Multi-Objective Bayesian Optimization via Adaptive $\varepsilon$-Constraint Decomposition

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 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.