  Impactful applications such as materials discovery, hardware design, neural
architecture search, or portfolio optimization require optimizing
high-dimensional black-box functions with mixed and combinatorial input spaces.
While Bayesian optimization has recently made significant progress in solving
such problems, an in-depth analysis reveals that the current state-of-the-art
methods are not reliable. Their performances degrade substantially when the
unknown optima of the function do not have a certain structure. To fill the
need for a reliable algorithm for combinatorial and mixed spaces, this paper
proposes Bounce that relies on a novel map of various variable types into
nested embeddings of increasing dimensionality. Comprehensive experiments show
that Bounce reliably achieves and often even improves upon state-of-the-art
performance on a variety of high-dimensional problems.
