# Multi-fidelity Bayesian Optimization: A Review

arXiv: https://arxiv.org/abs/2311.13050 · HTML: https://mlsanity.com/paper/2311.13050/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 174 references that are in the map.
- First posted on arXiv 21 Nov 2023.

## Builds on (most cited first, 18 of 18)

- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1706.03673/) (2017)
- [Greed is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation](https://mlsanity.com/paper/1911.12809/) (2019)
- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Overview of Gaussian process based multi-fidelity techniques with variable relationship between fidelities](https://mlsanity.com/paper/2006.16728/) (2020)
- [Latent Map Gaussian Processes for Mixed Variable Metamodeling](https://mlsanity.com/paper/2102.03935/) (2021)
- [Bayesian Optimization using Deep Gaussian Processes](https://mlsanity.com/paper/1905.03350/) (2019)
- [Multi-fidelity modeling with different input domain definitions using Deep Gaussian Processes](https://mlsanity.com/paper/2006.15924/) (2020)
- [Enhanced data efficiency using deep neural networks and Gaussian processes for aerodynamic design optimization](https://mlsanity.com/paper/2008.06731/) (2020)
- [Multi-fidelity machine-learning with uncertainty quantification and Bayesian optimization for materials design: Application to ternary random alloys](https://mlsanity.com/paper/2006.00139/) (2020)
- [Upper Trust Bound Feasibility Criterion for Mixed Constrained Bayesian Optimization with Application to Aircraft Design](https://mlsanity.com/paper/2005.05067/) (2020)
- [A graphical multi-fidelity Gaussian process model, with application to emulation of heavy-ion collisions](https://mlsanity.com/paper/2108.00306/) (2021)
- [Bi-fidelity Stochastic Gradient Descent for Structural Optimization under Uncertainty](https://mlsanity.com/paper/1911.10420/) (2019)
- [mfEGRA: Multifidelity Efficient Global Reliability Analysis through Active Learning for Failure Boundary Location](https://mlsanity.com/paper/1910.02497/) (2019)
- [Adaptive Reliability Analysis for Multi-fidelity Models using a Collective Learning Strategy](https://mlsanity.com/paper/2109.10219/) (2021)

## Built on by (most cited first, 12 of 12)

- [Epsilon-Greedy Thompson Sampling to Bayesian Optimization](https://mlsanity.com/paper/2403.00540/) (2024)
- [Automated design of nonreciprocal thermal emitters via Bayesian optimization](https://mlsanity.com/paper/2409.09192/) (2024)
- [Multi-fidelity Machine Learning for Uncertainty Quantification and Optimization](https://mlsanity.com/paper/2410.23482/) (2024)
- [Sampling from Gaussian Processes: A Tutorial and Applications in Global Sensitivity Analysis and Optimization](https://mlsanity.com/paper/2507.14746/) (2025)
- [Bayesian Optimization under Uncertainty for Training a Scale Parameter in Stochastic Models](https://mlsanity.com/paper/2510.06439/) (2025)
- [Digital Twins and Civil Engineering Phases: Reorienting Adoption Strategies](https://mlsanity.com/paper/2403.02426/) (2024)
- [Bayesian Neural Network Surrogates for Bayesian Optimization of Carbon Capture and Storage Operations](https://mlsanity.com/paper/2507.21803/) (2025)
- [A Constrained Multi-Fidelity Bayesian Optimization Method](https://mlsanity.com/paper/2510.10984/) (2025)
- [Real-Time Performance Analysis of Multi-Fidelity Residual Physics-Informed Neural Process-Based State Estimation for Robotic Systems](https://mlsanity.com/paper/2511.08231/) (2025)
- [MAST: A Multi-fidelity Augmented Surrogate model via Spatial Trust-weighting](https://mlsanity.com/paper/2602.20974/) (2026)
- [Optimization of time-consuming experimental conditions using pseudo-experimental data guided by adaptive polynomial regression](https://mlsanity.com/paper/2607.22238/) (2026)
- [MF-SCBO : Multi-fidelity Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2609.29941/) (2026)

## Abstract (arXiv)

Resided at the intersection of multi-fidelity optimization (MFO) and Bayesian optimization (BO), MF BO has found a niche in solving expensive engineering design optimization problems, thanks to its advantages in incorporating physical and mathematical understandings of the problems, saving resources, addressing exploitation-exploration trade-off, considering uncertainty, and processing parallel computing. The increasing number of works dedicated to MF BO suggests the need for a comprehensive review of this advanced optimization technique. In this paper, we survey recent developments of two essential ingredients of MF BO: Gaussian process (GP) based MF surrogates and acquisition functions. We first categorize the existing MF modeling methods and MFO strategies to locate MF BO in a large family of surrogate-based optimization and MFO algorithms. We then exploit the common properties shared between the methods from each ingredient of MF BO to describe important GP-based MF surrogate models and review various acquisition functions. By doing so, we expect to provide a structured understanding of MF BO. Finally, we attempt to reveal important aspects that require further research for applications of MF BO in solving intricate yet important design optimization problems, including constrained optimization, high-dimensional optimization, optimization under uncertainty, and multi-objective optimization.