Self-Concordant Perturbations for Linear Bandits
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910020391665664 |
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| author | Lévy, Lucas Valeau, Jean-Lou Akhavan, Arya Rebeschini, Patrick |
| author_facet | Lévy, Lucas Valeau, Jean-Lou Akhavan, Arya Rebeschini, Patrick |
| contents | We consider the adversarial linear bandits setting and present a unified algorithmic framework that bridges Follow-the-Regularized-Leader (FTRL) and Follow-the-Perturbed-Leader (FTPL) methods, extending the known connection between them from the full-information setting. Within this framework, we introduce self-concordant perturbations, a family of probability distributions that mirror the role of self-concordant barriers previously employed in the FTRL-based SCRiBLe algorithm. Using this idea, we design a novel FTPL-based algorithm that combines self-concordant regularization with efficient stochastic exploration. Our approach achieves a regret of $\mathcal{O}(d\sqrt{n \ln n})$ on both the $d$-dimensional hypercube and the $\ell_2$ ball. On the $\ell_2$ ball, this matches the rate attained by SCRiBLe. For the hypercube, this represents a $\sqrt{d}$ improvement over these methods and matches the optimal bound up to logarithmic factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24187 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-Concordant Perturbations for Linear Bandits Lévy, Lucas Valeau, Jean-Lou Akhavan, Arya Rebeschini, Patrick Machine Learning We consider the adversarial linear bandits setting and present a unified algorithmic framework that bridges Follow-the-Regularized-Leader (FTRL) and Follow-the-Perturbed-Leader (FTPL) methods, extending the known connection between them from the full-information setting. Within this framework, we introduce self-concordant perturbations, a family of probability distributions that mirror the role of self-concordant barriers previously employed in the FTRL-based SCRiBLe algorithm. Using this idea, we design a novel FTPL-based algorithm that combines self-concordant regularization with efficient stochastic exploration. Our approach achieves a regret of $\mathcal{O}(d\sqrt{n \ln n})$ on both the $d$-dimensional hypercube and the $\ell_2$ ball. On the $\ell_2$ ball, this matches the rate attained by SCRiBLe. For the hypercube, this represents a $\sqrt{d}$ improvement over these methods and matches the optimal bound up to logarithmic factors. |
| title | Self-Concordant Perturbations for Linear Bandits |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.24187 |