  Quality Diversity (QD) algorithms such as MAP-Elites are a class of
optimisation techniques that attempt to find a set of high-performing points
from an objective function while enforcing behavioural diversity of the points
over one or more interpretable, user chosen, feature functions.
  In this paper we propose the Bayesian Optimisation of Elites (BOP-Elites)
algorithm that uses techniques from Bayesian Optimisation to explicitly model
both quality and diversity with Gaussian Processes. By considering user defined
regions of the feature space as 'niches' our task is to find the optimal
solution in each niche. We propose a novel acquisition function to
intelligently choose new points that provide the highest expected improvement
to the ensemble problem of identifying the best solution in every niche. In
this way each function evaluation enriches our modelling and provides insight
to the whole problem, naturally balancing exploration and exploitation of the
search space. The resulting algorithm is very effective in identifying the
parts of the search space that belong to a niche in feature space, and finding
the optimal solution in each niche. It is also significantly more sample
efficient than simpler benchmark approaches. BOP-Elites goes further than
existing QD algorithms by quantifying the uncertainty around our predictions
and offering additional illumination of the search space through surrogate
models.
