Non-Reversible Langevin Algorithms for Constrained Sampling

• URL: http://arxiv.org/abs/2501.11743v1
• Date: Mon, 20 Jan 2025 21:04:29 GMT
• Title: Non-Reversible Langevin Algorithms for Constrained Sampling
• Authors: Hengrong Du, Qi Feng, Changwei Tu, Xiaoyu Wang, Lingjiong Zhu,
• Abstract summary: We consider the constrained sampling problem where the goal is to sample from a target distribution on a constrained domain. We propose skew-reflected non-reversible Langevin dynamics (SRNLD) We obtain non-asymptotic convergence rate of SRNLD to the target distribution in both total variation and 1-Wasserstein distances.
• Score: 13.472207533177151
• License:
• Abstract: We consider the constrained sampling problem where the goal is to sample from a target distribution on a constrained domain. We propose skew-reflected non-reversible Langevin dynamics (SRNLD), a continuous-time stochastic differential equation with skew-reflected boundary. We obtain non-asymptotic convergence rate of SRNLD to the target distribution in both total variation and 1-Wasserstein distances. By breaking reversibility, we show that the convergence is faster than the special case of the reversible dynamics. Based on the discretization of SRNLD, we propose skew-reflected non-reversible Langevin Monte Carlo (SRNLMC), and obtain non-asymptotic discretization error from SRNLD, and convergence guarantees to the target distribution in 1-Wasserstein distance. We show better performance guarantees than the projected Langevin Monte Carlo in the literature that is based on the reversible dynamics. Numerical experiments are provided for both synthetic and real datasets to show efficiency of the proposed algorithms.

Related papers

• Constrained Sampling with Primal-Dual Langevin Monte Carlo [15.634831573546041]
  This work considers the problem of sampling from a probability distribution known up to a normalization constant. It satisfies a set of statistical constraints specified by the expected values of general nonlinear functions. We put forward a discrete-time primal-dual Langevin Monte Carlo algorithm (PD-LMC) that simultaneously constrains the target distribution and samples from it.
  arXiv  Detail & Related papers  (2024-11-01T13:26:13Z)
• Faster Sampling via Stochastic Gradient Proximal Sampler [28.422547264326468]
  Proximal samplers (SPS) for sampling from non-log-concave distributions are studied. We show that the convergence to the target distribution can be guaranteed as long as the algorithm trajectory is bounded. We provide two implementable variants based on Langevin dynamics (SGLD) and Langevin-MALA, giving rise to SPS-SGLD and SPS-MALA.
  arXiv  Detail & Related papers  (2024-05-27T00:53:18Z)
• Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems [78.96969465641024]
  We extend mean-field Langevin dynamics to minimax optimization over probability distributions for the first time with symmetric and provably convergent updates. We also study time and particle discretization regimes and prove a new uniform-in-time propagation of chaos result.
  arXiv  Detail & Related papers  (2023-12-02T13:01:29Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)
• Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reduction [49.66486092259376]
  The mean-field Langevin dynamics (MFLD) is a nonlinear generalization of the Langevin dynamics that incorporates a distribution-dependent drift. Recent works have shown that MFLD globally minimizes an entropy-regularized convex functional in the space of measures. We provide a framework to prove a uniform-in-time propagation of chaos for MFLD that takes into account the errors due to finite-particle approximation, time-discretization, and gradient approximation.
  arXiv  Detail & Related papers  (2023-06-12T16:28:11Z)
• Utilising the CLT Structure in Stochastic Gradient based Sampling : Improved Analysis and Faster Algorithms [14.174806471635403]
  We consider approximations of sampling algorithms, such as Gradient Langevin Dynamics (SGLD) and the Random Batch Method (RBM) for Interacting Particle Dynamcs (IPD) We observe that the noise introduced by the approximation is nearly Gaussian due to the Central Limit Theorem (CLT) while the driving Brownian motion is exactly Gaussian. We harness this structure to absorb the approximation error inside the diffusion process, and obtain improved convergence guarantees for these algorithms.
  arXiv  Detail & Related papers  (2022-06-08T10:17:40Z)
• Robust Estimation for Nonparametric Families via Generative Adversarial Networks [92.64483100338724]
  We provide a framework for designing Generative Adversarial Networks (GANs) to solve high dimensional robust statistics problems. Our work extend these to robust mean estimation, second moment estimation, and robust linear regression. In terms of techniques, our proposed GAN losses can be viewed as a smoothed and generalized Kolmogorov-Smirnov distance.
  arXiv  Detail & Related papers  (2022-02-02T20:11:33Z)
• Differentiable Annealed Importance Sampling and the Perils of Gradient Noise [68.44523807580438]
  Annealed importance sampling (AIS) and related algorithms are highly effective tools for marginal likelihood estimation. Differentiability is a desirable property as it would admit the possibility of optimizing marginal likelihood as an objective. We propose a differentiable algorithm by abandoning Metropolis-Hastings steps, which further unlocks mini-batch computation.
  arXiv  Detail & Related papers  (2021-07-21T17:10:14Z)
• Faster Convergence of Stochastic Gradient Langevin Dynamics for Non-Log-Concave Sampling [110.88857917726276]
  We provide a new convergence analysis of gradient Langevin dynamics (SGLD) for sampling from a class of distributions that can be non-log-concave. At the core of our approach is a novel conductance analysis of SGLD using an auxiliary time-reversible Markov Chain.
  arXiv  Detail & Related papers  (2020-10-19T15:23:18Z)
• Non-Convex Optimization via Non-Reversible Stochastic Gradient Langevin Dynamics [27.097121544378528]
  Gradient Langevin Dynamics (SGLD) is a powerful algorithm for optimizing a non- objective gradient. NSGLD is based on discretization of the non-reversible diffusion.
  arXiv  Detail & Related papers  (2020-04-06T17:11:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.