A Vector Bernstein Inequality for Self-Normalized Martingales
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.
Cite
Text
Ziemann. "A Vector Bernstein Inequality for Self-Normalized Martingales." Transactions on Machine Learning Research, 2025.Markdown
[Ziemann. "A Vector Bernstein Inequality for Self-Normalized Martingales." Transactions on Machine Learning Research, 2025.](https://mlanthology.org/tmlr/2025/ziemann2025tmlr-vector/)BibTeX
@article{ziemann2025tmlr-vector,
title = {{A Vector Bernstein Inequality for Self-Normalized Martingales}},
author = {Ziemann, Ingvar},
journal = {Transactions on Machine Learning Research},
year = {2025},
url = {https://mlanthology.org/tmlr/2025/ziemann2025tmlr-vector/}
}