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A Vector Bernstein Inequality for Self-Normalized Martingales
Ingvar Ziemann · 2024-12-30 · via math.PR updates on arXiv.org

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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