A Note on the Convergence of Mirrored Stein Variational Gradient Descent under (L_0,L_1)-Smoothness Condition

06/20/2022

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by   Lukang Sun, et al.

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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 ∇Ψ_#π∝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.