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

Conference item

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

Authors: Borghi, G; Carrillo, JA

• Publication status: Accepted
• Peer review status: Peer reviewed
• Host title: Proceedings of the International Conference on Machine Learning (PMLR 306)
• Acceptance date: 2026-04-30
• Event title: 43rd International Conference on Machine Learning (ICML 2026)
• Event location: Seoul, South Korea
• Event website: https://icml.cc/
• Event start date: 2026-07-06
• Event end date: 2026-07-11
• Language: English