  The increasing availability of structured but high dimensional data has
opened new opportunities for optimization. One emerging and promising avenue is
the exploration of unsupervised methods for projecting structured high
dimensional data into low dimensional continuous representations, simplifying
the optimization problem and enabling the application of traditional
optimization methods. However, this line of research has been purely
methodological with little connection to the needs of practitioners so far. In
this paper, we study the effect of different search space design choices for
performing Bayesian Optimization in high dimensional structured datasets. In
particular, we analyse the influence of the dimensionality of the latent space,
the role of the acquisition function and evaluate new methods to automatically
define the optimization bounds in the latent space. Finally, based on
experimental results using synthetic and real datasets, we provide
recommendations for the practitioners.
