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

• URL: http://arxiv.org/abs/2511.03606v1
• Date: Wed, 05 Nov 2025 16:27:02 GMT
• Title: Vector-valued self-normalized concentration inequalities beyond sub-Gaussianity
• Authors: Diego Martinez-Taboada, Tomas Gonzalez, Aaditya Ramdas,
• Abstract summary: We provide concentration bounds for self-normalized processes with light tails beyond sub-Gaussianity (such as Bennett or Bernstein bounds)<n>We illustrate the relevance of our results in the context of online linear regression, with applications in ( Kernelized) linear bandits.
• Score: 35.13282725119597
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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