Sharp analysis of linear ensemble sampling

arXiv:2602.08026v1 Announce Type: cross
Abstract: 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 $tilde O(d^{3/2}sqrt n)$ 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. Intriguingly, this continuous-time lens is not forced; it appears natural–and perhaps necessary: the discrete-time problem seems to be asking for a continuous-time solution, and we know of no other way to obtain a sharp ES bound.