# Correcting boundary over-exploration deficiencies in Bayesian optimization with virtual derivative sign observations

arXiv: https://arxiv.org/abs/1704.00963 · HTML: https://mlsanity.com/paper/1704.00963/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2017.

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

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- [Domain Knowledge Injection in Bayesian Search for New Materials](https://mlsanity.com/paper/2311.15162/) (2023)
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- [Boundary Variance Inflation Causes Acquisition Bias in Gaussian Processes](https://mlsanity.com/paper/2606.07561/) (2026)
- [How Many Initial Points Does Bayesian Optimization Need?](https://mlsanity.com/paper/2607.04356/) (2026)
- [High-dimensional Multi-objective Bayesian Optimization with Learned Variable Interactions](https://mlsanity.com/paper/2608.11713/) (2026)
- [Bayesian Optimization with Rich Auxiliary Information via LLMs](https://mlsanity.com/paper/2609.19437/) (2026)
- [STREGO: A Scalable Implementation of a Trust-Region Framework for Noisy Bayesian Optimization](https://mlsanity.com/paper/2610.14338/) (2026)
- [Understanding Hidden Spatial Preferences in Bayesian Optimization](https://mlsanity.com/paper/2610.14696/) (2026)

## Abstract (arXiv)

Bayesian optimization (BO) is a global optimization strategy designed to find the minimum of an expensive black-box function, typically defined on a compact subset of Rd, by using a Gaussian process (GP) as a surrogate model for the objective. Although currently available acquisition functions address this goal with different degree of success, an over-exploration effect of the contour of the search space is typically observed. However, in problems like the configuration of machine learning algorithms, the function domain is conservatively large and with a high probability the global minimum does not sit on the boundary of the domain. We propose a method to incorporate this knowledge into the search process by adding virtual derivative observations in the gp at the boundary of the search space. We use the properties of GPs to impose conditions on the partial derivatives of the objective. The method is applicable with any acquisition function, it is easy to use and consistently reduces the number of evaluations required to optimize the objective irrespective of the acquisition used. We illustrate the benefits of our approach in an extensive experimental comparison.