A combinatorial multi-armed bandit approach to correlation clustering

Given a graph whose edges are assigned positive-type and negative-type weights, the problem of correlation clustering aims at grouping the graph vertices so as to minimize (resp. maximize) the sum of negative-type (resp. positive-type) intra-cluster weights plus the sum of positive-type (resp. negative-type) inter-cluster weights. In correlation clustering, it is typically assumed that the weights are readily available. This is a rather strong hypothesis, which is unrealistic in several scenarios. To overcome this limitation, in this work we focus on the setting where edge weights of a correlation-clustering instance are unknown, and they have to be estimated in multiple rounds, while performing the clustering. The clustering solutions produced in the various rounds provide a feedback to properly adjust the weight estimates, and the goal is to maximize the cumulative quality of the clusterings. We tackle this problem by resorting to the reinforcement-learning paradigm, and, specifically, we design for the first time a Combinatorial Multi-Armed Bandit (CMAB) framework for correlation clustering. We provide a variety of contributions, namely (1) formulations of the minimization and maximization variants of correlation clustering in a CMAB setting; (2) adaptation of well-established CMAB algorithms to the correlation-clustering context; (3) regret analyses to theoretically bound the accuracy of these algorithms; (4) design of further (heuristic) algorithms to have the probability constraint satisfied at every round (key condition to soundly adopt efficient yet effective algorithms for correlation clustering as CMAB oracles); (5) extensive experimental comparison among a variety of both CMAB and non-CMAB approaches for correlation clustering.