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

arXiv: https://arxiv.org/abs/2604.15959 · HTML: https://mlsanity.com/paper/2604.15959/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 64 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Builds on (most cited first, 26 of 26)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations](https://mlsanity.com/paper/1805.12168/) (2018)
- [Predictive Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/1511.05467/) (2015)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2009.01721/) (2020)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [Multi-objective Bayesian Optimization using Pareto-frontier Entropy](https://mlsanity.com/paper/1906.00127/) (2019)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Uncertainty-Aware Search Framework for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2204.05944/) (2022)
- [Computer-Aided Multi-Objective Optimization in Small Molecule Discovery](https://mlsanity.com/paper/2210.07209/) (2022)
- [Multi-objective Bayesian optimisation with preferences over objectives](https://mlsanity.com/paper/1902.04228/) (2019)
- [Pareto Front-Diverse Batch Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2406.08799/) (2024)
- [Parallel Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2004.00601/) (2020)
- [qPOTS: Efficient batch multiobjective Bayesian optimization via Pareto optimal Thompson sampling](https://mlsanity.com/paper/2310.15788/) (2023)
- [Constrained Multi-Objective Optimization for Automated Machine Learning](https://mlsanity.com/paper/1908.04909/) (2019)
- [Constrained Multi-objective Bayesian Optimization through Optimistic Constraints Estimation](https://mlsanity.com/paper/2411.03641/) (2024)
- [MOBO-OSD: Batch Multi-Objective Bayesian Optimization via Orthogonal Search Directions](https://mlsanity.com/paper/2510.20872/) (2025)
- [Interactive Multi-Objective Probabilistic Preference Learning with Soft and Hard Bounds](https://mlsanity.com/paper/2506.21887/) (2025)
- [An Interactive Framework for Finding the Optimal Trade-off in Differential Privacy](https://mlsanity.com/paper/2509.04290/) (2025)

## Abstract (arXiv)

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.