arXiv:2609.40193v1 Announce Type: new
Abstract: We establish near-linear accuracy bounds for the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA). The target is $\pi\propto e^{-f-g}$, w...
By Yuchen Xin, Zhihua Zhang
arXiv:2409. 08469v4 Announce Type: replace-cross Abstract: We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics.
By Sayan Banerjee, Krishnakumar Balasubramanian, Promit Ghosal
arXiv:2608. 13467v1 Announce Type: new Abstract: We study the Moreau--Yosida unadjusted Langevin algorithm (MYULA) for the nonsmooth composite target \[ \pi(dx)\propto \exp\{-f(x)-g(x)\}\,dx, \qquad x\in\mathbb R^d, \] where \(f\) is \(m\)-strongly convex with \(L_f\)-Lipschitz gradient and \(g\) is convex and \(G\)-Lipschitz.
By Yuchen Xin, Zhihua Zhang
arXiv:2606. 27767v1 Announce Type: new Abstract: Optimizing functionals over the space of probability measures is now ubiquitous in machine learning.
By Cl\'ement Bonet, Pierre-Cyril Aubin-Frankowski, Youssef Mroueh
arXiv:2608. 06283v1 Announce Type: new Abstract: We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex.
By Iosif Lytras, Nikolaos Makras, Sotirios Sabanis
The paper proves quantitative convergence to the target distribution and uniform‑in‑time propagation of chaos for Langevin‑regularized Stein variational gradient descent (SVGD). It shows that both the Stein interaction and the Langevin drift dissipate the same relative entropy, yielding exponential convergence under a log‑Sobolev inequality and providing finite‑particle entropy identities for empirical measures. Two finite‑time approaches—synchronous coupling and moving‑product entropy—are developed to give explicit Wasserstein, kernel Stein discrepancy, and total variation bounds, leading to polynomial uniform‑in‑time propagation of chaos rates.
By Sayan Banerjee, Dohyeon Kim