mlsanityData to 7 Oct 2026

Constrained Sampling with Primal-Dual Langevin Monte Carlo

arXiv 2411.00568 ↗First posted 1 Nov 2024stat.ML cs.LG math.OCcited by 10

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Abstract (arXiv)

This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem finds applications in, e.g., Bayesian inference, where it can constrain moments to evaluate counterfactual scenarios or enforce desiderata such as prediction fairness. Methods developed to handle support constraints, such as those based on mirror maps, barriers, and penalties, are not suited for this task. This work therefore relies on gradient descent-ascent dynamics in Wasserstein space to put forward a discrete-time primal-dual Langevin Monte Carlo algorithm (PD-LMC) that simultaneously constrains the target distribution and samples from it. We analyze the convergence of PD-LMC under standard assumptions on the target distribution and constraints, namely (strong) convexity and log-Sobolev inequalities. To do so, we bring classical optimization arguments for saddle-point algorithms to the geometry of Wasserstein space. We illustrate the relevance and effectiveness of PD-LMC in several applications.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 31 of its 76 references that are in the map. First posted on arXiv 1 Nov 2024.

Builds on

31 of 76 references.

References · 31

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19 more
  1. 2020Last Iterate is Slower than Averaged Iterate in Smooth Convex-Concave Saddle Point Problemscited by 59
  2. 2020Wasserstein Control of Mirror Langevin Monte Carlocited by 55
  3. 2020Efficient constrained sampling via the mirror-Langevin algorithmcited by 55
  4. 2015Sampling from a log-concave distribution with Projected Langevin Monte Carlocited by 52
  5. 2018On the Convergence and Robustness of Training GANs with Regularized Optimal Transportcited by 51
  6. 2020Probably Approximately Correct Constrained Learningcited by 47
  7. 2021Constrained Learning with Non-Convex Lossescited by 42
  8. 2019Accelerated Information Gradient flowcited by 38
  9. 2020Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithmcited by 34
  10. 2020Projected Stochastic Gradient Langevin Algorithms for Constrained Sampling and Non-Convex Learningcited by 33
  11. 2022Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Spacecited by 28
  12. 2021Sampling with Mirrored Stein Operatorscited by 17
  13. 2022Sampling with Mollified Interaction Energy Descentcited by 17
  14. 2019Bounding the error of discretized Langevin algorithms for non-strongly log-concave targetscited by 16
  15. 2022Nest Your Adaptive Algorithm for Parameter-Agnostic Nonconvex Minimax Optimizationcited by 16
  16. 2023Fast sampling from constrained spaces using the Metropolis-adjusted Mirror Langevin algorithmcited by 11
  17. 2015Asymptotic convergence of constrained primal-dual dynamicscited by 8
  18. 2022Unbiased constrained sampling with Self-Concordant Barrier Hamiltonian Monte Carlocited by 6
  19. 2023Accelerated Primal-dual Scheme for a Class of Stochastic Nonconvex-concave Saddle Point Problemscited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 4; 2026: 6.

10 papers.

  1. 2025Constrained Diffusers for Safe Planning and Controlcited by 9
  2. 2025Strictly Constrained Generative Modeling via Split Augmented Langevin Samplingcited by 6
  3. 2025Projected Coupled Diffusion for Test-Time Constrained Joint Generationcited by 6
  4. 2026Constrained Flow Optimization via Sequential Fine Tuning for Molecular Designcited by 2
  5. 2026Unlearning in Diffusion Models: A Unified Framework with KL Divergence and Likelihood Constraintscited by 2
  6. 2026Constrained Diffusion Models with Primal-Dual Inferencecited by 2
  7. 2026DiRecT: Safe Diffusion-Based Planning via Receding-Horizon Denoisingcited by 1
  8. 2025Sampling with Shielded Langevin Monte Carlo Using Navigation Potentialscited by 0
  9. 2026Kinetic Langevin Splitting Schemes for Constrained Samplingcited by 0
  10. 2026Generative Modeling by Value-Driven Transportcited by 0