Active clustering with bandit feedback
<|reference_start|>Active clustering with bandit feedback: 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.<|reference_end|>
@article{thuot2024active,
    title={Active clustering with bandit feedback},
    author={Victor Thuot (MISTEA), Alexandra Carpentier, Christophe Giraud
  (CELESTE), Nicolas Verzelen (MISTEA)},
    journal={arXiv preprint arXiv:2406.11485},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.11485},
    primaryClass={stat.ML cs.LG}
}