# Constrained multi-fidelity Bayesian optimization with automatic stop condition

arXiv: https://arxiv.org/abs/2503.01126 · HTML: https://mlsanity.com/paper/2503.01126/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 47 references that are in the map.
- First posted on arXiv 3 Mar 2025.

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

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [Latent Map Gaussian Processes for Mixed Variable Metamodeling](https://mlsanity.com/paper/2102.03935/) (2021)
- [Multi-fidelity Bayesian Optimization with Max-value Entropy Search and its parallelization](https://mlsanity.com/paper/1901.08275/) (2019)
- [Multi-Fidelity Cost-Aware Bayesian Optimization](https://mlsanity.com/paper/2211.02732/) (2022)
- [GP+: A Python Library for Kernel-based learning via Gaussian Processes](https://mlsanity.com/paper/2312.07694/) (2023)
- [Data Fusion with Latent Map Gaussian Processes](https://mlsanity.com/paper/2112.02206/) (2021)
- [Constrained Bayesian Optimization Under Partial Observations: Balanced Improvements and Provable Convergence](https://mlsanity.com/paper/2312.03212/) (2023)
- [Transition Constrained Bayesian Optimization via Markov Decision Processes](https://mlsanity.com/paper/2402.08406/) (2024)
- [Bayesian Parameter Inference and Uncertainty Quantification for a Computational Pulmonary Hemodynamics Model Using Gaussian Processes](https://mlsanity.com/paper/2502.14251/) (2025)

## Built on by (most cited first, 2 of 2)

- [Cost-aware Stopping for Bayesian Optimization](https://mlsanity.com/paper/2507.12453/) (2025)
- [Constrained Bayesian Optimisation with Multiple Information Sources](https://mlsanity.com/paper/2607.00865/) (2026)

## Abstract (arXiv)

Bayesian optimization (BO) is increasingly employed in critical applications to find the optimal design with minimal cost. While BO is known for its sample efficiency, relying solely on costly high-fidelity data can still result in high costs. This is especially the case in constrained search spaces where BO must not only optimize but also ensure feasibility. A related issue in the BO literature is the lack of a systematic stopping criterion. To solve these challenges, we develop a constrained cost-aware multi-fidelity BO (CMFBO) framework whose goal is to minimize overall sampling costs by utilizing inexpensive low-fidelity sources while ensuring feasibility. In our case, the constraints can change across the data sources and may be even black-box functions. We also introduce a systematic stopping criterion that addresses the long-lasting issue associated with BO's convergence assessment. Our framework is publicly available on GitHub through the GP+ Python package and herein we validate it's efficacy on multiple benchmark problems.