A novel Bayesian Optimization method based on a linearized link-function to accounts the under-presented class by using a GP surrogate model. This method is based on Laplace’s method and Gauss-Newton approximations to the Hessian. Our method can improve generalization and be useful when validation data is unavailable (e.g., in nonstationary settings) to solve heteroscedastic behaviours. Our experiments demonstrate that our BO by Gauss-Newton approach competes favorably with state-of-the-art blackbox optimization algorithms.