超越单调性的邻近点法与外梯度法的收敛性：负共单调情形
最优化与控制
2023-07-19 v3
摘要
极小极大优化与变分不等式的算法通常在单调性假设下被研究。受非单调机器学习应用的启发，我们延续[Diakonikolas等人，2021；Lee与Kim，2021；Pethick等人，2022；Böhm，2022]的工作路线，旨在通过考虑更弱的否定共单调性（negative comonotonicity）假设来超越单调性。具体而言，我们在此设定下对邻近点法、外梯度法和乐观梯度法给出了紧致复杂度分析，从而澄清了它们在单调性之外成立保证的一些问题。
引用
@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}
}
备注
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