Constrained Multi-objective Bayesian Optimization through Optimistic Constraints Estimation

Diantong Li, Fengxue Zhang, Chong Liu, Yuxin Chen
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:370-378, 2025.

Abstract

Multi-objective Bayesian optimization has been widely adopted in scientific experiment design, including drug discovery and hyperparameter optimization. In practice, regulatory or safety concerns often impose additional thresholds on certain attributes of the experimental outcomes. Previous work has primarily focused on constrained single-objective optimization tasks or active search under constraints. The existing constrained multi-objective algorithms address the issue with heuristics and approximations, posing challenges to the analysis of the sample efficiency. We propose a novel constrained multi-objective Bayesian optimization algorithm \textbf{COMBOO} that balances active learning of the level-set defined on multiple unknowns with multi-objective optimization within the feasible region. We provide both theoretical analysis and empirical evidence, demonstrating the efficacy of our approach on various synthetic benchmarks and real-world applications.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-li25a, title = {Constrained Multi-objective Bayesian Optimization through Optimistic Constraints Estimation}, author = {Li, Diantong and Zhang, Fengxue and Liu, Chong and Chen, Yuxin}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {370--378}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/li25a/li25a.pdf}, url = {https://proceedings.mlr.press/v258/li25a.html}, abstract = {Multi-objective Bayesian optimization has been widely adopted in scientific experiment design, including drug discovery and hyperparameter optimization. In practice, regulatory or safety concerns often impose additional thresholds on certain attributes of the experimental outcomes. Previous work has primarily focused on constrained single-objective optimization tasks or active search under constraints. The existing constrained multi-objective algorithms address the issue with heuristics and approximations, posing challenges to the analysis of the sample efficiency. We propose a novel constrained multi-objective Bayesian optimization algorithm \textbf{COMBOO} that balances active learning of the level-set defined on multiple unknowns with multi-objective optimization within the feasible region. We provide both theoretical analysis and empirical evidence, demonstrating the efficacy of our approach on various synthetic benchmarks and real-world applications.} }
Endnote
%0 Conference Paper %T Constrained Multi-objective Bayesian Optimization through Optimistic Constraints Estimation %A Diantong Li %A Fengxue Zhang %A Chong Liu %A Yuxin Chen %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-li25a %I PMLR %P 370--378 %U https://proceedings.mlr.press/v258/li25a.html %V 258 %X Multi-objective Bayesian optimization has been widely adopted in scientific experiment design, including drug discovery and hyperparameter optimization. In practice, regulatory or safety concerns often impose additional thresholds on certain attributes of the experimental outcomes. Previous work has primarily focused on constrained single-objective optimization tasks or active search under constraints. The existing constrained multi-objective algorithms address the issue with heuristics and approximations, posing challenges to the analysis of the sample efficiency. We propose a novel constrained multi-objective Bayesian optimization algorithm \textbf{COMBOO} that balances active learning of the level-set defined on multiple unknowns with multi-objective optimization within the feasible region. We provide both theoretical analysis and empirical evidence, demonstrating the efficacy of our approach on various synthetic benchmarks and real-world applications.
APA
Li, D., Zhang, F., Liu, C. & Chen, Y.. (2025). Constrained Multi-objective Bayesian Optimization through Optimistic Constraints Estimation. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:370-378 Available from https://proceedings.mlr.press/v258/li25a.html.

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