# Constrained Bayesian Optimization with Adaptive Active Learning of Unknown Constraints

arXiv: https://arxiv.org/abs/2310.08751 · HTML: https://mlsanity.com/paper/2310.08751/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 12 Oct 2023.

## Builds on (most cited first, 16 of 16)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [Predictive Entropy Search for Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1502.05312/) (2015)
- [Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation](https://mlsanity.com/paper/1610.07379/) (2016)
- [Bayesian optimization under mixed constraints with a slack-variable augmented Lagrangian](https://mlsanity.com/paper/1605.09466/) (2016)
- [Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Bound](https://mlsanity.com/paper/2102.09788/) (2021)
- [Constrained Bayesian Optimization with Max-Value Entropy Search](https://mlsanity.com/paper/1910.07003/) (2019)
- [Risk-averse Heteroscedastic Bayesian Optimization](https://mlsanity.com/paper/2111.03637/) (2021)
- [An Information-Theoretic Framework for Unifying Active Learning Problems](https://mlsanity.com/paper/2012.10695/) (2020)
- [Learning Regions of Interest for Bayesian Optimization with Adaptive Level-Set Estimation](https://mlsanity.com/paper/2307.13371/) (2023)

## Built on by (most cited first, 2 of 2)

- [Constrained Multi-objective Bayesian Optimization through Optimistic Constraints Estimation](https://mlsanity.com/paper/2411.03641/) (2024)
- [A Constrained Multi-Fidelity Bayesian Optimization Method](https://mlsanity.com/paper/2510.10984/) (2025)

## Abstract (arXiv)

Optimizing objectives under constraints, where both the objectives and constraints are black box functions, is a common scenario in real-world applications such as scientific experimental design, design of medical therapies, and industrial process optimization. One popular approach to handling these complex scenarios is Bayesian Optimization (BO). In terms of theoretical behavior, BO is relatively well understood in the unconstrained setting, where its principles have been well explored and validated. However, when it comes to constrained Bayesian optimization (CBO), the existing framework often relies on heuristics or approximations without the same level of theoretical guarantees. In this paper, we delve into the theoretical and practical aspects of constrained Bayesian optimization, where the objective and constraints can be independently evaluated and are subject to noise. By recognizing that both the objective and constraints can help identify high-confidence regions of interest (ROI), we propose an efficient CBO framework that intersects the ROIs identified from each aspect to determine the general ROI. The ROI, coupled with a novel acquisition function that adaptively balances the optimization of the objective and the identification of feasible regions, enables us to derive rigorous theoretical justifications for its performance. We showcase the efficiency and robustness of our proposed CBO framework through empirical evidence and discuss the fundamental challenge of deriving practical regret bounds for CBO algorithms.