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A Vector Bernstein Inequality for Self-Normalized Martingales

Authors
Ingvar Ziemann
Year
2024
Preprint
Identifiers
arXiv 2412.20949

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.

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