Preferential Heteroscedastic Bayesian Optimization with
Informative Noise Distribution
Sinaga, Marshal, Martinelli, Julien, Garg, Vikas, and Kaski, Samuel
NeurIPS 2023 Workshop on Adaptive Experimental Design and Active Learning in the Real World 2024
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.