Boundary Variance Inflation Causes Acquisition Bias in Gaussian Processes

• URL: http://arxiv.org/abs/2606.07561v1
• Date: Mon, 25 May 2026 15:59:40 GMT
• Title: Boundary Variance Inflation Causes Acquisition Bias in Gaussian Processes
• Abstract summary: Gaussian processes with stationary kernels on bounded domains exhibit inflated posterior variance near the boundary.<n>We trace the root cause to a simple geometric mechanism.<n>We introduce a function-free selection-profile diagnostic for arbitrary acquisitions, kernels, and bounded-domain shells.
• Score: 4.936911993071877
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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