One Step Preference Elicitation in Multi-Objective Bayesian Optimization
This addresses the challenge of limited evaluations in expensive optimization problems for decision-makers, though it is incremental as it builds on existing methods like ParEGO.
The paper tackles the problem of expensive multi-objective optimization with unknown decision-maker preferences by proposing a one-step preference elicitation method within Bayesian optimization, allowing a final search based on learned preferences. Empirical results show that this approach finds solutions significantly better in terms of true preferences compared to selecting from a generated Pareto front at the end.
We consider a multi-objective optimization problem with objective functions that are expensive to evaluate. The decision maker (DM) has unknown preferences, and so the standard approach is to generate an approximation of the Pareto front and let the DM choose from the generated non-dominated designs. However, especially for expensive to evaluate problems where the number of designs that can be evaluated is very limited, the true best solution according to the DM's unknown preferences is unlikely to be among the small set of non-dominated solutions found, even if these solutions are truly Pareto optimal. We address this issue by using a multi-objective Bayesian optimization algorithm and allowing the DM to select a preferred solution from a predicted continuous Pareto front just once before the end of the algorithm rather than selecting a solution after the end. This allows the algorithm to understand the DM's preferences and make a final attempt to identify a more preferred solution. We demonstrate the idea using ParEGO, and show empirically that the found solutions are significantly better in terms of true DM preferences than if the DM would simply pick a solution at the end.