Bernstein-type dimension-free concentration for self-normalised martingales
Probability
2026-05-19 v2 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.2507.20982,
title = {Bernstein-type dimension-free concentration for self-normalised martingales},
author = {Arya Akhavan and Amitis Shidani and Alex Ayoub and David Janz},
journal= {arXiv preprint arXiv:2507.20982},
year = {2026}
}