Tight Non-asymptotic Inference via Sub-Gaussian Intrinsic Moment Norm
Abstract
In non-asymptotic learning, variance-type parameters of sub-Gaussian distributions are of paramount importance. However, directly estimating these parameters using the empirical moment generating function (MGF) is infeasible. To address this, we suggest using the sub-Gaussian intrinsic moment norm [Buldygin and Kozachenko (2000), Theorem 1.3] achieved by maximizing a sequence of normalized moments. Significantly, the suggested norm can not only reconstruct the exponential moment bounds of MGFs but also provide tighter sub-Gaussian concentration inequalities. In practice, we provide an intuitive method for assessing whether data with a finite sample size is sub-Gaussian, utilizing the sub-Gaussian plot. The intrinsic moment norm can be robustly estimated via a simple plug-in approach. Our theoretical findings are also applicable to reinforcement learning, including the multi-armed bandit scenario.
Keywords
Cite
@article{arxiv.2303.07287,
title = {Tight Non-asymptotic Inference via Sub-Gaussian Intrinsic Moment Norm},
author = {Huiming Zhang and Haoyu Wei and Guang Cheng},
journal= {arXiv preprint arXiv:2303.07287},
year = {2026}
}
Comments
This manuscript has been withdrawn by the authors as it is not yet ready for public release. Further improvements and revisions are required before a final version can be considered for distribution