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

Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing multiple expensive black-box functions. However, existing MOBO methods often struggle with coverage, scalability, and handling constraints and preferences. In this work we propose *STAGE-BO, Sequential Targeting Adaptive Gap-Filling $\varepsilon$-Constraint Bayesian Optimization*: by analyzing the coverage of the surrogate Pareto front, our method identifies the Pareto front point with the largest uncovered gap, and uses its coordinates to define adaptive constraints in $\varepsilon$-constraint method, which transforms the problem into a sequence of inequality-constrained subproblems, efficiently solved via constrained expected improvement acquisition. Our approach provides uniform Pareto coverage without hypervolume computation and naturally handles constraints and preferences. Experiments on synthetic and real-world benchmarks demonstrate superior coverage and competitive hypervolume performance against state-of-the-art baselines. Our code implementation can be found at https://github.com/YangYaohong1/STAGE-BO.

Many practical optimization problems require balancing multiple goals, such as performance versus cost. In these settings, there is usually not one best solution, but a set of trade-offs. Existing multi-objective Bayesian optimization methods often focus too heavily on hypervolume maximization, which is computationally expensive. We propose STAGE-BO, a method that explicitly looks for under-explored gaps in the current trade-off front and chooses new experiments to fill them. This produces a better-covered set of solutions without relying on expensive hypervolume calculations, and it also naturally handles constraints and preferences. Experiments on synthetic and real-world problems show that STAGE-BO recovers more evenly distributed trade-offs while remaining competitive on standard performance measures.