Bayesian Optimisation for Mixed-Variable Inputs using Value Proposals

Abstract: 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.