English

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

Machine Learning 2026-05-18 v2 Machine Learning Statistics Theory Statistics Theory

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.

Cite

@article{arxiv.2511.03606,
  title  = {Vector-valued self-normalized concentration inequalities beyond sub-Gaussianity},
  author = {Diego Martinez-Taboada and Tomas Gonzalez and Aaditya Ramdas},
  journal= {arXiv preprint arXiv:2511.03606},
  year   = {2026}
}
R2 v1 2026-07-01T07:23:05.789Z