mlsanityData to 7 Oct 2026

Is There an Analog of Nesterov Acceleration for MCMC?

arXiv 1902.00996 ↗First posted 4 Feb 2019stat.ML cs.LG cs.NAcited by 19

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Abstract (arXiv)

We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an underdamped form of the Langevin algorithm performs accelerated gradient descent in this metric. To characterize the convergence of the algorithm, we construct a Lyapunov functional and exploit hypocoercivity of the underdamped Langevin algorithm. As an application, we show that accelerated rates can be obtained for a class of nonconvex functions with the Langevin algorithm.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Feb 2019.

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Citing papers per year: 2021: 11; 2022: 6; 2023: 0; 2024: 1; 2025: 0; 2026: 1.

19 papers.

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  1. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusioncited by 230
  2. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
  3. 2021Projected Wasserstein gradient descent for high-dimensional Bayesian inferencecited by 24
  4. 2021A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1cited by 21
  5. 2021Sampling with Mirrored Stein Operatorscited by 17
  6. 2022Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Conditioncited by 16
  7. 2021On Convergence of Federated Averaging Langevin Dynamicscited by 14
  8. 2021When is the Convergence Time of Langevin Algorithms Dimension Independent? A Composite Optimization Viewpointcited by 12
  9. 2021Universal Approximation for Log-concave Distributions using Well-conditioned Normalizing Flowscited by 7
  10. 2022Accelerating Hamiltonian Monte Carlo via Chebyshev Integration Timecited by 7
  11. 2022Statistical and Computational Trade-offs in Variational Inference: A Case Study in Inferential Model Selectioncited by 7
  12. 2021Simulated annealing from continuum to discretization: a convergence analysis via the Eyring--Kramers lawcited by 5
7 more
  1. 2022Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agentscited by 5
  2. 2021A Unifying and Canonical Description of Measure-Preserving Diffusionscited by 4
  3. 2022Federated Learning with a Sampling Algorithm under Isoperimetrycited by 4
  4. 2021De-randomizing MCMC dynamics with the diffusion Stein operatorcited by 3
  5. 2021A New Framework for Variance-Reduced Hamiltonian Monte Carlocited by 0
  6. 2024An Improved Analysis of Langevin Algorithms with Prior Diffusion for Non-Log-Concave Samplingcited by 0
  7. 2026One-Step Generative Modeling via Unbalanced Optimal Transportcited by 0