Abstract Standard Bayesian Optimization assumes homoscedastic (constant) noise across the entire search space. When standard Gaussian Process (GP) models encounter a highly noisy localized region, the Marginal Log-Likelihood optimization is forced to absorb that localized variance into a single global noise parameter. This inflates uncertainty across the entire surrogate model, causing the optimizer to over-explore and waste search budget.
The HeteroscedasticGPSampler natively supports input-dependent observation noise. By explicitly passing the known or estimated noise variance of a trial via a user-defined noise_func, this sampler maps and isolates high-variance regions.