Anchored Stein Variational Gradient Descent Algorithm for Non-smooth Sampling

arXiv:2610.36018v1 Announce Type: cross Abstract: We introduce a Stein variational framework for sampling from a target density ppropto 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 ppropto 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.

Source: arXiv cs.LG | 2026-10-28