User Preference Meets Pareto-Optimality in Multi-Objective Bayesian Optimization

TL;DR

This work tackles the challenge of incorporating user preferences into multi-objective Bayesian optimization without needing to exhaustively estimate the entire Pareto-front. It proposes PUB-MOBO, a three-stage framework that combines preference-driven utility exploration, outcome evaluation, and a local gradient-descent step (MGDA) guided by Gradient Information to steer search toward near-Pareto-optimal regions, all under a novel Preference-Dominated Utility Function (PDUF). Empirical results on synthetic benchmarks (DTLZ1/DTLZ2/DH1) and real-world problems (Vehicle Safety, Conceptual Marine Design, Car Side Impact) show reduced utility regret and closer proximity to the Pareto-front compared to strong baselines, validating the importance of reducing gradient uncertainty during local search. The approach enables efficient, user-aligned MOBO for expensive black-box objectives and suggests that Local Gradient Descent can enhance other MOBO methods by incorporating gradient-based refinements informed by user preferences.

Abstract

Incorporating user preferences into multi-objective Bayesian optimization (MOBO) allows for personalization of the optimization procedure. Preferences are often abstracted in the form of an unknown utility function, estimated through pairwise comparisons of potential outcomes. However, utility-driven MOBO methods can yield solutions that are dominated by nearby solutions, as non-dominance is not enforced. Additionally, classical MOBO commonly relies on estimating the entire Pareto-front to identify the Pareto-optimal solutions, which can be expensive and ignore user preferences. Here, we present a new method, termed preference-utility-balanced MOBO (PUB-MOBO), that allows users to disambiguate between near-Pareto candidate solutions. PUB-MOBO combines utility-based MOBO with local multi-gradient descent to refine user-preferred solutions to be near-Pareto-optimal. To this end, we propose a novel preference-dominated utility function that concurrently preserves user-preferences and dominance amongst candidate solutions. A key advantage of PUB-MOBO is that the local search is restricted to a (small) region of the Pareto-front directed by user preferences, alleviating the need to estimate the entire Pareto-front. PUB-MOBO is tested on three synthetic benchmark problems: DTLZ1, DTLZ2 and DH1, as well as on three real-world problems: Vehicle Safety, Conceptual Marine Design, and Car Side Impact. PUB-MOBO consistently outperforms state-of-the-art competitors in terms of proximity to the Pareto-front and utility regret across all the problems.

Figures (3)

• Figure 1: Contour plots of (a) the commonly used negative $l_1$ distance Utility function (b) the proposed PDUF.
• Figure 2: Median and 25-75 percentiles performance comparison on synthetic benchmarks on 20 random seeds with a 100 outcome evaluation budget. Plot titles indicate MOO benchmark; horizontal axis is either number of outcome evaluations or number of user queries. Vertical axis indicates simple regret of utility (user satisfaction) and distance from the Pareto-front (optimality).
• Figure 3: Median and 25-75 percentiles performance comparison on real-world benchmarks. Analogous description to Fig. \ref{['fig:synthetic']}.