Accelerated Mixing Time of Randomized Hamiltonian Monte Carlo

arXiv:2607.12902 · stat.ML, cs.DS, cs.LG, math.PR, math.ST, stat.CO · Submitted 2026-07-14 · Read on arXiv

Siddharth Mitra, Vishwak Srinivasan, Xiuyuan Wang, Andre Wibisono

stat.ML, cs.DS, cs.LG, math.PR, math.ST, stat.CO

Submitted: 2026-07-14

Comments: 74 pages

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Hamiltonian Monte Carlo — 29× in this paper
• Langevin Dynamics — 23× in this paper · explained in 3 episodes
• Wasserstein Distance — 16× in this paper · explained in 5 episodes
• Randomized Hamiltonian Monte Carlo — 12× in this paper
• Gradient Flow — 11× in this paper · explained in 2 episodes
• No-U-Turn Sampler — 7× in this paper
• Convergence Guarantees — 6× in this paper · explained in 3 episodes
• Optimal Transport — 5× in this paper · explained in 5 episodes
• Fisher Information — 4× in this paper · explained in 4 episodes
• Kullback-Leibler (KL) Divergence — 2× in this paper · explained in 6 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Diffusion Processes — 1× in this paper · explained in 2 episodes
• Editor — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Geometric interpretation — 1× in this paper · explained in 2 episodes
• Markov Chain Monte Carlo — 1× in this paper
• Mean-Field Dynamics — 1× in this paper · explained in 2 episodes
• Non-asymptotic Analysis — 1× in this paper · explained in 2 episodes
• Query Complexity — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Structural Properties — 1× in this paper · explained in 2 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Uncertainty Quantification — 1× in this paper · explained in 9 episodes

Sources

• Tail-Sensitive KL and R'enyi Convergence of Unadjusted Hamiltonian Monte Carlo via One-Shot Couplings
• Mixing of the No-U-Turn Sampler and the Geometry of Gaussian Concentration
• Second order quantitative bounds for unadjusted generalized Hamiltonian Monte Carlo
• When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?
• Sharp hypocoercive convergence estimates for underdamped Langevin dynamics via the modified $L^2$ method
• A Theoretical Comparison of No-U-Turn Sampler Variants: Necessary and Sufficient Convergence Conditions and Mixing Time Analysis under Gaussian Targets
• Space-Time Log-Sobolev Inequality and Hypocoercive Hypercontractivity for Underdamped Langevin Dynamics
• A sharp hypocoercive entropy decay estimate for underdamped Langevin dynamics
• On the entropic convergence for piecewise deterministic samplers: speedup and obstruction
• On Accelerated Mixing of the No-U-turn Sampler
• Frictionless Hamiltonian Descent and Coordinate Hamiltonian Descent for Strongly Convex Quadratic Problems

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