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 $d$.

翻译：在本说明中,我们为人口限值的镜像斯坦变异梯度方法~(MSVGD)确定了一种血缘利玛值。这种血缘利玛值并不依赖于MSVGD的路径信息,而是依赖于对镜像分布的简单假设 $\ nabla\ Psi ⁇ pi\ propto\ exp(-V)$。我们的分析表明,MSVGD值可以适用于更广泛的非摩特的受限抽样问题。我们还调查了人口限值MSVGD值的复杂程度。