The paper introduces Reflected Anchored Langevin Dynamics (RALD), a reflected diffusion that can converge to non‑differentiable target distributions on constrained domains. By employing a smooth anchored reference potential and scaling the drift and noise covariance with a state‑dependent factor, the authors derive an Euler‑Maruyama discretization with projection, yielding the Reflected Anchored Langevin Monte Carlo (RALMC) algorithm. Explicit convergence bounds and iteration complexity in the 2‑Wasserstein distance are proven, and numerical experiments confirm the theoretical predictions and empirical performance.
First order Langevin algorithms for constrained sampling in machine learning, such as projected Langevin Monte Carlo which are based on discretizations of reflected Langevin dynamics, require differen...
The paper introduces Hessian-free high-resolution (HFHR) dynamics, an extension of underdamped Langevin dynamics that incorporates reversible position diffusion for sampling in machine learning. It provides an explicit quantitative contraction rate under a position Poincaré inequality, weighted Hessian and Laplacian bounds, and a compact Sobolev embedding, even when the potential is non‑convex. For the HFHR Monte Carlo algorithm, a path‑space Girsanov argument yields a non‑asymptotic convergence bound and an explicit iteration complexity in total variation distance, improving on previous HFHR results and demonstrating benefits of a positive diffusion parameter through numerical experiments.
The paper introduces non‑reversible anchored Langevin dynamics (NALD) and its reflected variant (NRALD) for sampling target distributions that may be non‑smooth and heavy‑tailed, both in Euclidean space and on constrained domains. By adding a circulation drift through a divergence‑free skew‑symmetric matrix field and a stream potential, the methods preserve the target distribution without needing density derivatives, admit a random‑time‑change representation, and can be applied with normal reflection on bounded domains. The authors demonstrate that breaking reversibility leads to faster convergence to the target distribution, as shown by finite‑time non‑asymptotic analysis, large‑deviations results, and asymptotic variance reduction, with numerical experiments confirming the algorithms’ efficiency.
arXiv:2407.05790v4 Announce Type: replace-cross Abstract: This paper introduces and analyses interacting underdamped Langevin algorithms, termed Kinetic Interacting Particle Langevin Monte Carlo (KIP...
arXiv:2609. 17577v1 Announce Type: cross Abstract: We study Langevin diffusion and Langevin Monte Carlo (LMC) when the target distribution changes over time.
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:2512. 08022v2 Announce Type: replace-cross Abstract: We propose a novel diffusion-based posterior sampling method within a plug-and-play framework.
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.
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.
The paper introduces Langevin-Informed Transfer Learning (LITL), a method that recovers target Langevin dynamics from biased source samples using only black-box feedback. LITL learns the leading spectral structure of the target infinitesimal generator and the projected drift via Dirichlet representation learning, enabling kinetic reconstruction and slow-manifold gradient estimation. The authors provide finite-sample guarantees for eigenvalue, eigenfunction, and drift estimation, and demonstrate LITL’s ability to recover physical transition timescales, build kinetic structure from static generative samples, reconstruct spherical symmetries, and steer latent representations in trained neural networks.
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. 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.