Bayesian Optimization with Gaussian Processes: Noisy and Constrained Settings

Bayesian optimization (BO) is a sample-efficient framework for optimizing expensive black-box functions, where each evaluation is costly or requires a physical experiment. This talk introduces the core formulation: a Gaussian process surrogate over the objective and an acquisition function that trades off exploration and exploitation to select the next evaluation. I then move to two settings where the basic scheme falls short. In the noisy case, the best observed value is no longer a reliable incumbent, and acquisition functions must reason about the posterior rather than raw observations. In the constrained case, feasibility is itself an unknown black-box function and must be modeled and integrated into the acquisition. I present the main algorithmic approaches for each. The talk concludes with a selection of application examples showing how these methods are used in practice.