@inproceedings{
mart{\'\i}nez-rubio2023accelerated,
title={Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties},
author={David Mart{\'\i}nez-Rubio and Christophe Roux and Christopher Criscitiello and Sebastian Pokutta},
booktitle={OPT 2023: Optimization for Machine Learning},
year={2023},
url={https://openreview.net/forum?id=zjTqK4X21G}
}
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.
Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties
David Martínez-Rubio Christophe Roux Christopher Criscitiello Sebastian Pokutta