# On the Effects of Heterogeneous Errors on Multi-fidelity Bayesian Optimization

arXiv: https://arxiv.org/abs/2309.02771 · HTML: https://mlsanity.com/paper/2309.02771/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 27 references that are in the map.
- First posted on arXiv 6 Sep 2023.

## Builds on (most cited first, 10 of 10)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1811.00755/) (2018)
- [Multi-Fidelity Bayesian Optimization via Deep Neural Networks](https://mlsanity.com/paper/2007.03117/) (2020)
- [Latent Map Gaussian Processes for Mixed Variable Metamodeling](https://mlsanity.com/paper/2102.03935/) (2021)
- [Multi-Fidelity Cost-Aware Bayesian Optimization](https://mlsanity.com/paper/2211.02732/) (2022)
- [Distributed Variational Inference in Sparse Gaussian Process Regression and Latent Variable Models](https://mlsanity.com/paper/1402.1389/) (2014)
- [Data Fusion with Latent Map Gaussian Processes](https://mlsanity.com/paper/2112.02206/) (2021)
- [An Efficient Multi-fidelity Bayesian Optimization Approach for Analog Circuit Synthesis](https://mlsanity.com/paper/1912.00392/) (2019)
- [Probabilistic Neural Data Fusion for Learning from an Arbitrary Number of Multi-fidelity Data Sets](https://mlsanity.com/paper/2301.13271/) (2023)

## Built on by (most cited first, 1 of 1)

- [Adaptive Multi-Fidelity Reinforcement Learning for Variance Reduction in Engineering Design Optimization](https://mlsanity.com/paper/2503.18229/) (2025)

## Abstract (arXiv)

Bayesian optimization (BO) is a sequential optimization strategy that is increasingly employed in a wide range of areas including materials design. In real world applications, acquiring high-fidelity (HF) data through physical experiments or HF simulations is the major cost component of BO. To alleviate this bottleneck, multi-fidelity (MF) methods are used to forgo the sole reliance on the expensive HF data and reduce the sampling costs by querying inexpensive low-fidelity (LF) sources whose data are correlated with HF samples. However, existing multi-fidelity BO (MFBO) methods operate under the following two assumptions that rarely hold in practical applications: (1) LF sources provide data that are well correlated with the HF data on a global scale, and (2) a single random process can model the noise in the fused data. These assumptions dramatically reduce the performance of MFBO when LF sources are only locally correlated with the HF source or when the noise variance varies across the data sources. In this paper, we dispense with these incorrect assumptions by proposing an MF emulation method that (1) learns a noise model for each data source, and (2) enables MFBO to leverage highly biased LF sources which are only locally correlated with the HF source. We illustrate the performance of our method through analytical examples and engineering problems on materials design.