<p>We introduce a general approach to learn an additively decomposable multiattribute utility function from preference information provided by a Decision Maker. The decompositions under considerations here involve several non-necessarily disjoint factors grouping subsets of attributes in interaction. Such decompositions known as Generalized Additive Independence (GAI) utility functions allow interactions between attributes while preserving some additive decomposability of the evaluation model. More precisely, we focus in this paper on the determination of sparse ANOVA-like decompositions of the utility function that best fit preference data and have good generalizing performance. Our learning approach aims to identify the factors of interacting attributes and the utility functions defined on these factors. The proposed approach applies both to continuous and discrete attributes. We present the computational models of this learning approach and then perform numerical tests on both synthetic and real data to demonstrate its practical effectiveness.</p>