mlsanityData to 7 Oct 2026

Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics

arXiv 2405.07839 ↗First posted 13 May 2024cs.LG cs.AI stat.MLcited by 7

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Abstract (arXiv)

Replica exchange stochastic gradient Langevin dynamics (reSGLD) is an effective sampler for non-convex learning in large-scale datasets. However, the simulation may encounter stagnation issues when the high-temperature chain delves too deeply into the distribution tails. To tackle this issue, we propose reflected reSGLD (r2SGLD): an algorithm tailored for constrained non-convex exploration by utilizing reflection steps within a bounded domain. Theoretically, we observe that reducing the diameter of the domain enhances mixing rates, exhibiting a textitquadratic behavior. Empirically, we test its performance through extensive experiments, including identifying dynamical systems with physical constraints, simulations of constrained multi-modal distributions, and image classification tasks. The theoretical and empirical findings highlight the crucial role of constrained exploration in improving the simulation efficiency.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 26 of its 65 references that are in the map. First posted on arXiv 13 May 2024.

Builds on

26 of 65 references.

References · 26

  1. 2017Stochastic Gradient Descent as Approximate Bayesian Inferencecited by 298
  2. 2019Cyclical Stochastic Gradient MCMC for Bayesian Deep Learningcited by 203
  3. 2021PySINDy: A comprehensive Python package for robust sparse system identificationcited by 88
  4. 2018Mirrored Langevin Dynamicscited by 61
  5. 2020Efficient constrained sampling via the mirror-Langevin algorithmcited by 55
  6. 2015Sampling from a log-concave distribution with Projected Langevin Monte Carlocited by 52
  7. 2017Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlocited by 43
  8. 2016On the Convergence of Stochastic Gradient MCMC Algorithms with High-Order Integratorscited by 35
  9. 2017Beyond Log-concavity: Provable Guarantees for Sampling Multi-modal Distributions using Simulated Tempering Langevin Monte Carlocited by 33
  10. 2019Stochastic Runge-Kutta Accelerates Langevin Monte Carlo and Beyondcited by 33
  11. 2020Non-convex Learning via Replica Exchange Stochastic Gradient MCMCcited by 33
  12. 2020Projected Stochastic Gradient Langevin Algorithms for Constrained Sampling and Non-Convex Learningcited by 33
14 more
  1. 2017Convergence Rate of Riemannian Hamiltonian Monte Carlo and Faster Polytope Volume Computationcited by 32
  2. 2020MOTS: Minimax Optimal Thompson Samplingcited by 28
  3. 2022Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Spacecited by 28
  4. 2020A Contour Stochastic Gradient Langevin Dynamics Algorithm for Simulations of Multi-modal Distributionscited by 26
  5. 2020Fast Convergence of Langevin Dynamics on Manifold: Geodesics meet Log-Sobolevcited by 16
  6. 2020Accelerating Nonconvex Learning via Replica Exchange Langevin Diffusioncited by 15
  7. 2016Stochastic Quasi-Newton Langevin Monte Carlocited by 14
  8. 2024Reflected Schr"odinger Bridge for Constrained Generative Modelingcited by 12
  9. 2022Sampling in Constrained Domains with Orthogonal-Space Variational Gradient Descentcited by 11
  10. 2024Accelerating Approximate Thompson Sampling with Underdamped Langevin Monte Carlocited by 10
  11. 2022Interacting Contour Stochastic Gradient Langevin Dynamicscited by 9
  12. 2022Accelerating Hamiltonian Monte Carlo via Chebyshev Integration Timecited by 7
  13. 2022Non-reversible Parallel Tempering for Deep Posterior Approximationcited by 7
  14. 2022Unbiased constrained sampling with Self-Concordant Barrier Hamiltonian Monte Carlocited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 4; 2026: 2.

7 papers.

  1. 2025Non-Reversible Langevin Algorithms for Constrained Samplingcited by 7
  2. 2024LES-SINDy: Laplace-Enhanced Sparse Identification of Nonlinear Dynamical Systemscited by 4
  3. 2025Morephy-Net: An Evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Neural Operator Learning Networkscited by 3
  4. 2025Accelerating Constrained Sampling: A Large Deviations Approachcited by 2
  5. 2026Decentralized Proximal Stochastic Gradient Langevin Dynamicscited by 2
  6. 2025BLADE: Bayesian Langevin Active Discovery with Replica Exchange for Identification of Complex Systemscited by 0
  7. 2026Fast PAC Global Optimization via Restarted Langevin: Exploration, Exploitation, and Degenerate Coolingcited by 0