Variational inference via Gaussian interacting particles in the Bures-Wasserstein geometry

Giacomo Borghi, Jose A. Carrillo
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:9242-9268, 2026.

Abstract

Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that stochastically explore the search space and self-organize around global minima via a consensus-based optimization (CBO) mechanism. Its construction relies on the Linearized Bures–Wasserstein (LBW) space, a novel parametrization of Gaussian measures we introduce for efficient computations. We establish well-posedness and study the convergence properties of the particle dynamics via a mean-field approximation. Numerical experiments on variational inference tasks demonstrate the algorithm’s robustness and superior performance with respect to deterministic gradient-based method in presence of low-dimensional non log-concave targets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-borghi26a, title = {Variational inference via {G}aussian interacting particles in the Bures-{W}asserstein geometry}, author = {Borghi, Giacomo and Carrillo, Jose A.}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {9242--9268}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/borghi26a/borghi26a.pdf}, url = {https://proceedings.mlr.press/v306/borghi26a.html}, abstract = {Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that stochastically explore the search space and self-organize around global minima via a consensus-based optimization (CBO) mechanism. Its construction relies on the Linearized Bures–Wasserstein (LBW) space, a novel parametrization of Gaussian measures we introduce for efficient computations. We establish well-posedness and study the convergence properties of the particle dynamics via a mean-field approximation. Numerical experiments on variational inference tasks demonstrate the algorithm’s robustness and superior performance with respect to deterministic gradient-based method in presence of low-dimensional non log-concave targets.} }
Endnote
%0 Conference Paper %T Variational inference via Gaussian interacting particles in the Bures-Wasserstein geometry %A Giacomo Borghi %A Jose A. Carrillo %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-borghi26a %I PMLR %P 9242--9268 %U https://proceedings.mlr.press/v306/borghi26a.html %V 306 %X Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that stochastically explore the search space and self-organize around global minima via a consensus-based optimization (CBO) mechanism. Its construction relies on the Linearized Bures–Wasserstein (LBW) space, a novel parametrization of Gaussian measures we introduce for efficient computations. We establish well-posedness and study the convergence properties of the particle dynamics via a mean-field approximation. Numerical experiments on variational inference tasks demonstrate the algorithm’s robustness and superior performance with respect to deterministic gradient-based method in presence of low-dimensional non log-concave targets.
APA
Borghi, G. & Carrillo, J.A.. (2026). Variational inference via Gaussian interacting particles in the Bures-Wasserstein geometry. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:9242-9268 Available from https://proceedings.mlr.press/v306/borghi26a.html.

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