Stability-based Generalization Analysis of Randomized Coordinate Descent for Pairwise Learning
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909522421874688 |
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| author | Wu, Liang Hu, Ruixi Lei, Yunwen |
| author_facet | Wu, Liang Hu, Ruixi Lei, Yunwen |
| contents | Pairwise learning includes various machine learning tasks, with ranking and metric learning serving as the primary representatives. While randomized coordinate descent (RCD) is popular in various learning problems, there is much less theoretical analysis on the generalization behavior of models trained by RCD, especially under the pairwise learning framework. In this paper, we consider the generalization of RCD for pairwise learning. We measure the on-average argument stability for both convex and strongly convex objective functions, based on which we develop generalization bounds in expectation. The early-stopping strategy is adopted to quantify the balance between estimation and optimization. Our analysis further incorporates the low-noise setting into the excess risk bound to achieve the optimistic bound as $O(1/n)$, where $n$ is the sample size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01530 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability-based Generalization Analysis of Randomized Coordinate Descent for Pairwise Learning Wu, Liang Hu, Ruixi Lei, Yunwen Machine Learning Pairwise learning includes various machine learning tasks, with ranking and metric learning serving as the primary representatives. While randomized coordinate descent (RCD) is popular in various learning problems, there is much less theoretical analysis on the generalization behavior of models trained by RCD, especially under the pairwise learning framework. In this paper, we consider the generalization of RCD for pairwise learning. We measure the on-average argument stability for both convex and strongly convex objective functions, based on which we develop generalization bounds in expectation. The early-stopping strategy is adopted to quantify the balance between estimation and optimization. Our analysis further incorporates the low-noise setting into the excess risk bound to achieve the optimistic bound as $O(1/n)$, where $n$ is the sample size. |
| title | Stability-based Generalization Analysis of Randomized Coordinate Descent for Pairwise Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2503.01530 |