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arXiv · 2602.08026

Sharp analysis of linear ensemble sampling

David Janz·Arya Akhavan·Csaba Szepesvári
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Abstract

We analyse linear ensemble sampling (ES) with standard Gaussian perturbations in stochastic linear bandits. We show that for ensemble size $m=\Theta(d\log n)$, ES attains $\tilde O(d^{3/2}\sqrt n)$ 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.

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David Janz, Arya Akhavan, Csaba Szepesvári. 2026-02-08. Sharp analysis of linear ensemble sampling. https://arxiv.org/abs/2602.08026

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