Active clustering with bandit feedback

TL;DR

This paper addresses the active clustering problem using bandit feedback, deriving lower bounds on observation budget and introducing an efficient algorithm that nearly matches these bounds, outperforming uniform sampling.

Contribution

It provides the first non-asymptotic lower bound for the active clustering with bandit feedback and proposes a computationally efficient algorithm that approaches this bound.

Findings

The ACB algorithm matches the lower bound in most regimes.

Active clustering can outperform uniform sampling strategies.

No computation-information gap exists in the active setting.

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.