  Bayesian optimisation presents a sample-efficient methodology for global
optimisation. Within this framework, a crucial performance-determining
subroutine is the maximisation of the acquisition function, a task complicated
by the fact that acquisition functions tend to be non-convex and thus
nontrivial to optimise. In this paper, we undertake a comprehensive empirical
study of approaches to maximise the acquisition function. Additionally, by
deriving novel, yet mathematically equivalent, compositional forms for popular
acquisition functions, we recast the maximisation task as a compositional
optimisation problem, allowing us to benefit from the extensive literature in
this field. We highlight the empirical advantages of the compositional approach
to acquisition function maximisation across 3958 individual experiments
comprising synthetic optimisation tasks as well as tasks from Bayesmark. Given
the generality of the acquisition function maximisation subroutine, we posit
that the adoption of compositional optimisers has the potential to yield
performance improvements across all domains in which Bayesian optimisation is
currently being applied.
