Convergence of Proximal Point and Extragradient-Based Methods Beyond Monotonicity: the Case of Negative Comonotonicity
Abstract
Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works [Diakonikolas et al., 2021, Lee and Kim, 2021, Pethick et al., 2022, B\"ohm, 2022] aiming at going beyond monotonicity by considering the weaker negative comonotonicity assumption. In particular, we provide tight complexity analyses for the Proximal Point, Extragradient, and Optimistic Gradient methods in this setup, closing some questions on their working guarantees beyond monotonicity.
Keywords
Cite
@article{arxiv.2210.13831,
title = {Convergence of Proximal Point and Extragradient-Based Methods Beyond Monotonicity: the Case of Negative Comonotonicity},
author = {Eduard Gorbunov and Adrien Taylor and Samuel Horváth and Gauthier Gidel},
journal= {arXiv preprint arXiv:2210.13831},
year = {2023}
}
Comments
ICML 2023. 28 pages, 2 figures. Changes in V2: missing reference was added. Changes in V3: ICML formatting was applied, missing references were added, Table 1 was added. Code: https://github.com/eduardgorbunov/Proximal_Point_and_Extragradient_based_methods_negative_comonotonicity