We present a novel approach to help decision-makers efficiently identify preferred solutions from the Pareto set of a multi-objective optimization problem. Our method uses a Bayesian model to estimate the decision-maker's utility function based on pairwise comparisons. Aided by this model, a principled elicitation strategy selects queries interactively to balance exploration and exploitation, guiding the discovery of high-utility solutions. The approach is flexible: it can be used interactively or a posteriori after estimating the Pareto front through standard multi-objective optimization techniques. Additionally, at the end of the elicitation phase, it generates a reduced menu of high-quality solutions, simplifying the decision-making process. Through experiments on test problems with up to nine objectives, our method demonstrates superior performance in finding high-utility solutions with a small number of queries. We also provide an open-source implementation of our method to support its adoption by the broader community.

We introduce a new incremental preference elicitation procedure able to deal with noisy responses of a Decision Maker (DM). The originality of the contribution is to propose a Bayesian approach for determining a preferred solution in a multiobjective decision problem involving a combinatorial set of alternatives. We assume that the preferences of the DM are represented by an aggregation function whose parameters are unknown and that the uncertainty about them is represented by a density function on the parameter space. Pairwise comparison queries are used to reduce this uncertainty (by Bayesian revision). The query selection strategy is based on the solution of a mixed integer linear program with a combinatorial set of variables and constraints, which requires to use columns and constraints generation methods. Numerical tests are provided to show the practicability of the approach.

Effective techniques for eliciting user preferences have taken on added importance as recommender systems (RSs) become increasingly interactive and conversational. A common and conceptually appealing Bayesian criterion for selecting queries is expected value of information (EVOI). Unfortunately, it is computationally prohibitive to construct queries with maximum EVOI in RSs with large item spaces. We tackle this issue by introducing a continuous formulation of EVOI as a differentiable network that can be optimized using gradient methods available in modern machine learning (ML) computational frameworks (e.g., TensorFlow, PyTorch). We exploit this to develop a novel, scalable Monte Carlo method for EVOI optimization, which is more scalable for large item spaces than methods requiring explicit enumeration of items.