# Bayesian Optimisation for Constrained Problems

arXiv: https://arxiv.org/abs/2105.13245 · HTML: https://mlsanity.com/paper/2105.13245/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 41 references that are in the map.
- First posted on arXiv 27 May 2021.

## Builds on (most cited first, 11 of 11)

- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [Multi-Information Source Optimization](https://mlsanity.com/paper/1603.00389/) (2016)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [A General Framework for Constrained Bayesian Optimization using Information-based Search](https://mlsanity.com/paper/1511.09422/) (2015)
- [Bayesian optimization under mixed constraints with a slack-variable augmented Lagrangian](https://mlsanity.com/paper/1605.09466/) (2016)
- [Simulation optimization: A review of algorithms and applications](https://mlsanity.com/paper/1706.08591/) (2017)
- [Discretization-free Knowledge Gradient Methods for Bayesian Optimization](https://mlsanity.com/paper/1707.06541/) (2017)
- [A New Knowledge Gradient-based Method for Constrained Bayesian Optimization](https://mlsanity.com/paper/2101.08743/) (2021)

## Built on by (most cited first, 9 of 9)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [LLaMEA-BO: A Large Language Model Evolutionary Algorithm for Automatically Generating Bayesian Optimization Algorithms](https://mlsanity.com/paper/2505.21034/) (2025)
- [PF2ES: Parallel Feasible Pareto Frontier Entropy Search for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2204.05411/) (2022)
- [Feasibility-Driven Trust Region Bayesian Optimization](https://mlsanity.com/paper/2506.14619/) (2025)
- [Convergence Rates of Constrained Expected Improvement](https://mlsanity.com/paper/2505.11323/) (2025)
- [Bayesian Optimization for Non-Convex Two-Stage Stochastic Optimization Problems](https://mlsanity.com/paper/2408.17387/) (2024)
- [Constrained Best Arm Identification with Tests for Feasibility](https://mlsanity.com/paper/2511.09808/) (2025)
- [Hyperparameter Optimization of Constraint Programming Solvers](https://mlsanity.com/paper/2601.11389/) (2026)
- [Local Constrained Bayesian Optimization](https://mlsanity.com/paper/2603.07965/) (2026)

## Abstract (arXiv)

Many real-world optimisation problems such as hyperparameter tuning in machine learning or simulation-based optimisation can be formulated as expensive-to-evaluate black-box functions. A popular approach to tackle such problems is Bayesian optimisation (BO), which builds a response surface model based on the data collected so far, and uses the mean and uncertainty predicted by the model to decide what information to collect next. In this paper, we propose a novel variant of the well-known Knowledge Gradient acquisition function that allows it to handle constraints. We empirically compare the new algorithm with four other state-of-the-art constrained Bayesian optimisation algorithms and demonstrate its superior performance. We also prove theoretical convergence in the infinite budget limit.