# Predictive Entropy Search for Bayesian Optimization with Unknown Constraints

arXiv: https://arxiv.org/abs/1502.05312 · HTML: https://mlsanity.com/paper/1502.05312/

## Key facts

- Cited by 51 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2015.

## Built on by (most cited first, 30 of 51)

- [Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning: Analysis of the Black-Box Optimization Challenge 2020](https://mlsanity.com/paper/2104.10201/) (2021)
- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
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- [Looping in the Human Collaborative and Explainable Bayesian Optimization](https://mlsanity.com/paper/2310.17273/) (2023)
- [Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Bound](https://mlsanity.com/paper/2102.09788/) (2021)
- [A General Framework for User-Guided Bayesian Optimization](https://mlsanity.com/paper/2311.14645/) (2023)
- [Meta-Learning Priors for Safe Bayesian Optimization](https://mlsanity.com/paper/2210.00762/) (2022)
- [A Bayesian Optimization Framework for Finding Local Optima in Expensive Multi-Modal Functions](https://mlsanity.com/paper/2210.06635/) (2022)
- [Safe and Efficient Model-free Adaptive Control via Bayesian Optimization](https://mlsanity.com/paper/2101.07825/) (2021)
- [c-TPE: Tree-structured Parzen Estimator with Inequality Constraints for Expensive Hyperparameter Optimization](https://mlsanity.com/paper/2211.14411/) (2022)
- [OpenBox: A Python Toolkit for Generalized Black-box Optimization](https://mlsanity.com/paper/2304.13339/) (2023)
- [Constrained Bayesian Optimization Under Partial Observations: Balanced Improvements and Provable Convergence](https://mlsanity.com/paper/2312.03212/) (2023)
- [Advancing Deep Active Learning & Data Subset Selection: Unifying Principles with Information-Theory Intuitions](https://mlsanity.com/paper/2401.04305/) (2024)
- [Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approach](https://mlsanity.com/paper/2306.05843/) (2023)
- [HypBO: Accelerating Black-Box Scientific Experiments Using Experts' Hypotheses](https://mlsanity.com/paper/2308.11787/) (2023)
- [Boundary Exploration for Bayesian Optimization With Unknown Physical Constraints](https://mlsanity.com/paper/2402.07692/) (2024)
- [Constrained Multi-objective Bayesian Optimization through Optimistic Constraints Estimation](https://mlsanity.com/paper/2411.03641/) (2024)
- [Failure-averse Active Learning for Physics-constrained Systems](https://mlsanity.com/paper/2110.14443/) (2021)
- [Posterior Inference in Latent Space for Scalable Constrained Black-box Optimization](https://mlsanity.com/paper/2507.00480/) (2025)
- [Exploring Bayesian Deep Learning for Urgent Instructor Intervention Need in MOOC Forums](https://mlsanity.com/paper/2104.12643/) (2021)
- [Two-step Lookahead Bayesian Optimization with Inequality Constraints](https://mlsanity.com/paper/2112.02833/) (2021)
- [TS-RSR: A provably efficient approach for batch Bayesian Optimization](https://mlsanity.com/paper/2403.04764/) (2024)
- [Active Learning with Selective Time-Step Acquisition for PDEs](https://mlsanity.com/paper/2511.18107/) (2025)
- [A sampling criterion for constrained Bayesian optimization with uncertainties](https://mlsanity.com/paper/2103.05706/) (2021)
- [Domain Knowledge Injection in Bayesian Search for New Materials](https://mlsanity.com/paper/2311.15162/) (2023)
- [A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Lifting](https://mlsanity.com/paper/2404.12219/) (2024)
- [A New Knowledge Gradient-based Method for Constrained Bayesian Optimization](https://mlsanity.com/paper/2101.08743/) (2021)
- [Bayesian Optimization and Deep Learning forsteering wheel angle prediction](https://mlsanity.com/paper/2110.13629/) (2021)

## Abstract (arXiv)

Unknown constraints arise in many types of expensive black-box optimization problems. Several methods have been proposed recently for performing Bayesian optimization with constraints, based on the expected improvement (EI) heuristic. However, EI can lead to pathologies when used with constraints. For example, in the case of decoupled constraints---i.e., when one can independently evaluate the objective or the constraints---EI can encounter a pathology that prevents exploration. Additionally, computing EI requires a current best solution, which may not exist if none of the data collected so far satisfy the constraints. By contrast, information-based approaches do not suffer from these failure modes. In this paper, we present a new information-based method called Predictive Entropy Search with Constraints (PESC). We analyze the performance of PESC and show that it compares favorably to EI-based approaches on synthetic and benchmark problems, as well as several real-world examples. We demonstrate that PESC is an effective algorithm that provides a promising direction towards a unified solution for constrained Bayesian optimization.