# Constrained Bayesian Optimization with Max-Value Entropy Search

arXiv: https://arxiv.org/abs/1910.07003 · HTML: https://mlsanity.com/paper/1910.07003/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2019.

## Built on by (most cited first, 20 of 20)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Bound](https://mlsanity.com/paper/2102.09788/) (2021)
- [A Bayesian Optimization Framework for Finding Local Optima in Expensive Multi-Modal Functions](https://mlsanity.com/paper/2210.06635/) (2022)
- [Interactively Learning Preference Constraints in Linear Bandits](https://mlsanity.com/paper/2206.05255/) (2022)
- [c-TPE: Tree-structured Parzen Estimator with Inequality Constraints for Expensive Hyperparameter Optimization](https://mlsanity.com/paper/2211.14411/) (2022)
- [Constrained Bayesian Optimization Under Partial Observations: Balanced Improvements and Provable Convergence](https://mlsanity.com/paper/2312.03212/) (2023)
- [OVD-Explorer: Optimism Should Not Be the Sole Pursuit of Exploration in Noisy Environments](https://mlsanity.com/paper/2312.12145/) (2023)
- [Constrained Multi-objective Bayesian Optimization through Optimistic Constraints Estimation](https://mlsanity.com/paper/2411.03641/) (2024)
- [Two-step Lookahead Bayesian Optimization with Inequality Constraints](https://mlsanity.com/paper/2112.02833/) (2021)
- [A sampling criterion for constrained Bayesian optimization with uncertainties](https://mlsanity.com/paper/2103.05706/) (2021)
- [Pareto-frontier Entropy Search with Variational Lower Bound Maximization](https://mlsanity.com/paper/2501.19073/) (2025)
- [A New Knowledge Gradient-based Method for Constrained Bayesian Optimization](https://mlsanity.com/paper/2101.08743/) (2021)
- [Constrained Bayesian Optimization with Adaptive Active Learning of Unknown Constraints](https://mlsanity.com/paper/2310.08751/) (2023)
- [Information-theoretic Bayesian Optimization: Survey and Tutorial](https://mlsanity.com/paper/2502.06789/) (2025)
- [Local Entropy Search over Descent Sequences for Bayesian Optimization](https://mlsanity.com/paper/2511.19241/) (2025)
- [Information-Theoretic Safe Bayesian Optimization](https://mlsanity.com/paper/2402.15347/) (2024)
- [You Only Train Once](https://mlsanity.com/paper/2506.04349/) (2025)
- [Local Constrained Bayesian Optimization](https://mlsanity.com/paper/2603.07965/) (2026)
- [Constrained Bayesian Optimisation with Multiple Information Sources](https://mlsanity.com/paper/2607.00865/) (2026)

## Abstract (arXiv)

Bayesian optimization (BO) is a model-based approach to sequentially optimize expensive black-box functions, such as the validation error of a deep neural network with respect to its hyperparameters. In many real-world scenarios, the optimization is further subject to a priori unknown constraints. For example, training a deep network configuration may fail with an out-of-memory error when the model is too large. In this work, we focus on a general formulation of Gaussian process-based BO with continuous or binary constraints. We propose constrained Max-value Entropy Search (cMES), a novel information theoretic-based acquisition function implementing this formulation. We also revisit the validity of the factorized approximation adopted for rapid computation of the MES acquisition function, showing empirically that this leads to inaccurate results. On an extensive set of real-world constrained hyperparameter optimization problems we show that cMES compares favourably to prior work, while being simpler to implement and faster than other constrained extensions of Entropy Search.