We propose an approach to learn a multiattribute utility function to model, explain or predict the value system of a Decision Maker. The main challenge of the modelling task is to describe human values and preferences in the presence of interacting attributes while keeping the utility function as simple as possible. We focus on the generalized additive decomposable utility model which allows interactions between attributes while preserving some additive decomposability of the evaluation model. We present a learning approach able to identify the factors of interacting attributes and to learn the utility functions defined on these factors. This approach relies on the determination of a sparse representation of the ANOVA decomposition of the multiattribute utility function using multiple kernel learning. It applies to both continuous and discrete attributes. Numerical tests are performed to demonstrate the practical efficiency of the learning approach.

Multicriteria decision making requires defining the result of conflicting and possibly interacting criteria. Allowing criteria interactions in a decision model increases the complexity of the preference learning task due to the combinatorial nature of the possible interactions. In this paper, we propose an approach to learn a decision model in which the interaction pattern is revealed from preference data and kept as simple as possible. We consider weighted aggregation functions like multilinear utilities or Choquet integrals, admitting representations including non-linear terms measuring the joint benefit or penalty attached to some combinations of criteria. The weighting coefficients known as Möbius masses model positive or negative synergies among criteria. We propose an approach to learn the Möbius masses, based on iterative reweighted least square for sparse recovery, and dualization to improve scalability. This approach is applied to learn sparse representations of the multilinear utility model and conjunctive/disjunctive forms of the discrete Choquet integral from preferences examples, in aggregation problems possibly involving more than 20 criteria.

This paper deals with preference elicitation within Choquet Expected Utility (CEU) theory for decision making under uncertainty. We consider the Savage’s framework with a finite set of states and assume that preferences of the Decision Maker over acts are observable. The CEU model involves two parameters that must be tuned to the value system of the decision maker: a set function (capacity) modeling weights attached to events, of size exponential in the number of states, and a utility function defined on the space of outcomes. Our aim is to learn a sparse representation of the CEU model from preference data. We propose and test a preference learning approach based on a spline representation of utilities and the sparse learning of capacities to obtain CEU models achieving a good tradeoff between the aim of sparsity and the expressivity required by preference data.