Cost-Free Fairness in Online Correlation Clustering

Eric Balkanski, Jason Chatzitheodorou, Andreas Maggiori

Abstract:

In the correlation clustering problem, the input is a signed graph where the sign indicates whether pairs of nodes should be placed in the same cluster or not. The goal is to create a clustering that minimizes the number of disagreements with these signs.
Correlation clustering is a key unsupervised learning problem with many practical applications, and it has been widely studied in various settings, including versions with fairness constraints and cases where nodes arrive online.
In this paper, we explore a problem that combines these two settings: nodes arrive online, reveal their membership in protected groups upon arrival and we are only allowed to output fair clusters, i.e., clusters where the representation of each protected group is upper bounded by a user specified constant in the beginning of the arrival sequence.
Our aim is to maintain an approximately optimal fair clustering while minimizing the worst-case recourse of a node, i.e., the number of times a node changes clusters.
We present an algorithm that achieves worst-case logarithmic recourse per node while maintaining a constant-factor fair approximate clustering. Additionally, our approach simplifies the algorithm and analysis used in prior work in the online setting with recourse.

Submission Number: 81