We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex. We introduce the Subgradient Tamed Unadjusted Langevin Algorithm (SG-TULA), a discretisation of the Langevin diffusion that operates directly on subgradients, without relying on computationally demanding smoothing procedures.
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.
arXiv:2405. 15379v3 Announce Type: replace-cross Abstract: In this paper, we study the problem of sampling from log-concave distributions supported on convex and compact sets, with a particular focus on the randomized midpoint discretization of both overdamped and kinetic Langevin diffusions in constrained domains.
arXiv:2606. 16257v1 Announce Type: cross Abstract: Sampling from high-dimensional, non-log-concave distributions with unnormalized densities is a fundamental challenge in machine learning, particularly when the exact gradient of the potential is unavailable and must be approximated via stochastic gradients that exhibit high variance under a fixed budget of gradient computations per iteration.
arXiv:2604. 17838v2 Announce Type: replace Abstract: Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.
arXiv:2512. 08022v2 Announce Type: replace-cross Abstract: We propose a novel diffusion-based posterior sampling method within a plug-and-play framework.
arXiv:2607. 07519v1 Announce Type: new Abstract: We address the problem of efficiently sampling multimodal probability distributions, where standard Markov Chain Monte Carlo methods often suffer from poor mixing and mode trapping.
arXiv:2608. 11544v1 Announce Type: cross Abstract: We propose CVaR-penalized Generative Particle Algorithm (CVaR-GPA), a robust, tail-agnostic algorithm for fine-tuning generative models to learn heavy-tailed distributions and capture extreme events, requiring no prior knowledge or estimation of the target's tail characteristics.
arXiv:2608. 02430v1 Announce Type: cross Abstract: We provide new estimates in Wasserstein distance for the asymptotic bias of the unadjusted Langevin algorithm, in the classical setting of log-smooth strongly log-concave measures.
arXiv:2603. 11319v2 Announce Type: replace Abstract: We consider the robustness of score-based generative modeling to errors in the estimate of the score function.
arXiv:2607. 15208v1 Announce Type: cross Abstract: Unadjusted samplers such as unadjusted Hamiltonian Monte Carlo and underdamped Langevin are well-known to be biased.
arXiv:2607. 04775v1 Announce Type: cross Abstract: Score-based Generative Models (SGMs) have achieved impressive performance in data generation across a wide range of applications.
arXiv:2608. 05460v1 Announce Type: cross Abstract: This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semicontinuous, prox-bounded function.