Learning-Rate-Free Stochastic Optimization over Riemannian Manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914823312244736 |
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| author | Dodd, Daniel Sharrock, Louis Nemeth, Christopher |
| author_facet | Dodd, Daniel Sharrock, Louis Nemeth, Christopher |
| contents | In recent years, interest in gradient-based optimization over Riemannian manifolds has surged. However, a significant challenge lies in the reliance on hyperparameters, especially the learning rate, which requires meticulous tuning by practitioners to ensure convergence at a suitable rate. In this work, we introduce innovative learning-rate-free algorithms for stochastic optimization over Riemannian manifolds, eliminating the need for hand-tuning and providing a more robust and user-friendly approach. We establish high probability convergence guarantees that are optimal, up to logarithmic factors, compared to the best-known optimally tuned rate in the deterministic setting. Our approach is validated through numerical experiments, demonstrating competitive performance against learning-rate-dependent algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02296 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning-Rate-Free Stochastic Optimization over Riemannian Manifolds Dodd, Daniel Sharrock, Louis Nemeth, Christopher Machine Learning Optimization and Control In recent years, interest in gradient-based optimization over Riemannian manifolds has surged. However, a significant challenge lies in the reliance on hyperparameters, especially the learning rate, which requires meticulous tuning by practitioners to ensure convergence at a suitable rate. In this work, we introduce innovative learning-rate-free algorithms for stochastic optimization over Riemannian manifolds, eliminating the need for hand-tuning and providing a more robust and user-friendly approach. We establish high probability convergence guarantees that are optimal, up to logarithmic factors, compared to the best-known optimally tuned rate in the deterministic setting. Our approach is validated through numerical experiments, demonstrating competitive performance against learning-rate-dependent algorithms. |
| title | Learning-Rate-Free Stochastic Optimization over Riemannian Manifolds |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2406.02296 |