Sharp analysis of linear ensemble sampling

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.

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2602.08026 [cs.LG]

(or arXiv:2602.08026v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2602.08026 Focus to learn more arXiv-issued DOI via DataCite

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