  Batch Bayesian optimisation and Bayesian quadrature have been shown to be
sample-efficient methods of performing optimisation and quadrature where
expensive-to-evaluate objective functions can be queried in parallel. However,
current methods do not scale to large batch sizes -- a frequent desideratum in
practice (e.g. drug discovery or simulation-based inference). We present a
novel algorithm, SOBER, which permits scalable and diversified batch global
optimisation and quadrature with arbitrary acquisition functions and kernels
over discrete and mixed spaces. The key to our approach is to reformulate batch
selection for global optimisation as a quadrature problem, which relaxes
acquisition function maximisation (non-convex) to kernel recombination
(convex). Bridging global optimisation and quadrature can efficiently solve
both tasks by balancing the merits of exploitative Bayesian optimisation and
explorative Bayesian quadrature. We show that SOBER outperforms 11 competitive
baselines on 12 synthetic and diverse real-world tasks.
