Query-Efficient Correlation Clustering with Noisy Oracle

Yuko Kuroki, Atsushi Miyauchi, Francesco Bonchi, Wei Chen

Keywords: Correlation Clustering; Online Learning; Pure Exploration of Multi-armed Bandits

TL;DR: We study a general correlation clustering problem with noisy weighted similarity queries, introducing two novel online learning formulations and designing efficient algorithms with theoretical guarantees.

Abstract: 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 weighted similarity between two elements. Our setting encompasses many application domains in which the similarity function is costly to compute and inherently noisy. We introduce 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.

Primary Area: Optimization (convex and non-convex, discrete, stochastic, robust)

Submission Number: 9191