Stability and Sharper Risk Bounds with Convergence Rate $\tilde{O}(1/n^2)$
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912677052284928 |
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| author | Zhu, Bowei Li, Shaojie Yi, Mingyang Liu, Yong |
| author_facet | Zhu, Bowei Li, Shaojie Yi, Mingyang Liu, Yong |
| contents | Prior work (Klochkov $\&$ Zhivotovskiy, 2021) establishes at most $O\left(\log (n)/n\right)$ excess risk bounds via algorithmic stability for strongly-convex learners with high probability. We show that under the similar common assumptions -- - Polyak-Lojasiewicz condition, smoothness, and Lipschitz continous for losses -- - rates of $O\left(\log^2(n)/n^2\right)$ are at most achievable. To our knowledge, our analysis also provides the tightest high-probability bounds for gradient-based generalization gaps in nonconvex settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09766 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability and Sharper Risk Bounds with Convergence Rate $\tilde{O}(1/n^2)$ Zhu, Bowei Li, Shaojie Yi, Mingyang Liu, Yong Machine Learning Prior work (Klochkov $\&$ Zhivotovskiy, 2021) establishes at most $O\left(\log (n)/n\right)$ excess risk bounds via algorithmic stability for strongly-convex learners with high probability. We show that under the similar common assumptions -- - Polyak-Lojasiewicz condition, smoothness, and Lipschitz continous for losses -- - rates of $O\left(\log^2(n)/n^2\right)$ are at most achievable. To our knowledge, our analysis also provides the tightest high-probability bounds for gradient-based generalization gaps in nonconvex settings. |
| title | Stability and Sharper Risk Bounds with Convergence Rate $\tilde{O}(1/n^2)$ |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2410.09766 |