Smoothed Picard Hamiltonian Monte Carlo

arXiv:2609.06906 · math.ST, cs.DS, cs.LG, cs.NA, math.NA, stat.TH · Submitted 2026-09-07 · Read on arXiv

math.ST, cs.DS, cs.LG, cs.NA, math.NA, stat.TH

Submitted: 2026-09-07

Updated: 2026-09-29

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

Terminology

• Accuracy — 2× in this paper · explained in 1 episode

Sources

• Tail-Sensitive KL and R'enyi Convergence of Unadjusted Hamiltonian Monte Carlo via One-Shot Couplings
• High-accuracy sampling for diffusion models and log-concave distributions
• Exact simulation of diffusions and improved algorithms for log-concave sampling
• When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?
• The shifted ODE method for underdamped Langevin MCMC
• Zeroth-order Logconcave Sampling
• Space-Time Log-Sobolev Inequality and Hypocoercive Hypercontractivity for Underdamped Langevin Dynamics
• Algorithmic Theory of ODEs and Sampling from Well-conditioned Logconcave Densities
• A sharp hypocoercive entropy decay estimate for underdamped Langevin dynamics
• Rapid Mixing of Hamiltonian Monte Carlo on Strongly Log-Concave Distributions
• Accelerated Mixing Time of Randomized Hamiltonian Monte Carlo
• On the entropic convergence for piecewise deterministic samplers: speedup and obstruction
• Theoretical guarantees for stochastic gradient sampling methods via Gaussian convolution inequalities
• Algorithmic warm starts for Hamiltonian Monte Carlo

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