{"ID":2889717,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.20982","arxiv_id":"2507.20982","title":"Bernstein-type dimension-free concentration for self-normalised martingales","abstract":"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.","short_abstract":"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 w...","url_abs":"https://arxiv.org/abs/2507.20982","url_pdf":"https://arxiv.org/pdf/2507.20982v2","authors":"[\"Arya Akhavan\",\"Amitis Shidani\",\"Alex Ayoub\",\"David Janz\"]","published":"2025-07-28T16:44:20Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\"]","methods":"[]","has_code":false}