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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2501.18381 |
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| _version_ | 1866917906867027968 |
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| author | Roux, Christophe Martínez-Rubio, David Pokutta, Sebastian |
| author_facet | Roux, Christophe Martínez-Rubio, David Pokutta, Sebastian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Implicit Riemannian Optimism with Applications to Min-Max Problems Roux, Christophe Martínez-Rubio, David Pokutta, Sebastian Optimization and Control Machine Learning 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. |
| title | Implicit Riemannian Optimism with Applications to Min-Max Problems |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2501.18381 |