# Sharp analysis of linear ensemble sampling

arXiv: https://arxiv.org/abs/2602.08026 · HTML: https://mlsanity.com/paper/2602.08026/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 8 Feb 2026.

## Builds on (most cited first, 13 of 13)

- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Randomized Prior Functions for Deep Reinforcement Learning](https://mlsanity.com/paper/1806.03335/) (2018)
- [Deep Exploration via Randomized Value Functions](https://mlsanity.com/paper/1703.07608/) (2017)
- [Ensemble Sampling](https://mlsanity.com/paper/1705.07347/) (2017)
- [An Analysis of Ensemble Sampling](https://mlsanity.com/paper/2203.01303/) (2022)
- [Ensembles for Uncertainty Estimation: Benefits of Prior Functions and Bootstrapping](https://mlsanity.com/paper/2206.03633/) (2022)
- [On Frequentist Regret of Linear Thompson Sampling](https://mlsanity.com/paper/2006.06790/) (2020)
- [Deep Exploration for Recommendation Systems](https://mlsanity.com/paper/2109.12509/) (2021)
- [Stochastic Low-rank Tensor Bandits for Multi-dimensional Online Decision Making](https://mlsanity.com/paper/2007.15788/) (2020)
- [When and why randomised exploration works (in linear bandits)](https://mlsanity.com/paper/2502.08870/) (2025)
- [Ensemble sampling for linear bandits: small ensembles suffice](https://mlsanity.com/paper/2311.08376/) (2023)
- [Improved Regret of Linear Ensemble Sampling](https://mlsanity.com/paper/2411.03932/) (2024)
- [Provable Anytime Ensemble Sampling Algorithms in Nonlinear Contextual Bandits](https://mlsanity.com/paper/2510.10730/) (2025)

## Built on by (most cited first, 1 of 1)

- [Linear Ensemble Sampling with Smaller Ensembles](https://mlsanity.com/paper/2609.13954/) (2026)

## 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.