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

TL;DR

The paper introduces STAGE-BO, a novel Bayesian optimization method that improves Pareto front coverage by adaptively filling gaps with constraints, applicable to constrained and preference-based multi-objective problems.

Contribution

It proposes a gap-based adaptive constraint approach for better Pareto front coverage without hypervolume computation, enhancing scalability and applicability.

Findings

Achieves superior Pareto coverage on benchmarks.

Demonstrates competitive hypervolume performance.

Effectively handles constrained and preference-based optimization.

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.