Boundary Variance Inflation Causes Acquisition Bias in Gaussian Processes

Abstract:Gaussian processes with stationary kernels on bounded domains exhibit inflated posterior variance near the boundary. Despite being a long-recognized artifact in geostatistics and a source of over-exploration in Bayesian optimization, the causes and effects of boundary-induced acquisition bias are underexplored. We trace the root cause to a simple geometric mechanism: the truncation of the kernel correlation neighborhood at the domain boundary creates an observation-independent distortion that worsens with dimensionality. We show how this distortion manifests across three acquisition classes: variance maximization concentrates selections at the corners, whereas negative integrated posterior variance and expected predictive information gain move selections inward to axis-aligned interior shells. These patterns arise without reference to any objective function, meaning that acquisition behavior can be dominated by kernel geometry rather than the desired task-specific uncertainty. To quantify this, we introduce a function-free selection-profile diagnostic for arbitrary acquisitions, kernels, and bounded-domain geometries.

Machine Learning (cs.LG); Methodology (stat.ME); Machine Learning (stat.ML)

arXiv:2606.07561 [cs.LG]

(or arXiv:2606.07561v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.07561 Focus to learn more arXiv-issued DOI via DataCite

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