  Bayesian optimisation (BO) algorithms have shown remarkable success in
applications involving expensive black-box functions. Traditionally BO has been
set as a sequential decision-making process which estimates the utility of
query points via an acquisition function and a prior over functions, such as a
Gaussian process. Recently, however, a reformulation of BO via density-ratio
estimation (BORE) allowed reinterpreting the acquisition function as a
probabilistic binary classifier, removing the need for an explicit prior over
functions and increasing scalability. In this paper, we present a theoretical
analysis of BORE's regret and an extension of the algorithm with improved
uncertainty estimates. We also show that BORE can be naturally extended to a
batch optimisation setting by recasting the problem as approximate Bayesian
inference. The resulting algorithms come equipped with theoretical performance
guarantees and are assessed against other batch and sequential BO baselines in
a series of experiments.
