Finding Interior Optimum of Black-box Constrained Objective with Bayesian Optimization

Fengxue Zhang, Yuxin Chen
Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, PMLR 286:5000-5029, 2025.

Abstract

Optimizing objectives under constraints, where both the objectives and constraints are black box functions, is a common challenge in real-world applications such as medical therapy design, industrial process optimization, and hyperparameter optimization. Bayesian Optimization (BO) is a popular approach for tackling these complex scenarios. However, constrained Bayesian Optimization (CBO) often relies on heuristics, approximations, or relaxation of objectives, which can lead to weaker theoretical guarantees compared to canonical BO. In this paper, we address this gap by focusing on identifying the interior optimum of the constrained objective, deliberately excluding boundary candidates susceptible to noise perturbations. Our approach leverages the insight that jointly optimizing the objective and learning the constraints can help pinpoint high-confidence **regions of interest** (ROI) likely to contain the interior optimum. We introduce an efficient CBO framework, which intersects these ROIs within a discretized search space to determine a general ROI. Within this ROI, we optimize the acquisition functions, balancing constraints learning and objective optimization. We showcase the efficiency and robustness of our proposed framework by deriving high-probability regret bounds and validating its performance through extensive empirical evaluations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v286-zhang25h, title = {Finding Interior Optimum of Black-box Constrained Objective with Bayesian Optimization}, author = {Zhang, Fengxue and Chen, Yuxin}, booktitle = {Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence}, pages = {5000--5029}, year = {2025}, editor = {Chiappa, Silvia and Magliacane, Sara}, volume = {286}, series = {Proceedings of Machine Learning Research}, month = {21--25 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v286/main/assets/zhang25h/zhang25h.pdf}, url = {https://proceedings.mlr.press/v286/zhang25h.html}, abstract = {Optimizing objectives under constraints, where both the objectives and constraints are black box functions, is a common challenge in real-world applications such as medical therapy design, industrial process optimization, and hyperparameter optimization. Bayesian Optimization (BO) is a popular approach for tackling these complex scenarios. However, constrained Bayesian Optimization (CBO) often relies on heuristics, approximations, or relaxation of objectives, which can lead to weaker theoretical guarantees compared to canonical BO. In this paper, we address this gap by focusing on identifying the interior optimum of the constrained objective, deliberately excluding boundary candidates susceptible to noise perturbations. Our approach leverages the insight that jointly optimizing the objective and learning the constraints can help pinpoint high-confidence **regions of interest** (ROI) likely to contain the interior optimum. We introduce an efficient CBO framework, which intersects these ROIs within a discretized search space to determine a general ROI. Within this ROI, we optimize the acquisition functions, balancing constraints learning and objective optimization. We showcase the efficiency and robustness of our proposed framework by deriving high-probability regret bounds and validating its performance through extensive empirical evaluations.} }
Endnote
%0 Conference Paper %T Finding Interior Optimum of Black-box Constrained Objective with Bayesian Optimization %A Fengxue Zhang %A Yuxin Chen %B Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2025 %E Silvia Chiappa %E Sara Magliacane %F pmlr-v286-zhang25h %I PMLR %P 5000--5029 %U https://proceedings.mlr.press/v286/zhang25h.html %V 286 %X Optimizing objectives under constraints, where both the objectives and constraints are black box functions, is a common challenge in real-world applications such as medical therapy design, industrial process optimization, and hyperparameter optimization. Bayesian Optimization (BO) is a popular approach for tackling these complex scenarios. However, constrained Bayesian Optimization (CBO) often relies on heuristics, approximations, or relaxation of objectives, which can lead to weaker theoretical guarantees compared to canonical BO. In this paper, we address this gap by focusing on identifying the interior optimum of the constrained objective, deliberately excluding boundary candidates susceptible to noise perturbations. Our approach leverages the insight that jointly optimizing the objective and learning the constraints can help pinpoint high-confidence **regions of interest** (ROI) likely to contain the interior optimum. We introduce an efficient CBO framework, which intersects these ROIs within a discretized search space to determine a general ROI. Within this ROI, we optimize the acquisition functions, balancing constraints learning and objective optimization. We showcase the efficiency and robustness of our proposed framework by deriving high-probability regret bounds and validating its performance through extensive empirical evaluations.
APA
Zhang, F. & Chen, Y.. (2025). Finding Interior Optimum of Black-box Constrained Objective with Bayesian Optimization. Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 286:5000-5029 Available from https://proceedings.mlr.press/v286/zhang25h.html.

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