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We study the problem of learning to partition users into groups, where onemust learn the compatibilities between the users to achieve optimal groupings.We define four natural objectives that optimize for average and worst casecompatibilities and propose new algorithms for adaptively learning optimalgroupings. When we do not impose any structure on the compatibilities, we showthat the group formation objectives considered are $NP$ hard to solve and weeither give approximation guarantees or prove inapproximability results. Wethen introduce an elegant structure, namely that of \textit{intrinsic scores},that makes many of these problems polynomial time solvable. We explicitlycharacterize the optimal groupings under this structure and show that theoptimal solutions are related to \emph{homophilous} and \emph{heterophilous}partitions, well-studied in the psychology literature. For one of the fourobjectives, we show $NP$ hardness under the score structure and give a$\frac{1}{2}$ approximation algorithm for which no constant approximation wasknown thus far. Finally, under the score structure, we propose an online lowsample complexity PAC algorithm for learning the optimal partition. Wedemonstrate the efficacy of the proposed algorithm on synthetic and real worlddatasets.

Learning to Partition using Score Based Compatibilities