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arXiv · 2406.11485

Active clustering with bandit feedback

Victor Thuot·Alexandra Carpentier·Christophe Giraud·Nicolas Verzelen
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Abstract

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.

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Victor Thuot, Alexandra Carpentier, Christophe Giraud, Nicolas Verzelen. 2024-06-17. Active clustering with bandit feedback. https://arxiv.org/abs/2406.11485

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