Bayesian optimization over the probability simplex

Abstract Gaussian Process based Bayesian Optimization is largely adopted for solving problems where the inputs are in Euclidean spaces. In this paper we associate to discrete probability distributions which elements of simplex. To search new design space, need a distance between distributions. The optimal transport (aka Wasserstein distance) chosen due its mathematical structure and computational strategies enabled by it. Both GP acquisition function generalized an functional over optimize two methods proposed, one on auto differentiation other proximal-point algorithm gradient flow. Finally, report preliminary set results class whose dimension ranges from 5 100. These show that embedding optimization process simplex enables effective performance standard improves with increase problem dimensionality.