Learning Sparse Representations of Preferences within Choquet Expected Utility Theory

Margot Herin, Patrice Perny, Nataliya Sokolovska

Keywords: Preference Learning, Choquet Expected Utility, Decision Under Uncertainty, Sparsity

Abstract: 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.