Information Theoretic Bayesian Optimization over the Probability Simplex
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912959195774976 |
|---|---|
| author | Pavesi, Federico Candelieri, Antonio Jaquier, Noémie |
| author_facet | Pavesi, Federico Candelieri, Antonio Jaquier, Noémie |
| contents | 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 Matérn 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09793 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Information Theoretic Bayesian Optimization over the Probability Simplex Pavesi, Federico Candelieri, Antonio Jaquier, Noémie Machine Learning 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 Matérn 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. |
| title | Information Theoretic Bayesian Optimization over the Probability Simplex |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.09793 |