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

Diego Martinez-Taboada, Tomás González, Aaditya Ramdas

Keywords: self-normalized processes, concentration inequalities, online linear regression

TL;DR: We provide concentration inequalities for self-normalized processes with light tails beyond sub-Gaussianity, including Bernstein-type, Bennett-type, and empirical Bennett-type inequalities.

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 inequalities for self-normalized processes with light tails beyond sub-Gaussianity, including Bernstein-type, Bennett-type, and empirical Bennett-type inequalities. We illustrate the relevance of our results in the context of online linear regression, with applications in (kernelized) linear bandits.

Submission Number: 96