# Understanding Hidden Spatial Preferences in Bayesian Optimization

arXiv: https://arxiv.org/abs/2610.14696 · HTML: https://mlsanity.com/paper/2610.14696/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 10 Oct 2026.

## Builds on (most cited first, 12 of 12)

- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [πBO: Augmenting Acquisition Functions with User Beliefs for Bayesian Optimization](https://mlsanity.com/paper/2204.11051/) (2022)
- [Input Warping for Bayesian Optimization of Non-stationary Functions](https://mlsanity.com/paper/1402.0929/) (2014)
- [BOCK : Bayesian Optimization with Cylindrical Kernels](https://mlsanity.com/paper/1806.01619/) (2018)
- [Prediction-Oriented Bayesian Active Learning](https://mlsanity.com/paper/2304.08151/) (2023)
- [Correcting boundary over-exploration deficiencies in Bayesian optimization with virtual derivative sign observations](https://mlsanity.com/paper/1704.00963/) (2017)
- [We Still Don't Understand High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2512.00170/) (2025)
- [Correcting Boundary Bias and Observation Independence in Bayesian Experimental Design](https://mlsanity.com/paper/2602.01898/) (2026)
- [Boundary Variance Inflation Causes Acquisition Bias in Gaussian Processes](https://mlsanity.com/paper/2606.07561/) (2026)

## Abstract (arXiv)

Bayesian optimization uses posterior uncertainty to decide where to explore, but this uncertainty is not spatially neutral. On bounded domains, Gaussian-process posterior variance is typically larger near faces, edges, and corners, giving variance-based acquisition functions a systematic boundary bias. This spatial preference is usually inherited from the surrogate rather than chosen as part of the exploration strategy. We separate these roles by keeping the predictive model fixed and modifying the spatial preference of the exploration term. We control the preference with spatial weight fields and amortize their construction with neural surrogates. Controlled experiments show that the Gaussian process' default boundary bias changes which parts of the domain are explored and which optima are reached. We compare three alternative exploration principles and find, across standard benchmark functions and stochastic robot-pushing tasks, that they can often lower regret, particularly early in the optimization. The spatial structure of posterior uncertainty is therefore not a neutral default: it shapes the exploration strategy and can materially affect optimization performance.