  Many real-world optimisation problems are defined over both categorical and
continuous variables, yet efficient optimisation methods such asBayesian
Optimisation (BO) are not designed tohandle such mixed-variable search spaces.
Recent approaches to this problem cast the selection of the categorical
variables as a bandit problem, operating independently alongside a BO component
which optimises the continuous variables. In this paper, we adopt a holistic
view and aim to consolidate optimisation of the categorical and continuous
sub-spaces under a single acquisition metric. We derive candidates from the
ExpectedImprovement criterion, which we call value proposals, and use these
proposals to make selections on both the categorical and continuous components
of the input. We show that this unified approach significantly outperforms
existing mixed-variable optimisation approaches across several mixed-variable
black-box optimisation tasks.
