  The Stein Variational Gradient Descent (SVGD) algorithm is a deterministic
particle method for sampling. However, a mean-field analysis reveals that the
gradient flow corresponding to the SVGD algorithm (i.e., the Stein Variational
Gradient Flow) only provides a constant-order approximation to the Wasserstein
Gradient Flow corresponding to the KL-divergence minimization. In this work, we
propose the Regularized Stein Variational Gradient Flow, which interpolates
between the Stein Variational Gradient Flow and the Wasserstein Gradient Flow.
We establish various theoretical properties of the Regularized Stein
Variational Gradient Flow (and its time-discretization) including convergence
to equilibrium, existence and uniqueness of weak solutions, and stability of
the solutions. We provide preliminary numerical evidence of the improved
performance offered by the regularization.
