# Multi-Fidelity Cost-Aware Bayesian Optimization

arXiv: https://arxiv.org/abs/2211.02732 · HTML: https://mlsanity.com/paper/2211.02732/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 69 references that are in the map.
- First posted on arXiv 4 Nov 2022.

## Builds on (most cited first, 20 of 20)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Practical Multi-fidelity Bayesian Optimization for Hyperparameter Tuning](https://mlsanity.com/paper/1903.04703/) (2019)
- [Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables](https://mlsanity.com/paper/1910.01688/) (2019)
- [The reparameterization trick for acquisition functions](https://mlsanity.com/paper/1712.00424/) (2017)
- [Bayesian Optimization of Composite Functions](https://mlsanity.com/paper/1906.01537/) (2019)
- [Parallel Bayesian Global Optimization of Expensive Functions](https://mlsanity.com/paper/1602.05149/) (2016)
- [A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors](https://mlsanity.com/paper/1806.07504/) (2018)
- [BOAH: A Tool Suite for Multi-Fidelity Bayesian Optimization & Analysis of Hyperparameters](https://mlsanity.com/paper/1908.06756/) (2019)
- [Group kernels for Gaussian process metamodels with categorical inputs](https://mlsanity.com/paper/1802.02368/) (2018)
- [Latent Map Gaussian Processes for Mixed Variable Metamodeling](https://mlsanity.com/paper/2102.03935/) (2021)
- [Multi-Fidelity Multi-Objective Bayesian Optimization: An Output Space Entropy Search Approach](https://mlsanity.com/paper/2011.01542/) (2020)
- [Data Fusion with Latent Map Gaussian Processes](https://mlsanity.com/paper/2112.02206/) (2021)
- [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)
- [Scalable Gaussian Processes for Data-Driven Design using Big Data with Categorical Factors](https://mlsanity.com/paper/2106.15356/) (2021)
- [Two-step Lookahead Bayesian Optimization with Inequality Constraints](https://mlsanity.com/paper/2112.02833/) (2021)
- [Bayesian Optimization with Automatic Prior Selection for Data-Efficient Direct Policy Search](https://mlsanity.com/paper/1709.06919/) (2017)

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

- [Operator Learning with Gaussian Processes](https://mlsanity.com/paper/2409.04538/) (2024)
- [Bayesian optimization as a flexible and efficient design framework for sustainable process systems](https://mlsanity.com/paper/2401.16373/) (2024)
- [A Latent Variable Approach for Non-Hierarchical Multi-Fidelity Adaptive Sampling](https://mlsanity.com/paper/2310.03298/) (2023)
- [Multifidelity Simulation-based Inference for Computationally Expensive Simulators](https://mlsanity.com/paper/2502.08416/) (2025)
- [Probabilistic Neural Data Fusion for Learning from an Arbitrary Number of Multi-fidelity Data Sets](https://mlsanity.com/paper/2301.13271/) (2023)
- [Bayesian Co-navigation: Dynamic Designing of the Materials Digital Twins via Active Learning](https://mlsanity.com/paper/2404.12899/) (2024)
- [Co-orchestration of Multiple Instruments to Uncover Structure-Property Relationships in Combinatorial Libraries](https://mlsanity.com/paper/2402.02198/) (2024)
- [Interpretable Multi-Source Data Fusion Through Latent Variable Gaussian Process](https://mlsanity.com/paper/2402.04146/) (2024)
- [Best Arm Identification with Resource Constraints](https://mlsanity.com/paper/2402.19090/) (2024)
- [Unveiling Processing--Property Relationships in Laser Powder Bed Fusion: The Synergy of Machine Learning and High-throughput Experiments](https://mlsanity.com/paper/2409.00248/) (2024)
- [Measurements with Noise: Bayesian Optimization for Co-optimizing Noise and Property Discovery in Automated Experiments](https://mlsanity.com/paper/2410.02717/) (2024)
- [Constrained multi-fidelity Bayesian optimization with automatic stop condition](https://mlsanity.com/paper/2503.01126/) (2025)
- [Deep Gaussian Process-based Cost-Aware Batch Bayesian Optimization for Complex Materials Design Campaigns](https://mlsanity.com/paper/2509.14408/) (2025)
- [On the Effects of Heterogeneous Errors on Multi-fidelity Bayesian Optimization](https://mlsanity.com/paper/2309.02771/) (2023)
- [Heterogenous Multi-Source Data Fusion Through Input Mapping and Latent Variable Gaussian Process](https://mlsanity.com/paper/2407.11268/) (2024)
- [Multi-fidelity Design of Porous Microstructures for Thermofluidic Applications](https://mlsanity.com/paper/2310.18505/) (2023)
- [Characterising harmful data sources when constructing multi-fidelity surrogate models](https://mlsanity.com/paper/2403.08118/) (2024)
- [Learning with a Budget: Identifying the Best Arm with Resource Constraints](https://mlsanity.com/paper/2602.24146/) (2026)
- [Optimization of time-consuming experimental conditions using pseudo-experimental data guided by adaptive polynomial regression](https://mlsanity.com/paper/2607.22238/) (2026)
- [On the Brittleness of Maximum Likelihood Estimation for Gaussian Process Hyperparameter Optimization](https://mlsanity.com/paper/2608.13793/) (2026)

## Abstract (arXiv)

Bayesian optimization (BO) is increasingly employed in critical applications such as materials design and drug discovery. An increasingly popular strategy in BO is to forgo the sole reliance on high-fidelity data and instead use an ensemble of information sources which provide inexpensive low-fidelity data. The overall premise of this strategy is to reduce the overall sampling costs by querying inexpensive low-fidelity sources whose data are correlated with high-fidelity samples. Here, we propose a multi-fidelity cost-aware BO framework that dramatically outperforms the state-of-the-art technologies in terms of efficiency, consistency, and robustness. We demonstrate the advantages of our framework on analytic and engineering problems and argue that these benefits stem from our two main contributions: (1) we develop a novel acquisition function for multi-fidelity cost-aware BO that safeguards the convergence against the biases of low-fidelity data, and (2) we tailor a newly developed emulator for multi-fidelity BO which enables us to not only simultaneously learn from an ensemble of multi-fidelity datasets, but also identify the severely biased low-fidelity sources that should be excluded from BO.