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Impactful applications such as materials discovery, hardware design, neuralarchitecture search, or portfolio optimization require optimizinghigh-dimensional black-box functions with mixed and combinatorial input spaces.While Bayesian optimization has recently made significant progress in solvingsuch problems, an in-depth analysis reveals that the current state-of-the-artmethods are not reliable. Their performances degrade substantially when theunknown optima of the function do not have a certain structure. To fill theneed for a reliable algorithm for combinatorial and mixed spaces, this paperproposes Bounce that relies on a novel map of various variable types intonested embeddings of increasing dimensionality. Comprehensive experiments showthat Bounce reliably achieves and often even improves upon state-of-the-artperformance on a variety of high-dimensional problems.

Bounce: a Reliable Bayesian Optimization Algorithm for Combinatorial and Mixed Spaces