Online Learning of Capacity-Based Preference Models

In multicriteria decision making, sophisticated decision models often involve a non-additive set function (named capacity) to define the weights of all subsets of criteria. This makes it possible to model criteria interactions, leaving room for a diversity of attitudes in criteria aggregation. Fitting a capacity-based decision model to a given Decision Maker is a challenging problem and several batch learning methods have been proposed in the literature to derive the capacity from a database of preference examples. In this paper, we introduce an online algorithm for learning a sparse representation of the capacity, designed for decision contexts where preference examples become available sequentially. Our method based on regularized dual averaging is also well fitted to decision contexts involving a large number of preference examples or a large number of criteria. Moreover, we propose a variant making it possible to include normative constraints on the capacity (e.g., monotonicity, supermodularity) while preserving scalability, based on the alternating direction method of multipliers.