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arXiv · 2501.18381

Implicit Riemannian Optimism with Applications to Min-Max Problems

Christophe Roux·David Martínez-Rubio·Sebastian Pokutta
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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.

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Christophe Roux, David Martínez-Rubio, Sebastian Pokutta. 2025-01-30. Implicit Riemannian Optimism with Applications to Min-Max Problems. https://arxiv.org/abs/2501.18381

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