# Efficient Robust Bayesian Optimization for Arbitrary Uncertain Inputs

arXiv: https://arxiv.org/abs/2310.20145 · HTML: https://mlsanity.com/paper/2310.20145/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 32 references that are in the map.
- First posted on arXiv 31 Oct 2023.

## Builds on (most cited first, 14 of 14)

- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [BANANAS: Bayesian Optimization with Neural Architectures for Neural Architecture Search](https://mlsanity.com/paper/1910.11858/) (2019)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [HEBO Pushing The Limits of Sample-Efficient Hyperparameter Optimisation](https://mlsanity.com/paper/2012.03826/) (2020)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Nystr"om Kernel Mean Embeddings](https://mlsanity.com/paper/2201.13055/) (2022)
- [Unscented Bayesian Optimization for Safe Robot Grasping](https://mlsanity.com/paper/1603.02038/) (2016)
- [Bayesian optimisation under uncertain inputs](https://mlsanity.com/paper/1902.07908/) (2019)
- [Heteroscedastic Treed Bayesian Optimisation](https://mlsanity.com/paper/1410.7172/) (2014)
- [Robust expected improvement for Bayesian optimization](https://mlsanity.com/paper/2302.08612/) (2023)
- [Bayesian Search for Robust Optima](https://mlsanity.com/paper/1904.11416/) (2019)

## Built on by (most cited first, 6 of 6)

- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [Robust Entropy Search for Safe Efficient Bayesian Optimization](https://mlsanity.com/paper/2405.19059/) (2024)
- [Bayesian Optimization under Uncertainty for Training a Scale Parameter in Stochastic Models](https://mlsanity.com/paper/2510.06439/) (2025)
- [Bayesian Optimization for Function-Valued Responses under Min-Max Criteria](https://mlsanity.com/paper/2512.07868/) (2025)
- [Maximally Robust Satisficing Bayesian Optimization](https://mlsanity.com/paper/2607.13652/) (2026)
- [Online Adaptive Kernel Mixing for Gaussian Process Decision Making](https://mlsanity.com/paper/2609.19891/) (2026)

## Abstract (arXiv)

Bayesian Optimization (BO) is a sample-efficient optimization algorithm widely employed across various applications. In some challenging BO tasks, input uncertainty arises due to the inevitable randomness in the optimization process, such as machining errors, execution noise, or contextual variability. This uncertainty deviates the input from the intended value before evaluation, resulting in significant performance fluctuations in the final result. In this paper, we introduce a novel robust Bayesian Optimization algorithm, AIRBO, which can effectively identify a robust optimum that performs consistently well under arbitrary input uncertainty. Our method directly models the uncertain inputs of arbitrary distributions by empowering the Gaussian Process with the Maximum Mean Discrepancy (MMD) and further accelerates the posterior inference via Nystrom approximation. Rigorous theoretical regret bound is established under MMD estimation error and extensive experiments on synthetic functions and real problems demonstrate that our approach can handle various input uncertainties and achieve state-of-the-art performance.