Smoothed Picard Hamiltonian Monte Carlo
Abstract
We develop a new low-accuracy sampler, called smoothed Picard Hamiltonian Monte Carlo, which combines Gaussian smoothing, Picard iteration, and higher-order discretization. For a log-concave target π∝ exp(−V) in dimension d satisfying 0 ≺ αI ⪯ ∇2 V ⪯ βI, with condition number κ:= β/α, smoothed Picard HMC returns a sample with √α W2(·,π) ≤ ε using Õ(κ2 + κ7/6 d1/6/ε1/3) gradient queries. We also prove stronger Wq bounds, and then develop an algorithmic framework, the recursive warm start generator, to upgrade these Wq bounds to stronger divergence guarantees. This produces a warm start for the proximal bouncy particle sampler, introduced in a companion work, leading to a high-accuracy log-concave sampler with complexity Õ((κ7/6 d1/6 + κ1/2 d1/4)polylog(1/ε)).
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BibTeX
@misc{chen2026smoothed,
title = {{Smoothed Picard Hamiltonian Monte Carlo}},
author = {Fan Chen and Sinho Chewi and Jianfeng Lu and Matthew S Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06906},
eprint = {2609.06906},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06906},
}
RIS
TY - UNPB
TI - Smoothed Picard Hamiltonian Monte Carlo
AU - Fan Chen
AU - Sinho Chewi
AU - Jianfeng Lu
AU - Matthew S Zhang
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.06906
UR - https://arxiv.org/abs/2609.06906
AB - We develop a new low-accuracy sampler, called smoothed Picard Hamiltonian Monte Carlo, which combines Gaussian smoothing, Picard iteration, and higher-order discretization. For a log-concave target π∝ exp(−V) in dimension d satisfying 0 ≺ αI ⪯ ∇^2 V ⪯ βI, with condition number κ:= β/α, smoothed Picard HMC returns a sample with √α W_2(·,π) ≤ ε using Õ(κ^2 + κ^7/6 d^1/6/ε^1/3) gradient queries. We also prove stronger W_q bounds, and then develop an algorithmic framework, the recursive warm start generator, to upgrade these W_q bounds to stronger divergence guarantees. This produces a warm start for the proximal bouncy particle sampler, introduced in a companion work, leading to a high-accuracy log-concave sampler with complexity Õ((κ^7/6 d^1/6 + κ^1/2 d^1/4)polylog(1/ε)).
ER -