# Bayesian Optimization with Unknown Constraints

arXiv: https://arxiv.org/abs/1403.5607 · HTML: https://mlsanity.com/paper/1403.5607/

## Key facts

- Cited by 109 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 22 Mar 2014.

## Built on by (most cited first, 30 of 109)

- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Hyperparameter Optimization: Foundations, Algorithms, Best Practices and Open Challenges](https://mlsanity.com/paper/2107.05847/) (2021)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Mirror Diffusion Models for Constrained and Watermarked Generation](https://mlsanity.com/paper/2310.01236/) (2023)
- [Bayesian Optimization with High-Dimensional Outputs](https://mlsanity.com/paper/2106.12997/) (2021)
- [Data-Driven Offline Optimization For Architecting Hardware Accelerators](https://mlsanity.com/paper/2110.11346/) (2021)
- [GoSafe: Globally Optimal Safe Robot Learning](https://mlsanity.com/paper/2105.13281/) (2021)
- [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)
- [On Kernelized Multi-Armed Bandits with Constraints](https://mlsanity.com/paper/2203.15589/) (2022)
- [Multi-Fidelity Cost-Aware Bayesian Optimization](https://mlsanity.com/paper/2211.02732/) (2022)
- [A Full-Stack Search Technique for Domain Optimized Deep Learning Accelerators](https://mlsanity.com/paper/2105.12842/) (2021)
- [Promoting Fairness through Hyperparameter Optimization](https://mlsanity.com/paper/2103.12715/) (2021)
- [GoSafeOpt: Scalable Safe Exploration for Global Optimization of Dynamical Systems](https://mlsanity.com/paper/2201.09562/) (2022)
- [An Efficient Batch Constrained Bayesian Optimization Approach for Analog Circuit Synthesis via Multi-objective Acquisition Ensemble](https://mlsanity.com/paper/2106.15412/) (2021)
- [TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusion](https://mlsanity.com/paper/2509.25171/) (2025)
- [Bayesian optimization with known experimental and design constraints for chemistry applications](https://mlsanity.com/paper/2203.17241/) (2022)
- [Interactively Learning Preference Constraints in Linear Bandits](https://mlsanity.com/paper/2206.05255/) (2022)
- [VABO: Violation-Aware Bayesian Optimization for Closed-Loop Control Performance Optimization with Unmodeled Constraints](https://mlsanity.com/paper/2110.07479/) (2021)
- [Bayesian Optimization with Formal Safety Guarantees via Online Conformal Prediction](https://mlsanity.com/paper/2306.17815/) (2023)
- [c-TPE: Tree-structured Parzen Estimator with Inequality Constraints for Expensive Hyperparameter Optimization](https://mlsanity.com/paper/2211.14411/) (2022)
- [Information-Theoretic Safe Exploration with Gaussian Processes](https://mlsanity.com/paper/2212.04914/) (2022)
- [Minimizing UCB: a Better Local Search Strategy in Local Bayesian Optimization](https://mlsanity.com/paper/2405.15285/) (2024)
- [Machine Learning with Knowledge Constraints for Process Optimization of Open-Air Perovskite Solar Cell Manufacturing](https://mlsanity.com/paper/2110.01387/) (2021)
- [PropertyDAG: Multi-objective Bayesian optimization of partially ordered, mixed-variable properties for biological sequence design](https://mlsanity.com/paper/2210.04096/) (2022)
- [Tuning Legged Locomotion Controllers via Safe Bayesian Optimization](https://mlsanity.com/paper/2306.07092/) (2023)
- [Constrained Causal Bayesian Optimization](https://mlsanity.com/paper/2305.20011/) (2023)
- [Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approach](https://mlsanity.com/paper/2306.05843/) (2023)
- [Constrained Bayesian Optimization Under Partial Observations: Balanced Improvements and Provable Convergence](https://mlsanity.com/paper/2312.03212/) (2023)

## Abstract (arXiv)

Recent work on Bayesian optimization has shown its effectiveness in global optimization of difficult black-box objective functions. Many real-world optimization problems of interest also have constraints which are unknown a priori. In this paper, we study Bayesian optimization for constrained problems in the general case that noise may be present in the constraint functions, and the objective and constraints may be evaluated independently. We provide motivating practical examples, and present a general framework to solve such problems. We demonstrate the effectiveness of our approach on optimizing the performance of online latent Dirichlet allocation subject to topic sparsity constraints, tuning a neural network given test-time memory constraints, and optimizing Hamiltonian Monte Carlo to achieve maximal effectiveness in a fixed time, subject to passing standard convergence diagnostics.