  Most research in Bayesian optimization (BO) has focused on \emph{direct
feedback} scenarios, where one has access to exact values of some
expensive-to-evaluate objective. This direction has been mainly driven by the
use of BO in machine learning hyper-parameter configuration problems. However,
in domains such as modelling human preferences, A/B tests, or recommender
systems, there is a need for methods that can replace direct feedback with
\emph{preferential feedback}, obtained via rankings or pairwise comparisons. In
this work, we present preferential batch Bayesian optimization (PBBO), a new
framework that allows finding the optimum of a latent function of interest,
given any type of parallel preferential feedback for a group of two or more
points. We do so by using a Gaussian process model with a likelihood specially
designed to enable parallel and efficient data collection mechanisms, which are
key in modern machine learning. We show how the acquisitions developed under
this framework generalize and augment previous approaches in Bayesian
optimization, expanding the use of these techniques to a wider range of
domains. An extensive simulation study shows the benefits of this approach,
both with simulated functions and four real data sets.
