ICML 2025poster0 citations
Implicit Riemannian Optimism with Applications to Min-Max Problems
Christophe Roux, David Martínez-Rubio, Sebastian Pokutta
Abstract
We introduce a Riemannian optimistic online learning algorithm for Hadamard manifolds based on inexact implicit updates. Unlike prior work, our method can handle in-manifold constraints, and matches the best known regret bounds in the Euclidean setting with no dependence on geometric constants, like the minimum curvature. Building on this, we develop algorithms for g-convex, g-concave smooth min-max problems on Hadamard manifolds. Notably, one method nearly matches the gradient oracle complexity of the lower bound for Euclidean problems, for the first time.
Riemannian OptimizationOptimistic algorithmsOnline OptimizationMin-Max optimization
BibTeX
@inproceedings{
roux2025implicit,
title={Implicit Riemannian Optimism with Applications to Min-Max Problems},
author={Christophe Roux and David Mart{\'\i}nez-Rubio and Sebastian Pokutta},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=Mz4J6GRZso}
}