Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties
Abstract
In this work, we study optimization problems of the form $\min_x \max_y f(x, y)$, where $f(x, y)$ is defined on a product Riemannian manifold $\mathcal{M} \times \mathcal{N}$ and is $\mu_x$-strongly geodesically convex (g-convex) in $x$ and $\mu_y$-strongly g-concave in $y$, for $\mu_x, \mu_y \geq 0$. We design accelerated methods when $f$ is $(L_x, L_y, L_{xy})$-smooth and $\mathcal{M}$, $\mathcal{N}$ are Hadamard. To that aim we introduce new g-convex optimization results, of independent interest: we show global linear convergence for metric-projected Riemannian gradient descent and improve existing accelerated methods by reducing geometric constants. Additionally, we complete the analysis of two previous works applying to the Riemannian min-max case by removing an assumption about iterates staying in a pre-specified compact set.
Cite
Text
Martínez-Rubio et al. "Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties." Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, 2025.Markdown
[Martínez-Rubio et al. "Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties." Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, 2025.](https://mlanthology.org/aistats/2025/martinezrubio2025aistats-accelerated/)BibTeX
@inproceedings{martinezrubio2025aistats-accelerated,
title = {{Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties}},
author = {Martínez-Rubio, David and Roux, Christophe and Criscitiello, Christopher and Pokutta, Sebastian},
booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics},
year = {2025},
pages = {280-288},
volume = {258},
url = {https://mlanthology.org/aistats/2025/martinezrubio2025aistats-accelerated/}
}