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.

翻译：自归一化过程的研究在从序列决策到计量经济学的广泛应用中起着至关重要的作用。虽然标量值过程的自归一化集中行为已得到广泛研究，但向量值过程，尤其是在亚高斯框架之外，仍然相对探索不足。在本研究中，我们为具有超越亚高斯性的轻尾（例如Bennett或Bernstein界）的自归一化过程提供了集中界。我们通过在线线性回归的案例，说明了我们结果的相关性，并将其应用于（核化）线性赌博机问题。