Constrained Bayesian optimization with barrier functions: Impact of heteroscedastic noise on the search and identification phases

Abstract

This PhD dissertation addresses constrained Bayesian optimization for expensive stochastic simulation optimization problems, with a particular focus on settings where objective and constraint evaluations are affected by heteroscedastic noise. While Bayesian optimization has proved highly effective for unconstrained and deterministic problems, its extension to constrained stochastic settings remains limited, especially when the variability of simulation outputs depends on the values of decision variables. Neglecting the presence of input-dependent (heteroscedastic) noise may distort both the search trajectory and the final solution identified by the algorithm. More specifically, the dissertation examines the impact of heteroscedastic noise on two critical phases of constrained Bayesian optimization: the search phase, during which new evaluation points are selected, and the identification phase, where the optimal solution is inferred from the available data. For the search phase, stochastic kriging models are employed to explicitly capture input-dependent noise in both objective and constraint functions. The resulting surrogate information is embedded into the acquisition function, leading to a substantially different sampling behavior compared to approaches based on homoscedastic assumptions. Numerical experiments show that this strategy improves the accuracy of the learned surrogates, refines the estimated feasible region, and yields solutions that are closer to the true optimum in both decision and objective spaces. For the identification phase, the thesis shows that existing constrained Bayesian optimization approaches may fail to return the true optimal solution, even when it has been sampled during the search. Two distinct mechanisms are responsible for this behavior. First, the algorithm may incorrectly classify the true optimum as infeasible,