A Vector Bernstein Inequality for Self-Normalized Martingales
Probability
2025-01-07 v2
Abstract
We prove a Bernstein inequality for vector-valued self-normalized martingales. We first give an alternative perspective of the corresponding sub-Gaussian bound due to Abbasi-Yadkori et al. via a PAC-Bayesian argument with Gaussian priors. By instantiating this argument to priors drawn uniformly over well-chosen ellipsoids, we obtain a Bernstein bound.
Keywords
Cite
@article{arxiv.2412.20949,
title = {A Vector Bernstein Inequality for Self-Normalized Martingales},
author = {Ingvar Ziemann},
journal= {arXiv preprint arXiv:2412.20949},
year = {2025}
}