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Information Theoretic Bayesian Optimization over the Probability Simplex

arXiv 2603.09793 ↗First posted 10 Mar 2026cs.LGcited by 0

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Abstract (arXiv)

Bayesian optimization is a data-efficient technique that has been shown to be extremely powerful to optimize expensive, black-box, and possibly noisy objective functions. Many applications involve optimizing probabilities and mixtures which naturally belong to the probability simplex, a constrained non-Euclidean domain defined by non-negative entries summing to one. This paper introduces α-GaBO, a novel family of Bayesian optimization algorithms over the probability simplex. Our approach is grounded in information geometry, a branch of Riemannian geometry which endows the simplex with a Riemannian metric and a class of connections. Based on information geometry theory, we construct Mat'ern kernels that reflect the geometry of the probability simplex, as well as a one-parameter family of geometric optimizers for the acquisition function. We validate our method on benchmark functions and on a variety of real-world applications including mixtures of components, mixtures of classifiers, and a robotic control task, showing its increased performance compared to constrained Euclidean approaches.

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References · 15

  1. 2020Mat'ern Gaussian processes on Riemannian manifoldscited by 82
  2. 2024Fisher Flow Matching for Generative Modeling over Discrete Datacited by 68
  3. 2015Probabilistic Numerics and Uncertainty in Computationscited by 59
  4. 2014Geodesic Exponential Kernels: When Curvature and Linearity Conflictcited by 47
  5. 2021Combining Latent Space and Structured Kernels for Bayesian Optimization over Combinatorial Spacescited by 45
  6. 2020Olympus: a benchmarking framework for noisy optimization and experiment planningcited by 28
  7. 2022Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact casecited by 25
  8. 2021Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernelscited by 24
  9. 2019Bayesian Optimization Meets Riemannian Manifolds in Robot Learningcited by 23
  10. 2024A survey and benchmark of high-dimensional Bayesian optimization of discrete sequencescited by 22
  11. 2017Riemannian Optimization via Frank-Wolfe Methodscited by 21
  12. 2020High-Dimensional Bayesian Optimization via Nested Riemannian Manifoldscited by 17
3 more
  1. 2023Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spacescited by 15
  2. 2019Simple algorithms for optimization on Riemannian manifolds with constraintscited by 14
  3. 2022Learning to Sequence and Blend Robot Skills via Differentiable Optimizationcited by 4

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