Study Identifies Boundary Variance Inflation as Source of Acquisition Bias in Gaussian Processes

A preprint submitted to arXiv traces a well-known but poorly understood artifact in Gaussian process (GP) modeling: inflated posterior variance near the boundaries of bounded domains. The authors attribute this to a purely geometric cause — stationary kernels rely on symmetric correlation neighborhoods, which are truncated at domain edges, producing observation-independent variance distortions that scale with dimensionality. The paper analyzes how this distortion propagates differently across three common acquisition function classes: variance maximization pushes selections toward corners, while negative integrated posterior variance and expected predictive information gain shift selections inward to axis-aligned interior shells. Critically, these patterns emerge without any reference to an objective function, meaning the optimizer may be responding to kernel geometry rather than genuine task uncertainty. To help practitioners detect and characterize this problem, the authors introduce a function-free selection-profile diagnostic applicable to arbitrary acquisitions, kernels, and bounded-domain geometries. The work connects a long-recognized issue in geostatistics to its consequences in Bayesian optimization, providing both a mechanistic explanation and a diagnostic tool.