In this paper we consider the problem of simultaneously eliciting the preferences of a group of users in an interactive way. We focus on constructive recommendation tasks, where the instance to be recommended should be synthesized by searching in a constrained configuration space rather than choosing among a set of pre-determined options. We adopt a setwise max-margin optimization method, that can be viewed as a generalization of max-margin learning to sets, supporting the identification of informative questions and encouraging sparsity in the parameter space. We extend setwise max-margin to multiple users and we provide strategies for choosing the user to be queried next and identifying an informative query to ask. At each stage of the interaction, each user is associated with a set of parameter weights (a sort of alternative options for the unknown user utility) that can be used to identify "similar" users and to propagate preference information between them. We present simulation results evaluating the effectiveness of our procedure, showing that our approach compares favorably with respect to straightforward adaptations in a multi-user setting of elicitation methods conceived for single users.
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