mlsanityData to 14 Oct 2026

Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo in the nonconvex stochastic gradient case

arXiv 2310.18774 ↗First posted 28 Oct 2023math.PR stat.CO stat.MLcited by 3

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Abstract (arXiv)

Contraction in Wasserstein 1-distance with explicit rates is established for generalized Hamiltonian Monte Carlo with stochastic gradients under possibly nonconvex conditions. The algorithms considered include splitting schemes of kinetic Langevin diffusion commonly used in molecular dynamics simulations. To accommodate the degenerate noise structure corresponding to inertia existing in the chain, a characteristically discrete-in-time coupling and contraction proof is devised. As consequence, quantitative Gaussian concentration bounds are provided for empirical averages. Convergence in Wasserstein 2-distance and total variation are also given, together with numerical bias estimates.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 18 of its 58 references that are in the map. First posted on arXiv 28 Oct 2023.

Builds on

18 of 58 references.

References · 18

  1. 2014Stochastic Gradient Hamiltonian Monte Carlocited by 343
  2. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 146
  3. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 133
  4. 2018Sharp convergence rates for Langevin dynamics in the nonconvex settingcited by 68
  5. 2018Sampling Can Be Faster Than Optimizationcited by 68
  6. 2018A Modern Take on the Bias-Variance Tradeoff in Neural Networkscited by 65
  7. 2019Fast mixing of Metropolized Hamiltonian Monte Carlo: Benefits of multi-step gradientscited by 51
  8. 2018Coupling and Convergence for Hamiltonian Monte Carlocited by 36
  9. 2018Non-asymptotic bounds for sampling algorithms without log-concavitycited by 35
  10. 2023Improved Discretization Analysis for Underdamped Langevin Monte Carlocited by 28
  11. 2021Local-Global MCMC kernels: the best of both worldscited by 22
  12. 2018A Framework for Adaptive MCMC Targeting Multimodal Distributionscited by 21
6 more
  1. 2016On the Geometric Ergodicity of Hamiltonian Monte Carlocited by 19
  2. 2018Simulated Tempering Langevin Monte Carlo II: An Improved Proof using Soft Markov Chain Decompositioncited by 18
  3. 2021Mixing Time Guarantees for Unadjusted Hamiltonian Monte Carlocited by 18
  4. 2021Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimensioncited by 11
  5. 2022Unadjusted Hamiltonian MCMC with Stratified Monte Carlo Time Integrationcited by 8
  6. 2022Unbiased Estimation using Underdamped Langevin Dynamicscited by 3

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Cited by year

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

3 papers.

  1. 2024Sampling from Bayesian Neural Network Posteriors with Symmetric Minibatch Splitting Langevin Dynamicscited by 13
  2. 2025Exponential Convergence Guarantees for Iterative Markovian Fittingcited by 3
  3. 2025Analysis of kinetic Langevin Monte Carlo under the stochastic exponential Euler discretization from underdamped all the way to overdampedcited by 0