Multi-Objective Bayesian Optimization via Adaptive \varepsilon-Constraints Decomposition

2026-04-17

AI Summary

This work addresses the challenges of insufficient Pareto front coverage, poor scalability, and difficulty in incorporating constraints and preferences in multi-objective Bayesian optimization by proposing STAGE-BO. The method identifies the largest geometric gap in the approximate Pareto front and transforms it into a sequence of adaptive ε-constrained subproblems, which are sequentially solved using a constrained expected improvement acquisition function to actively fill under-explored regions. Notably, STAGE-BO achieves uniform coverage without computing hypervolume and naturally accommodates both constraints and preference information. Experimental results demonstrate that STAGE-BO significantly outperforms existing methods on both synthetic and real-world benchmarks, achieving superior performance in terms of Pareto coverage and hypervolume metrics.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing expensive black-box functions with multiple objectives. However, existing MOBO methods often struggle with coverage, scalability with respect to the number of objectives, and integrating constraints and preferences. In this work, we propose \textit{STAGE-BO, Sequential Targeting Adaptive Gap-Filling $\varepsilon$-Constraint Bayesian Optimization}, that explicitly targets under-explored regions of the Pareto front. By analyzing the coverage of the approximate Pareto front, our method identifies the largest geometric gaps. These gaps are then used as constraints, which transforms the problem into a sequence of inequality-constrained subproblems, efficiently solved via constrained expected improvement acquisition. Our approach provides a uniform Pareto coverage without hypervolume computation and naturally applies to constrained and preference-based settings. Experiments on synthetic and real-world benchmarks demonstrate superior coverage and competitive hypervolume performance against state-of-the-art baselines.

Problem

• Multi-objective Bayesian Optimization
• Pareto front coverage
• Scalability
• Constraints
• Preferences

Innovation

• Multi-objective Bayesian Optimization
• ε-Constraint Method
• Pareto Front Coverage
• Constrained Expected Improvement
• Adaptive Decomposition