# Bayesian optimisation under uncertain inputs

arXiv: https://arxiv.org/abs/1902.07908 · HTML: https://mlsanity.com/paper/1902.07908/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2019.

## Built on by (most cited first, 18 of 18)

- [Robust Multi-Objective Bayesian Optimization Under Input Noise](https://mlsanity.com/paper/2202.07549/) (2022)
- [Bayesian Optimization for Cascade-type Multi-stage Processes](https://mlsanity.com/paper/2111.08330/) (2021)
- [Distributionally Robust Bayesian Optimization with varphi-divergences](https://mlsanity.com/paper/2203.02128/) (2022)
- [Active learning for distributionally robust level-set estimation](https://mlsanity.com/paper/2102.04000/) (2021)
- [Efficient Robust Bayesian Optimization for Arbitrary Uncertain Inputs](https://mlsanity.com/paper/2310.20145/) (2023)
- [Robust expected improvement for Bayesian optimization](https://mlsanity.com/paper/2302.08612/) (2023)
- [Robust Entropy Search for Safe Efficient Bayesian Optimization](https://mlsanity.com/paper/2405.19059/) (2024)
- [Robust Bayesian Target Value Optimization](https://mlsanity.com/paper/2301.04344/) (2023)
- [Robust Bayesian Satisficing](https://mlsanity.com/paper/2308.08291/) (2023)
- [Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation](https://mlsanity.com/paper/2312.10423/) (2023)
- [Sequential Decision Making on Unmatched Data using Bayesian Kernel Embeddings](https://mlsanity.com/paper/2210.13692/) (2022)
- [Bayesian Optimization for Non-Convex Two-Stage Stochastic Optimization Problems](https://mlsanity.com/paper/2408.17387/) (2024)
- [Indirect Query Bayesian Optimization with Integrated Feedback](https://mlsanity.com/paper/2412.13559/) (2024)
- [Robust Satisficing Gaussian Process Bandits Under Adversarial Attacks](https://mlsanity.com/paper/2506.01625/) (2025)
- [Bayesian Optimization under Uncertainty for Training a Scale Parameter in Stochastic Models](https://mlsanity.com/paper/2510.06439/) (2025)
- [Dose-finding design based on level set estimation in phase I cancer clinical trials](https://mlsanity.com/paper/2504.09157/) (2025)
- [Global Optimization on Graph-Structured Data via Gaussian Processes with Spectral Representations](https://mlsanity.com/paper/2511.07734/) (2025)
- [Accelerating Evolutionary Strategy via Rao-Blackwellizing Realization of Uncertain Input](https://mlsanity.com/paper/2608.02073/) (2026)

## Abstract (arXiv)

Bayesian optimisation (BO) has been a successful approach to optimise functions which are expensive to evaluate and whose observations are noisy. Classical BO algorithms, however, do not account for errors about the location where observations are taken, which is a common issue in problems with physical components. In these cases, the estimation of the actual query location is also subject to uncertainty. In this context, we propose an upper confidence bound (UCB) algorithm for BO problems where both the outcome of a query and the true query location are uncertain. The algorithm employs a Gaussian process model that takes probability distributions as inputs. Theoretical results are provided for both the proposed algorithm and a conventional UCB approach within the uncertain-inputs setting. Finally, we evaluate each method's performance experimentally, comparing them to other input noise aware BO approaches on simulated scenarios involving synthetic and real data.