拓展了非高斯轻尾向量自归一化浓度不等式，适用于在线线性回归。
Vector-valued self-normalized concentration inequalities beyond sub-Gaussianity
- 基于贝内特和伯恩斯坦界，推广向量自归一化过程的浓度分析
- 在核线性赌博机中实现更紧的置信区间，提升算法稳定性
- 适合关注在线学习与强化学习理论的研究者
自归一化过程在序列决策、计量经济学等领域至关重要。尽管标量情形下的自归一化浓度已有广泛研究，但向量情形尤其在非亚高斯框架下仍鲜有探索。本文针对轻尾分布（如贝内特或伯恩斯坦类型）的向量自归一化过程，提供了新的浓度界。结果在在线线性回归中具有实际意义，可直接应用于（核化）线性赌博机问题。
原文摘要 · Abstract (English)
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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