mlsanityData to 14 Oct 2026

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

arXiv 2511.03606 ↗First posted 5 Nov 2025stat.ML cs.LG math.STcited by 4

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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.

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

24 of 56 references.

References · 24

  1. 2017On Kernelized Multi-armed Banditscited by 352
  2. 2018Time-uniform, nonparametric, nonasymptotic confidence sequencescited by 229
  3. 2020Nearly Minimax Optimal Reinforcement Learning for Linear Mixture Markov Decision Processescited by 200
  4. 2020On Information Gain and Regret Bounds in Gaussian Process Banditscited by 158
  5. 2022Game-theoretic statistics and safe anytime-valid inferencecited by 155
  6. 2020Improved Optimistic Algorithms for Logistic Banditscited by 118
  7. 2018Information Directed Sampling and Bandits with Heteroscedastic Noisecited by 76
  8. 2022Nearly Minimax Optimal Reinforcement Learning for Linear Markov Decision Processescited by 57
  9. 2022Computationally Efficient Horizon-Free Reinforcement Learning for Linear Mixture MDPscited by 52
  10. 2020Admissible anytime-valid sequential inference must rely on nonnegative martingalescited by 48
  11. 2021Improved Variance-Aware Confidence Sets for Linear Bandits and Linear Mixture MDPcited by 45
  12. 2021Improved Regret Analysis for Variance-Adaptive Linear Bandits and Horizon-Free Linear Mixture MDPscited by 44
12 more
  1. 2023Variance-Dependent Regret Bounds for Linear Bandits and Reinforcement Learning: Adaptivity and Computational Efficiencycited by 40
  2. 2023On the Sublinear Regret of GP-UCBcited by 26
  3. 2023Kernelized Reinforcement Learning with Order Optimal Regret Boundscited by 20
  4. 2023Improved Algorithms for Stochastic Linear Bandits Using Tail Bounds for Martingale Mixturescited by 12
  5. 2023Time-Uniform Self-Normalized Concentration for Vector-Valued Processescited by 9
  6. 2024Second Order Bounds for Contextual Bandits with Function Approximationcited by 9
  7. 2024Tighter Confidence Bounds for Sequential Kernel Regressioncited by 8
  8. 2024Noise-Adaptive Confidence Sets for Linear Bandits and Application to Bayesian Optimizationcited by 6
  9. 2024Mean Estimation in Banach Spaces Under Infinite Variance and Martingale Dependencecited by 6
  10. 2025Generalized Kernelized Bandits: A Novel Self-Normalized Bernstein-Like Dimension-Free Inequality and Regret Boundscited by 4
  11. 2018Model Agnostic Time Series Analysis via Matrix Estimationcited by 3
  12. 2025A variational approach to dimension-free self-normalized concentrationcited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Kernel-based guarantees for nonlinear parametric models in Bayesian optimizationcited by 1
  2. 2026Optimal Rates for Differentially Private Hypothesis Testing with E-valuescited by 1
  3. 2026Bentkus-type asymptotic e-valuescited by 0
  4. 2026Sequential operator learning under dependent datacited by 0