Preferential Heteroscedastic Bayesian Optimization with Informative Noise Priors

Bayesian optimization is a robust framework for optimizing black-box, expensive-to-evaluatefunctions. It is often the case that black-box functions can only be queried by means ofpairwise comparisons between two candidate solutions, a setting known as PreferentialBO (PBO), for which efficient algorithms have been designed. Nevertheless, for high-dimensional problems, performing a comparison becomes cumbersome, typically for human subjects, and the binary information provided by a preference might become buriedin the noise induced by human answers in such a way that PBO becomes challenging. Tocircumvent this issue, we propose to account for the aleatoric uncertainty using suitableheteroscedastic noise models, based on an informative noise prior built from a user-specifiedset of reliable inputs. We empirically evaluate the proposed approach on a range of synthetic black-box functions, demonstrating a consistent improvement over homoscedasticPBO.