Query-Efficient Correlation Clustering with Noisy Oracle
Yuko Kuroki Atsushi Miyauchi Francesco Bonchi Wei Chen
We study a general clustering setting in which we have $n$ elements to be
clustered, and we aim to perform as few queries as possible to an oracle that
returns a noisy sample of the similarity between two elements. Our setting
encompasses many application domains in which the similarity function is costly
to compute and inherently noisy. We propose two novel formulations of online
learning problems rooted in the paradigm of Pure Exploration in Combinatorial
Multi-Armed Bandits (PE-CMAB): fixed confidence and fixed budget settings. For
both settings, we design algorithms that combine a sampling strategy with a
classic approximation algorithm for correlation clustering and study their
theoretical guarantees. Our results are the first examples of polynomial-time
algorithms that work for the case of PE-CMAB in which the underlying offline
optimization problem is NP-hard.