of Extra-gradient and Optimistic Gradient Methods For Nonconvex Minimax Problems" @default.
- W4306885929 doi "https://doi.org/10.48550/arxiv.2210.09382" @default.
- W4306885929 hasPublicationYear "2022" @default.
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