  Preferential Bayesian optimization (PBO) is a sample-efficient framework for
learning human preferences between candidate designs. PBO classically relies on
homoscedastic noise models to represent human aleatoric uncertainty. Yet, such
noise fails to accurately capture the varying levels of human aleatoric
uncertainty, particularly when the user possesses partial knowledge among
different pairs of candidates. For instance, a chemist with solid expertise in
glucose-related molecules may easily compare two compounds from that family
while struggling to compare alcohol-related molecules. Currently, PBO overlooks
this uncertainty during the search for a new candidate through the maximization
of the acquisition function, consequently underestimating the risk associated
with human uncertainty. To address this issue, we propose a heteroscedastic
noise model to capture human aleatoric uncertainty. This model adaptively
assigns noise levels based on the distance of a specific input to a predefined
set of reliable inputs known as anchors provided by the human. Anchors
encapsulate partial knowledge and offer insight into the comparative difficulty
of evaluating different candidate pairs. Such a model can be seamlessly
integrated into the acquisition function, thus leading to candidate design
pairs that elegantly trade informativeness and ease of comparison for the human
expert. We perform an extensive empirical evaluation of the proposed approach,
demonstrating a consistent improvement over homoscedastic PBO.
