# A General Framework for Constrained Bayesian Optimization using Information-based Search

arXiv: https://arxiv.org/abs/1511.09422 · HTML: https://mlsanity.com/paper/1511.09422/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2015.

## Built on by (most cited first, 30 of 50)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
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- [Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Bound](https://mlsanity.com/paper/2102.09788/) (2021)
- [Multi-objective Asynchronous Successive Halving](https://mlsanity.com/paper/2106.12639/) (2021)
- [On Kernelized Multi-Armed Bandits with Constraints](https://mlsanity.com/paper/2203.15589/) (2022)
- [GoSafeOpt: Scalable Safe Exploration for Global Optimization of Dynamical Systems](https://mlsanity.com/paper/2201.09562/) (2022)
- [Maximizing information from chemical engineering data sets: Applications to machine learning](https://mlsanity.com/paper/2201.10035/) (2022)
- [AntBO: Towards Real-World Automated Antibody Design with Combinatorial Bayesian Optimisation](https://mlsanity.com/paper/2201.12570/) (2022)
- [Can Fairness be Automated? Guidelines and Opportunities for Fairness-aware AutoML](https://mlsanity.com/paper/2303.08485/) (2023)
- [BOtied: Multi-objective Bayesian optimization with tied multivariate ranks](https://mlsanity.com/paper/2306.00344/) (2023)
- [On Safety in Safe Bayesian Optimization](https://mlsanity.com/paper/2403.12948/) (2024)
- [Interactively Learning Preference Constraints in Linear Bandits](https://mlsanity.com/paper/2206.05255/) (2022)
- [Bayesian Optimization with Formal Safety Guarantees via Online Conformal Prediction](https://mlsanity.com/paper/2306.17815/) (2023)
- [Bayesian Optimization of Function Networks with Partial Evaluations](https://mlsanity.com/paper/2311.02146/) (2023)
- [LLaMEA-BO: A Large Language Model Evolutionary Algorithm for Automatically Generating Bayesian Optimization Algorithms](https://mlsanity.com/paper/2505.21034/) (2025)
- [Bayesian Optimisation for Constrained Problems](https://mlsanity.com/paper/2105.13245/) (2021)
- [OpenBox: A Python Toolkit for Generalized Black-box Optimization](https://mlsanity.com/paper/2304.13339/) (2023)
- [Tuning Legged Locomotion Controllers via Safe Bayesian Optimization](https://mlsanity.com/paper/2306.07092/) (2023)
- [PropertyDAG: Multi-objective Bayesian optimization of partially ordered, mixed-variable properties for biological sequence design](https://mlsanity.com/paper/2210.04096/) (2022)
- [Tuning Particle Accelerators with Safety Constraints using Bayesian Optimization](https://mlsanity.com/paper/2203.13968/) (2022)
- [Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approach](https://mlsanity.com/paper/2306.05843/) (2023)
- [ESCADA: Efficient Safety and Context Aware Dose Allocation for Precision Medicine](https://mlsanity.com/paper/2111.13415/) (2021)
- [Bayesian Optimization for Distributionally Robust Chance-constrained Problem](https://mlsanity.com/paper/2201.13112/) (2022)
- [Knowledge Gradient for Multi-Objective Bayesian Optimization with Decoupled Evaluations](https://mlsanity.com/paper/2302.01310/) (2023)
- [Posterior Inference in Latent Space for Scalable Constrained Black-box Optimization](https://mlsanity.com/paper/2507.00480/) (2025)

## Abstract (arXiv)

We present an information-theoretic framework for solving global black-box optimization problems that also have black-box constraints. Of particular interest to us is to efficiently solve problems with decoupled constraints, in which subsets of the objective and constraint functions may be evaluated independently. For example, when the objective is evaluated on a CPU and the constraints are evaluated independently on a GPU. These problems require an acquisition function that can be separated into the contributions of the individual function evaluations. We develop one such acquisition function and call it Predictive Entropy Search with Constraints (PESC). PESC is an approximation to the expected information gain criterion and it compares favorably to alternative approaches based on improvement in several synthetic and real-world problems. In addition to this, we consider problems with a mix of functions that are fast and slow to evaluate. These problems require balancing the amount of time spent in the meta-computation of PESC and in the actual evaluation of the target objective. We take a bounded rationality approach and develop partial update for PESC which trades off accuracy against speed. We then propose a method for adaptively switching between the partial and full updates for PESC. This allows us to interpolate between versions of PESC that are efficient in terms of function evaluations and those that are efficient in terms of wall-clock time. Overall, we demonstrate that PESC is an effective algorithm that provides a promising direction towards a unified solution for constrained Bayesian optimization.