  Bayesian optimisation is a sample-efficient search methodology that holds
great promise for accelerating drug and materials discovery programs. A
frequently-overlooked modelling consideration in Bayesian optimisation
strategies however, is the representation of heteroscedastic aleatoric
uncertainty. In many practical applications it is desirable to identify inputs
with low aleatoric noise, an example of which might be a material composition
which consistently displays robust properties in response to a noisy
fabrication process. In this paper, we propose a heteroscedastic Bayesian
optimisation scheme capable of representing and minimising aleatoric noise
across the input space. Our scheme employs a heteroscedastic Gaussian process
(GP) surrogate model in conjunction with two straightforward adaptations of
existing acquisition functions. First, we extend the augmented expected
improvement (AEI) heuristic to the heteroscedastic setting and second, we
introduce the aleatoric noise-penalised expected improvement (ANPEI) heuristic.
Both methodologies are capable of penalising aleatoric noise in the suggestions
and yield improved performance relative to homoscedastic Bayesian optimisation
and random sampling on toy problems as well as on two real-world scientific
datasets. Code is available at:
\url{https://github.com/Ryan-Rhys/Heteroscedastic-BO}
