A regret minimization approach to fixed-point iterations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916970782261248 |
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| author | Kwon, Joon |
| author_facet | Kwon, Joon |
| contents | We propose a conversion scheme that turns regret minimizing algorithms into fixed point iterations, with convergence guarantees following from regret bounds. The resulting iterations can be seen as a grand extension of the classical Krasnoselskii--Mann iterations, as the latter are recovered by converting the Online Gradient Descent algorithm. This approach yields new simple iterations for finding fixed points of non-self operators. We also focus on converting algorithms from the AdaGrad family of regret minimizers, and thus obtain fixed point iterations with adaptive guarantees of a new kind. Numerical experiments on various problems demonstrate faster convergence of AdaGrad-based fixed point iterations over Krasnoselskii--Mann iterations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21653 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A regret minimization approach to fixed-point iterations Kwon, Joon Optimization and Control Machine Learning Numerical Analysis 47J26, 65K10, 68W27 G.1.6 We propose a conversion scheme that turns regret minimizing algorithms into fixed point iterations, with convergence guarantees following from regret bounds. The resulting iterations can be seen as a grand extension of the classical Krasnoselskii--Mann iterations, as the latter are recovered by converting the Online Gradient Descent algorithm. This approach yields new simple iterations for finding fixed points of non-self operators. We also focus on converting algorithms from the AdaGrad family of regret minimizers, and thus obtain fixed point iterations with adaptive guarantees of a new kind. Numerical experiments on various problems demonstrate faster convergence of AdaGrad-based fixed point iterations over Krasnoselskii--Mann iterations. |
| title | A regret minimization approach to fixed-point iterations |
| topic | Optimization and Control Machine Learning Numerical Analysis 47J26, 65K10, 68W27 G.1.6 |
| url | https://arxiv.org/abs/2509.21653 |