Bernstein-type dimension-free concentration for self-normalised martingales
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914576754278400 |
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| author | Akhavan, Arya Shidani, Amitis Ayoub, Alex Janz, David |
| author_facet | Akhavan, Arya Shidani, Amitis Ayoub, Alex Janz, David |
| contents | We introduce a dimension-free Bernstein-type tail inequality for self-normalised martingales, where the normalisation uses the predictable quadratic variation and the radius depends on the information gain of the observed covariance. As applications, we provide ellipsoidal confidence sequences for logistic regression with adaptively chosen Hilbert-valued covariates, and give instance-adaptive regret bounds for Hilbert-armed logistic bandits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20982 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bernstein-type dimension-free concentration for self-normalised martingales Akhavan, Arya Shidani, Amitis Ayoub, Alex Janz, David Probability Statistics Theory We introduce a dimension-free Bernstein-type tail inequality for self-normalised martingales, where the normalisation uses the predictable quadratic variation and the radius depends on the information gain of the observed covariance. As applications, we provide ellipsoidal confidence sequences for logistic regression with adaptively chosen Hilbert-valued covariates, and give instance-adaptive regret bounds for Hilbert-armed logistic bandits. |
| title | Bernstein-type dimension-free concentration for self-normalised martingales |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2507.20982 |