Vector-valued self-normalized concentration inequalities beyond sub-Gaussianity

Diego Martinez-Taboada; Tomas Gonzalez; Aaditya Ramdas

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arXiv · 2511.03606

Vector-valued self-normalized concentration inequalities beyond sub-Gaussianity

Diego Martinez-Taboada·Tomas Gonzalez·Aaditya Ramdas

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Abstract

The study of self-normalized processes plays a crucial role in a wide range of applications, from sequential decision-making to econometrics. While the behavior of self-normalized concentration has been widely investigated for scalar-valued processes, vector-valued processes remain comparatively underexplored, especially outside of the sub-Gaussian framework. In this contribution, we provide concentration bounds for self-normalized processes with light tails beyond sub-Gaussianity (such as Bennett or Bernstein bounds). We illustrate the relevance of our results in the context of online linear regression, with applications in (kernelized) linear bandits.

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Diego Martinez-Taboada, Tomas Gonzalez, Aaditya Ramdas. 2025-11-05. Vector-valued self-normalized concentration inequalities beyond sub-Gaussianity. https://arxiv.org/abs/2511.03606

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