Develop rigorous convergence theory for Stein variational gradient descent (SVGD)

Establish general convergence guarantees for Stein variational gradient descent that quantify when and how its particle system converges to the target distribution, including rates and conditions under which convergence holds.

Background

SVGD is presented as a deterministic particle-based method to approximate target distributions. It modifies the Wasserstein gradient flow by a kernelized operator and yields an implementable particle algorithm.

Despite widespread use, the authors note that convergence theory for SVGD remains incomplete, motivating the need for rigorous results on convergence behavior.