  We investigate the Active Clustering Problem (ACP). A learner interacts with
an $N$-armed stochastic bandit with $d$-dimensional subGaussian feedback. There
exists a hidden partition of the arms into $K$ groups, such that arms within
the same group, share the same mean vector. The learner's task is to uncover
this hidden partition with the smallest budget - i.e., the least number of
observation - and with a probability of error smaller than a prescribed
constant $\delta$. In this paper, (i) we derive a non-asymptotic lower bound
for the budget, and (ii) we introduce the computationally efficient ACB
algorithm, whose budget matches the lower bound in most regimes. We improve on
the performance of a uniform sampling strategy. Importantly, contrary to the
batch setting, we establish that there is no computation-information gap in the
active setting.
