Poisson Midpoint Method for Log Concave Sampling: Beyond the Strong Error Lower Bounds
Abstract
We study the problem of sampling from strongly log-concave distributions over $\mathbb{R}^d$ using the Poisson midpoint discretization (a variant of the randomized midpoint method) for overdamped/underdamped Langevin dynamics. We prove its convergence in the 2-Wasserstein distance ($\mathcal W_2$), achieving a cubic speedup in dependence on the target accuracy ($\epsilon$) over the Euler-Maruyama discretization, surpassing existing bounds for randomized midpoint methods. Notably, in the case of underdamped Langevin dynamics, we demonstrate the complexity of $\mathcal W_2$ convergence is much smaller than the complexity lower bounds for convergence in $L^2$ strong error established in the literature.
Cite
Text
Srinivasan and Nagaraj. "Poisson Midpoint Method for Log Concave Sampling: Beyond the Strong Error Lower Bounds." International Conference on Learning Representations, 2026.Markdown
[Srinivasan and Nagaraj. "Poisson Midpoint Method for Log Concave Sampling: Beyond the Strong Error Lower Bounds." International Conference on Learning Representations, 2026.](https://mlanthology.org/iclr/2026/srinivasan2026iclr-poisson/)BibTeX
@inproceedings{srinivasan2026iclr-poisson,
title = {{Poisson Midpoint Method for Log Concave Sampling: Beyond the Strong Error Lower Bounds}},
author = {Srinivasan, Rishikesh and Nagaraj, Dheeraj Mysore},
booktitle = {International Conference on Learning Representations},
year = {2026},
url = {https://mlanthology.org/iclr/2026/srinivasan2026iclr-poisson/}
}