Online Learning of Partitions in Additively Separable Hedonic Games

Coalition formation involves partitioning agents into disjoint coalitions based on their preferences over other agents. In reality, agents may lack enough information to assess their preferences before interacting with others. This motivates us to initiate the research on coalition formation from the viewpoint of online learning. At each round, a possibly different subset of a given set of agents arrives, that a learner then partitions into coalitions. Only afterwards, the agents' preferences, which possibly change over time, are revealed. The learner's goal is optimizing social cost by minimizing his (static or dynamic) regret. We show that even no-static regret is hard to approximate, and constant approximation in polynomial time is unattainable. Yet, for a fractional relaxation of our problem, we devise an algorithm that simultaneously gives the optimal static and dynamic regret. We then present a rounding scheme with an optimal dynamic regret, which converts our algorithm's output into a solution for our original problem.