Active Preference Elicitation by Bayesian Updating on Optimality Polyhedra

Abstract

We consider the problem of actively eliciting the preferences of a Decision Maker (DM) that may exhibit some versatility when answering preference queries. Given a set of multicriteria alternatives (choice set) and an aggregation function whose parameter values are unknown, we propose a new incremental elicitation method where the parameter space is partitioned into optimality polyhedra in the same way as in stochastic multicriteria acceptability analysis. Each polyhedron encompasses the subset of parameter values for which a given alternative is optimal (one optimality polyhedron, possibly empty, per alternative in the choice set). The uncertainty about the DM’s judgment is modeled by a probability distribution over the polyhedra of the partition. At each step of the elicitation procedure, the distribution is revised in a Bayesian manner using preference queries whose choice is based on the current solution strategy, that we adapt to minimize the expected regret of the recommended alternative. We interleave the analysis of the set of alternatives with the elicitation of the parameters of the aggregation function (weighted sum or ordered weighted average). Numerical tests have been performed to evaluate the interest of the proposed approach.