# A Constrained Multi-Fidelity Bayesian Optimization Method

arXiv: https://arxiv.org/abs/2510.10984 · HTML: https://mlsanity.com/paper/2510.10984/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 55 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Builds on (most cited first, 15 of 15)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Machine Learning of Linear Differential Equations using Gaussian Processes](https://mlsanity.com/paper/1701.02440/) (2017)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [Predictive Entropy Search for Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1502.05312/) (2015)
- [Bayesian optimization under mixed constraints with a slack-variable augmented Lagrangian](https://mlsanity.com/paper/1605.09466/) (2016)
- [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)
- [Bayesian Optimization for Policy Search via Online-Offline Experimentation](https://mlsanity.com/paper/1904.01049/) (2019)
- [Deep Multi-fidelity Gaussian Processes](https://mlsanity.com/paper/1604.07484/) (2016)
- [Multi-fidelity Bayesian Optimization: A Review](https://mlsanity.com/paper/2311.13050/) (2023)
- [Gaussian Process Optimization with Mutual Information](https://mlsanity.com/paper/1311.4825/) (2013)
- [Constrained Bayesian Optimization with Adaptive Active Learning of Unknown Constraints](https://mlsanity.com/paper/2310.08751/) (2023)

## Abstract (arXiv)

Recently, multi-fidelity Bayesian optimization (MFBO) has been successfully applied to many engineering design optimization problems, where the cost of high-fidelity simulations and experiments can be prohibitive. However, challenges remain for constrained optimization problems using the MFBO framework, particularly in efficiently identifying the feasible region defined by the constraints. In this paper, we propose a constrained multi-fidelity Bayesian optimization (CMFBO) method with novel acquisition functions. Specifically, we design efficient acquisition functions that 1) have analytically closed-form expressions; 2) are straightforward to implement; and 3) do not require feasible initial samples, an important feature often missing in commonly used acquisition functions such as expected constrained improvement (ECI). We demonstrate the effectiveness of our algorithms on synthetic test problems using different combinations of acquisition functions. Then, we apply the proposed method to a data-driven inertial confinement fusion (ICF) design problem, and a high-current joint design problem using finite element simulations with computational contact mechanics.