Learning Context-Dependent Choice Functions (1901.10860v4)

Abstract: Choice functions accept a set of alternatives as input and produce a preferred subset of these alternatives as output. We study the problem of learning such functions under conditions of context-dependence of preferences, which means that the preference in favor of a certain choice alternative may depend on what other options are also available. In spite of its practical relevance, this kind of context-dependence has received little attention in preference learning so far. We propose a suitable model based on context-dependent (latent) utility functions, thereby reducing the problem to the task of learning such utility functions. Practically, this comes with a number of challenges. For example, the set of alternatives provided as input to a choice function can be of any size, and the output of the function should not depend on the order in which the alternatives are presented. To meet these requirements, we propose two general approaches based on two representations of context-dependent utility functions, as well as instantiations in the form of appropriate end-to-end trainable neural network architectures. Moreover, to demonstrate the performance of both networks, we present extensive empirical evaluations on both synthetic and real-world datasets.