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

arXiv: https://arxiv.org/abs/2511.03606 · HTML: https://mlsanity.com/paper/2511.03606/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 56 references that are in the map.
- First posted on arXiv 5 Nov 2025.

## Builds on (most cited first, 24 of 24)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Nearly Minimax Optimal Reinforcement Learning for Linear Mixture Markov Decision Processes](https://mlsanity.com/paper/2012.08507/) (2020)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Improved Optimistic Algorithms for Logistic Bandits](https://mlsanity.com/paper/2002.07530/) (2020)
- [Information Directed Sampling and Bandits with Heteroscedastic Noise](https://mlsanity.com/paper/1801.09667/) (2018)
- [Nearly Minimax Optimal Reinforcement Learning for Linear Markov Decision Processes](https://mlsanity.com/paper/2212.06132/) (2022)
- [Computationally Efficient Horizon-Free Reinforcement Learning for Linear Mixture MDPs](https://mlsanity.com/paper/2205.11507/) (2022)
- [Admissible anytime-valid sequential inference must rely on nonnegative martingales](https://mlsanity.com/paper/2009.03167/) (2020)
- [Improved Variance-Aware Confidence Sets for Linear Bandits and Linear Mixture MDP](https://mlsanity.com/paper/2101.12745/) (2021)
- [Improved Regret Analysis for Variance-Adaptive Linear Bandits and Horizon-Free Linear Mixture MDPs](https://mlsanity.com/paper/2111.03289/) (2021)
- [Variance-Dependent Regret Bounds for Linear Bandits and Reinforcement Learning: Adaptivity and Computational Efficiency](https://mlsanity.com/paper/2302.10371/) (2023)
- [On the Sublinear Regret of GP-UCB](https://mlsanity.com/paper/2307.07539/) (2023)
- [Kernelized Reinforcement Learning with Order Optimal Regret Bounds](https://mlsanity.com/paper/2306.07745/) (2023)
- [Improved Algorithms for Stochastic Linear Bandits Using Tail Bounds for Martingale Mixtures](https://mlsanity.com/paper/2309.14298/) (2023)
- [Time-Uniform Self-Normalized Concentration for Vector-Valued Processes](https://mlsanity.com/paper/2310.09100/) (2023)
- [Second Order Bounds for Contextual Bandits with Function Approximation](https://mlsanity.com/paper/2409.16197/) (2024)
- [Tighter Confidence Bounds for Sequential Kernel Regression](https://mlsanity.com/paper/2403.12732/) (2024)
- [Noise-Adaptive Confidence Sets for Linear Bandits and Application to Bayesian Optimization](https://mlsanity.com/paper/2402.07341/) (2024)
- [Mean Estimation in Banach Spaces Under Infinite Variance and Martingale Dependence](https://mlsanity.com/paper/2411.11271/) (2024)
- [Generalized Kernelized Bandits: A Novel Self-Normalized Bernstein-Like Dimension-Free Inequality and Regret Bounds](https://mlsanity.com/paper/2508.01681/) (2025)
- [Model Agnostic Time Series Analysis via Matrix Estimation](https://mlsanity.com/paper/1802.09064/) (2018)
- [A variational approach to dimension-free self-normalized concentration](https://mlsanity.com/paper/2508.06483/) (2025)

## Built on by (most cited first, 4 of 4)

- [Kernel-based guarantees for nonlinear parametric models in Bayesian optimization](https://mlsanity.com/paper/2605.13160/) (2026)
- [Optimal Rates for Differentially Private Hypothesis Testing with E-values](https://mlsanity.com/paper/2605.28952/) (2026)
- [Bentkus-type asymptotic e-values](https://mlsanity.com/paper/2606.06332/) (2026)
- [Sequential operator learning under dependent data](https://mlsanity.com/paper/2608.24426/) (2026)

## Abstract (arXiv)

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.