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.

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