  Efficient optimisation of black-box problems that comprise both continuous
and categorical inputs is important, yet poses significant challenges. We
propose a new approach, Continuous and Categorical Bayesian Optimisation
(CoCaBO), which combines the strengths of multi-armed bandits and Bayesian
optimisation to select values for both categorical and continuous inputs. We
model this mixed-type space using a Gaussian Process kernel, designed to allow
sharing of information across multiple categorical variables, each with
multiple possible values; this allows CoCaBO to leverage all available data
efficiently. We extend our method to the batch setting and propose an efficient
selection procedure that dynamically balances exploration and exploitation
whilst encouraging batch diversity. We demonstrate empirically that our method
outperforms existing approaches on both synthetic and real-world optimisation
tasks with continuous and categorical inputs.
