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A Note on the Convergence of Mirrored Stein Variational Gradient Descent under (L₀,L₁)-Smoothness Condition

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arxiv 2206.09709 v1 pith:7C5AAGTZ submitted 2022-06-20 math.OC cs.LGmath.STstat.TH

A Note on the Convergence of Mirrored Stein Variational Gradient Descent under (L₀,L₁)-Smoothness Condition

Lukang Sun , Peter Richt\'arik This is my paper
classification math.OC cs.LGmath.STstat.TH
keywords msvgddescentmirroredgradientlemmalimitnotepopulation
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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 $\nabla\Psi_{\#}\pi\propto\exp(-V)$. 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 $d$.

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