Recently there has been a growing interest in non-linear utility models to represent the preferences of a decision maker. Such models are expressive as they are able to represent synergies between criteria, such as compensatory effects. This is the case of the discrete Choquet integral, a very flexible aggregator that subsumes linear models, leximin/lexicographic, the OWA operator. A key question is how to assess the parameters required in order to use such models. In this work, adopting a principled decision-theoretic approach, we consider adaptive elicitation with minimax regret.