Information Theoretic Bayesian Optimization over the Probability Simplex

Federico Pavesi, Antonio Candelieri, Noémie Jaquier
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:5356-5373, 2026.

Abstract

{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 $\alpha$-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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-pavesi26a, title = {Information Theoretic {Bayesian} Optimization over the Probability Simplex}, author = {Pavesi, Federico and Candelieri, Antonio and Jaquier, No\'{e}mie}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {5356--5373}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/pavesi26a/pavesi26a.pdf}, url = {https://proceedings.mlr.press/v337/pavesi26a.html}, abstract = {{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 $\alpha$-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.} }
Endnote
%0 Conference Paper %T Information Theoretic Bayesian Optimization over the Probability Simplex %A Federico Pavesi %A Antonio Candelieri %A Noémie Jaquier %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-pavesi26a %I PMLR %P 5356--5373 %U https://proceedings.mlr.press/v337/pavesi26a.html %V 337 %X {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 $\alpha$-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.
APA
Pavesi, F., Candelieri, A. & Jaquier, N.. (2026). Information Theoretic Bayesian Optimization over the Probability Simplex. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:5356-5373 Available from https://proceedings.mlr.press/v337/pavesi26a.html.

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