A Note on the Convergence of Mirrored Stein Variational Gradient Descent under $(L_0,L_1)-$Smoothness Condition
This work addresses constrained sampling problems in machine learning, but it appears incremental as it extends existing analysis to broader conditions.
The paper establishes a descent lemma for the population limit Mirrored Stein Variational Gradient Descent (MSVGD) under a smoothness condition, enabling its application to constrained sampling problems with non-smooth potentials, and investigates its complexity in terms of dimension d.
In this note, we establish a descent lemma for the population limit Mirrored Stein Variational Gradient Method~(MSVGD). This descent lemma does not rely on the path information of MSVGD but rather on a simple assumption for the mirrored distribution $\nablaΨ_{\#}π\propto\exp(-V)$. Our analysis demonstrates that MSVGD can be applied to a broader class of constrained sampling problems with non-smooth $V$. We also investigate the complexity of the population limit MSVGD in terms of dimension $d$.