Nonconvex-Nonconcave Min-Max Optimization on Riemannian Manifolds
Abstract
This work studies nonconvex-nonconcave min-max problems on Riemannian manifolds. We first characterize the local optimality of nonconvex-nonconcave problems on manifolds with a generalized notion of local minimax points. We then define the stability and convergence criteria of dynamical systems on manifolds and provide necessary and sufficient conditions of strictly stable equilibrium points for both continuous and discrete dynamics. Additionally, we propose several novel second-order methods on manifolds that provably converge to local minimax points asymptotically. We validate the empirical benefits of the proposed methods with extensive experiments.
Cite
Text
Han et al. "Nonconvex-Nonconcave Min-Max Optimization on Riemannian Manifolds." Transactions on Machine Learning Research, 2023.Markdown
[Han et al. "Nonconvex-Nonconcave Min-Max Optimization on Riemannian Manifolds." Transactions on Machine Learning Research, 2023.](https://mlanthology.org/tmlr/2023/han2023tmlr-nonconvexnonconcave/)BibTeX
@article{han2023tmlr-nonconvexnonconcave,
title = {{Nonconvex-Nonconcave Min-Max Optimization on Riemannian Manifolds}},
author = {Han, Andi and Mishra, Bamdev and Jawanpuria, Pratik and Gao, Junbin},
journal = {Transactions on Machine Learning Research},
year = {2023},
url = {https://mlanthology.org/tmlr/2023/han2023tmlr-nonconvexnonconcave/}
}