mlsanityData to 7 Oct 2026

Optimal Convergence Rate of Hamiltonian Monte Carlo for Strongly Logconcave Distributions

arXiv 1905.02313 ↗First posted 7 May 2019cs.DS cs.LG stat.MLcited by 28

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Abstract (arXiv)

We study Hamiltonian Monte Carlo (HMC) for sampling from a strongly logconcave density proportional to e-f where f:ℝd → ℝ is μ-strongly convex and L-smooth (the condition number is kappa = L/μ). We show that the relaxation time (inverse of the spectral gap) of ideal HMC is O(kappa), improving on the previous best bound of O(kappa1.5); we complement this with an example where the relaxation time is Omega(kappa). When implemented using a nearly optimal ODE solver, HMC returns an varepsilon-approximate point in 2-Wasserstein distance using widetildeO((kappa d)0.5 varepsilon-1) gradient evaluations per step and widetildeO((kappa d)1.5varepsilon-1) total time.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 May 2019.

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Citing papers per year: 2021: 7; 2022: 6; 2023: 6; 2024: 6; 2025: 2; 2026: 1.

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  1. 2022Private Convex Optimization via Exponential Mechanismcited by 47
  2. 2023Faster high-accuracy log-concave sampling via algorithmic warm startscited by 44
  3. 2021Lower Bounds on Metropolized Sampling Methods for Well-Conditioned Distributionscited by 19
  4. 2021Mixing Time Guarantees for Unadjusted Hamiltonian Monte Carlocited by 18
  5. 2021On Convergence of Federated Averaging Langevin Dynamicscited by 14
  6. 2023When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?cited by 12
  7. 2025Source-Guided Flow Matchingcited by 11
  8. 2022Condition-number-independent convergence rate of Riemannian Hamiltonian Monte Carlo with numerical integratorscited by 10
  9. 2024Accelerating Approximate Thompson Sampling with Underdamped Langevin Monte Carlocited by 10
  10. 2023Algorithmic Aspects of the Log-Laplace Transform and a Non-Euclidean Proximal Samplercited by 9
  11. 2021An Introduction to Hamiltonian Monte Carlo Method for Samplingcited by 8
  12. 2022Hamiltonian Monte Carlo for efficient Gaussian sampling: long and random stepscited by 8
16 more
  1. 2022Unadjusted Hamiltonian MCMC with Stratified Monte Carlo Time Integrationcited by 8
  2. 2022Accelerating Hamiltonian Monte Carlo via Chebyshev Integration Timecited by 7
  3. 2023Fit Like You Sample: Sample-Efficient Generalized Score Matching from Fast Mixing Diffusionscited by 6
  4. 2021Entropy-based adaptive Hamiltonian Monte Carlocited by 5
  5. 2024Faster Sampling via Stochastic Gradient Proximal Samplercited by 5
  6. 2023Mean-Square Analysis of Discretized Ito Diffusions for Heavy-tailed Samplingcited by 4
  7. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  8. 2024Bayesian Federated Learning with Hamiltonian Monte Carlo: Algorithm and Theorycited by 4
  9. 2025Feel-Good Thompson Sampling for Contextual Bandits: a Markov Chain Monte Carlo Showdowncited by 4
  10. 2021Hamiltonian Monte Carlo with Asymmetrical Momentum Distributionscited by 1
  11. 2022On the Dissipation of Ideal Hamiltonian Monte Carlo Samplercited by 1
  12. 2024Sampling with Adaptive Variance for Multimodal Distributionscited by 1
  13. 2026Mirror Langevin diffusions: Convergence rates and Markov chain approximationscited by 1
  14. 2021Truncated Log-concave Sampling with Reflective Hamiltonian Monte Carlocited by 0
  15. 2024On Convergence of the Alternating Directions SGHMC Algorithmcited by 0
  16. 2024Randomized Transport Plans via Hierarchical Fully Probabilistic Designcited by 0