# Accounting for Gaussian Process Imprecision in Bayesian Optimization

arXiv: https://arxiv.org/abs/2111.08299 · HTML: https://mlsanity.com/paper/2111.08299/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 24 references that are in the map.
- First posted on arXiv 16 Nov 2021.

## Builds on (most cited first, 2 of 2)

- [Bayesian optimization for materials design](https://mlsanity.com/paper/1506.01349/) (2015)
- [mlrMBO: A Modular Framework for Model-Based Optimization of Expensive Black-Box Functions](https://mlsanity.com/paper/1703.03373/) (2017)

## Built on by (most cited first, 13 of 13)

- [Robust Statistical Comparison of Random Variables with Locally Varying Scale of Measurement](https://mlsanity.com/paper/2306.12803/) (2023)
- [Explaining Bayesian Optimization by Shapley Values Facilitates Human-AI Collaboration](https://mlsanity.com/paper/2403.04629/) (2024)
- [Statistical Multicriteria Benchmarking via the GSD-Front](https://mlsanity.com/paper/2406.03924/) (2024)
- [Explainable Bayesian Optimization](https://mlsanity.com/paper/2401.13334/) (2024)
- [Semi-Supervised Learning guided by the Generalized Bayes Rule under Soft Revision](https://mlsanity.com/paper/2405.15294/) (2024)
- [A Statistical Case Against Empirical Human-AI Alignment](https://mlsanity.com/paper/2502.14581/) (2025)
- [Pseudo Label Selection is a Decision Problem](https://mlsanity.com/paper/2309.13926/) (2023)
- [Towards Bayesian Data Selection](https://mlsanity.com/paper/2406.12560/) (2024)
- [In all LikelihoodS: How to Reliably Select Pseudo-Labeled Data for Self-Training in Semi-Supervised Learning](https://mlsanity.com/paper/2303.01117/) (2023)
- [Reciprocal Learning](https://mlsanity.com/paper/2408.06257/) (2024)
- [Empirical Decision Theory](https://mlsanity.com/paper/2512.05677/) (2025)
- [Performative Learning Theory](https://mlsanity.com/paper/2602.04402/) (2026)
- [Self-Supervised Laplace Approximation for Bayesian Uncertainty Quantification](https://mlsanity.com/paper/2605.12208/) (2026)

## Abstract (arXiv)

Bayesian optimization (BO) with Gaussian processes (GP) as surrogate models is widely used to optimize analytically unknown and expensive-to-evaluate functions. In this paper, we propose Prior-mean-RObust Bayesian Optimization (PROBO) that outperforms classical BO on specific problems. First, we study the effect of the Gaussian processes' prior specifications on classical BO's convergence. We find the prior's mean parameters to have the highest influence on convergence among all prior components. In response to this result, we introduce PROBO as a generalization of BO that aims at rendering the method more robust towards prior mean parameter misspecification. This is achieved by explicitly accounting for GP imprecision via a prior near-ignorance model. At the heart of this is a novel acquisition function, the generalized lower confidence bound (GLCB). We test our approach against classical BO on a real-world problem from material science and observe PROBO to converge faster. Further experiments on multimodal and wiggly target functions confirm the superiority of our method.