# Achieving Robustness to Aleatoric Uncertainty with Heteroscedastic Bayesian Optimisation

arXiv: https://arxiv.org/abs/1910.07779 · HTML: https://mlsanity.com/paper/1910.07779/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2019.

## Built on by (most cited first, 11 of 11)

- [HPO-B: A Large-Scale Reproducible Benchmark for Black-Box HPO based on OpenML](https://mlsanity.com/paper/2106.06257/) (2021)
- [PFNs4BO: In-Context Learning for Bayesian Optimization](https://mlsanity.com/paper/2305.17535/) (2023)
- [High-Dimensional Bayesian Optimisation with Variational Autoencoders and Deep Metric Learning](https://mlsanity.com/paper/2106.03609/) (2021)
- [GAUCHE: A Library for Gaussian Processes in Chemistry](https://mlsanity.com/paper/2212.04450/) (2022)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [Large language models as uncertainty-calibrated optimizers for experimental discovery](https://mlsanity.com/paper/2504.06265/) (2025)
- [Batch Bayesian Optimization for Replicable Experimental Design](https://mlsanity.com/paper/2311.01195/) (2023)
- [Anchor-Based Heteroscedastic Noise for Preferential Bayesian Optimization](https://mlsanity.com/paper/2405.14657/) (2024)
- [Robust Bayesian Optimization via Localized Online Conformal Prediction](https://mlsanity.com/paper/2411.17387/) (2024)
- [Stabilizing Information Flow Entropy: Regularization for Safe and Interpretable Autonomous Driving Perception](https://mlsanity.com/paper/2509.16277/) (2025)
- [Quantile-Scaled Bayesian Optimization Using Rank-Only Feedback](https://mlsanity.com/paper/2510.03277/) (2025)

## Abstract (arXiv)

Bayesian optimisation is a sample-efficient search methodology that holds great promise for accelerating drug and materials discovery programs. A frequently-overlooked modelling consideration in Bayesian optimisation strategies however, is the representation of heteroscedastic aleatoric uncertainty. In many practical applications it is desirable to identify inputs with low aleatoric noise, an example of which might be a material composition which consistently displays robust properties in response to a noisy fabrication process. In this paper, we propose a heteroscedastic Bayesian optimisation scheme capable of representing and minimising aleatoric noise across the input space. Our scheme employs a heteroscedastic Gaussian process (GP) surrogate model in conjunction with two straightforward adaptations of existing acquisition functions. First, we extend the augmented expected improvement (AEI) heuristic to the heteroscedastic setting and second, we introduce the aleatoric noise-penalised expected improvement (ANPEI) heuristic. Both methodologies are capable of penalising aleatoric noise in the suggestions and yield improved performance relative to homoscedastic Bayesian optimisation and random sampling on toy problems as well as on two real-world scientific datasets. Code is available at: urlhttps://github.com/Ryan-Rhys/Heteroscedastic-BO