User-Preference Meets Pareto-Optimality: Multi-Objective Bayesian Optimization with Local Gradient Search

2025-02-10

AI Summary

This work addresses the insufficient integration of user preferences and Pareto optimality in multi-objective Bayesian optimization (MOBO). We propose a preference-utility balanced local optimization framework that abandons global Pareto front estimation and instead introduces a novel preference-driven utility function. Local multi-gradient descent is performed within the neighborhood of the preference-informed frontier, jointly optimizing for preference fidelity and solution nondominance. By integrating pairwise preference modeling with Gaussian process surrogates, the method enables efficient, personalized optimization. Evaluated on three synthetic benchmarks and three real-world engineering problems, our approach achieves statistically significant improvements over state-of-the-art methods on both Pareto distance and utility regret—two key metrics quantifying proximity to the true Pareto front and alignment with user preferences, respectively.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Learning Preferences or Rankings
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

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.

Problem

• Incorporates user preferences into multi-objective optimization.
• Ensures solutions are near-Pareto-optimal with local gradient search.
• Reduces need for full Pareto-front estimation via user-directed search.

Innovation

• Combines utility-based MOBO
• Uses local multi-gradient descent
• Restricts search to Pareto-front