arXiv AI By Bo Yuan, Wei Guo, Yongxin Chen

Reflected Proximal Dynamics for Accelerated High-Accuracy Log-Concave Sampling

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arXiv Machine Learning
Oct 9

Accelerating Non-Smooth and Heavy-Tailed Sampling

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.

By Pervez Ali, Xiaoyu Wang, Yingli Wang, Lingjiong Zhu
arXiv Machine Learning
Sep 23

Penalized Nonreversible Langevin for Constrained Sampling

The paper introduces penalized nonreversible Langevin algorithms for sampling from a target distribution constrained to a compact convex set. It combines a squared distance penalty with skew-symmetric perturbations that preserve the penalized Gibbs distribution, and provides nonasymptotic total variation and Wasserstein bounds under various smoothness and contraction assumptions. Numerical experiments demonstrate the methods on constrained Bayesian regression, classification, neural networks, and truncated sampling, highlighting acceleration in a stochastic quadratic model.

By Pervez Ali, Weihao Dong, Xiaoyu Wang
arXiv Machine Learning
Sep 10

Smoothed Picard Hamiltonian Monte Carlo

arXiv:2609.06906v1 Announce Type: cross Abstract: We develop a new low-accuracy sampler, called \emph{smoothed Picard Hamiltonian Monte Carlo}, which combines Gaussian smoothing, Picard iteration, an...

By Fan Chen, Sinho Chewi, Jianfeng Lu, Matthew S Zhang