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

• URL: http://arxiv.org/abs/2206.09709v1
• Date: Mon, 20 Jun 2022 11:04:18 GMT
• Title: A Note on the Convergence of Mirrored Stein Variational Gradient Descent under $(L_0,L_1)-$Smoothness Condition
• Authors: Lukang Sun, Peter Richt\'arik
• Abstract summary: 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 $nablaPsi_#piproptoexp(-V)$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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