Sharp analysis of linear ensemble sampling
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Abstract (arXiv)
We analyse linear ensemble sampling (ES) with standard Gaussian perturbations in stochastic linear bandits. We show that for ensemble size m=Theta(dlog n), ES attains tilde O(d3/2√ n) high-probability regret, closing the gap to the Thompson sampling benchmark while keeping computation comparable. The proof brings a new perspective on randomized exploration in linear bandits by reducing the analysis to a time-uniform exceedance problem for m independent Brownian motions. This continuous-time lens appears particularly natural here: it yields an exact representation of the relevant discrete-time processes, and we do not know another route to a sharp ES bound.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 13 of its 29 references that are in the map. First posted on arXiv 8 Feb 2026.
Builds on
13 of 29 references.
References · 13
- 2016Deep Exploration via Bootstrapped DQNcited by 518
- 2018Randomized Prior Functions for Deep Reinforcement Learningcited by 218
- 2017Deep Exploration via Randomized Value Functionscited by 155
- 2017Ensemble Samplingcited by 62
- 2022An Analysis of Ensemble Samplingcited by 23
- 2022Ensembles for Uncertainty Estimation: Benefits of Prior Functions and Bootstrappingcited by 19
- 2020On Frequentist Regret of Linear Thompson Samplingcited by 14
- 2021Deep Exploration for Recommendation Systemscited by 14
- 2020Stochastic Low-rank Tensor Bandits for Multi-dimensional Online Decision Makingcited by 10
- 2025When and why randomised exploration works (in linear bandits)cited by 8
- 2023Ensemble sampling for linear bandits: small ensembles sufficecited by 7
- 2024Improved Regret of Linear Ensemble Samplingcited by 6
1 more
Built on by
Citing papers per year: 2026: 1.
1 paper.
- 2026Linear Ensemble Sampling with Smaller Ensemblescited by 0
- 2026Linear Ensemble Sampling with Smaller Ensembles12 Sep 2026