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Kinetic Langevin Splitting Schemes for Constrained Sampling

arXiv 2603.23397 ↗First posted 24 Mar 2026stat.ME cs.NA math.NAcited by 0

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Abstract (arXiv)

Constrained sampling is an important and challenging task in computational statistics, concerned with generating samples from a distribution under certain constraints. There are numerous types of algorithm aimed at this task, ranging from general Markov chain Monte Carlo, to unadjusted Langevin methods. In this article we propose a series of new sampling algorithms based on the latter of these, specifically the kinetic Langevin dynamics. Our series of algorithms are motivated on advanced numerical methods which are splitting order schemes, which include the BU and BAO families of splitting schemes.Their advantage lies in the fact that they have favorable strong order (bias) rates and computationally efficiency. In particular we provide a number of theoretical insights which include a Wasserstein contraction and convergence results. We are able to demonstrate favorable results, such as improved complexity bounds over existing non-splitting methodologies. Our results are verified through numerical experiments on a range of models with constraints, which include a toy example and Bayesian linear regression.

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References · 21

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  3. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  4. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 131
  5. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 77
  6. 2018On sampling from a log-concave density using kinetic Langevin diffusionscited by 61
  7. 2017Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlocited by 43
  8. 2018Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Accelerationcited by 31
  9. 2022Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Spacecited by 28
  10. 2025Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Accelerationcited by 17
  11. 2022Penalized Overdamped and Underdamped Langevin Monte Carlo Algorithms for Constrained Samplingcited by 13
  12. 2024Sampling from Bayesian Neural Network Posteriors with Symmetric Minibatch Splitting Langevin Dynamicscited by 12
9 more
  1. 2024Constrained Sampling with Primal-Dual Langevin Monte Carlocited by 10
  2. 2022Wide Bayesian neural networks have a simple weight posterior: theory and accelerated samplingcited by 9
  3. 2021Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equationscited by 8
  4. 2023Unbiased Kinetic Langevin Monte Carlo with Inexact Gradientscited by 8
  5. 2025Non-Reversible Langevin Algorithms for Constrained Samplingcited by 7
  6. 2022Unbiased constrained sampling with Self-Concordant Barrier Hamiltonian Monte Carlocited by 6
  7. 2024The Poisson Midpoint Method for Langevin Dynamics: Provably Efficient Discretization for Diffusion Modelscited by 6
  8. 2022Unbiased Estimation using Underdamped Langevin Dynamicscited by 3
  9. 2024Randomized Midpoint Method for Log-Concave Sampling under Constraintscited by 2

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