Anchored Stein Variational Gradient Descent Algorithm for Non-smooth Sampling
Abstract
We introduce a Stein variational framework for sampling from a target density p∝ e−U when the target potential U is possibly non-smooth. The key idea is to introduce a smoother reference potential U0 and the anchor weight a=eU−U0. The resulting anchored Stein variational gradient descent (SVGD) algorithm is able to target p∝ e−U without computing the gradient of U and include standard SVGD as a special case. In particular, we allow the target potential U to be locally Lipschitz while the reference potential U0 is continuously differentiable, along with other suitable assumptions. Under this low regularity regime, we establish a Kullback-Leibler first variation formula for anchored perturbations, identify the corresponding steepest descent direction in the reproducing kernel Hilbert space and prove a nonasymptotic convergence bound for the anchored SVGD algorithm in terms of an anchored kernelized Stein discrepancy. Finally, we also provide guidance on constructing a suitable reference potential U0 based on U.
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BibTeX
@misc{dang2026anchored,
title = {{Anchored Stein Variational Gradient Descent Algorithm for Non-smooth Sampling}},
author = {Thanh Dang and Matthew X. Burns and Jiaming Liang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36018},
eprint = {2610.36018},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36018},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Anchored Stein Variational Gradient Descent Algorithm for Non-smooth Sampling
AU - Thanh Dang
AU - Matthew X. Burns
AU - Jiaming Liang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36018
UR - https://arxiv.org/abs/2610.36018
AB - We introduce a Stein variational framework for sampling from a target density p∝ e^−U when the target potential U is possibly non-smooth. The key idea is to introduce a smoother reference potential U_0 and the anchor weight a=e^U−U_0. The resulting anchored Stein variational gradient descent (SVGD) algorithm is able to target p∝ e^−U without computing the gradient of U and include standard SVGD as a special case. In particular, we allow the target potential U to be locally Lipschitz while the reference potential U_0 is continuously differentiable, along with other suitable assumptions. Under this low regularity regime, we establish a Kullback-Leibler first variation formula for anchored perturbations, identify the corresponding steepest descent direction in the reproducing kernel Hilbert space and prove a nonasymptotic convergence bound for the anchored SVGD algorithm in terms of an anchored kernelized Stein discrepancy. Finally, we also provide guidance on constructing a suitable reference potential U_0 based on U.
ER -