# Poisson-Corrector Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling

arXiv: https://arxiv.org/abs/2609.12594 · HTML: https://mlsanity.com/paper/2609.12594/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 13 references that are in the map.
- First posted on arXiv 11 Sep 2026.

## Builds on (most cited first, 7 of 7)

- [Analysis of Langevin Monte Carlo via convex optimization](https://mlsanity.com/paper/1802.09188/) (2018)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [Proximal Markov chain Monte Carlo algorithms](https://mlsanity.com/paper/1306.0187/) (2013)
- [Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithm](https://mlsanity.com/paper/2006.09270/) (2020)
- [An Efficient Sampling Algorithm for Non-smooth Composite Potentials](https://mlsanity.com/paper/1910.00551/) (2019)
- [Wasserstein mixing time of the unadjusted Langevin algorithm](https://mlsanity.com/paper/2608.02430/) (2026)
- [Active-Trace Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling](https://mlsanity.com/paper/2608.13467/) (2026)

## Built on by (most cited first, 1 of 1)

- [Near-Linear Accuracy Bounds for Moreau--Yosida Unadjusted Langevin Sampling](https://mlsanity.com/paper/2609.40193/) (2026)

## Abstract (arXiv)

We study the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA) for π(,d x)propto e-f(x)-g(x),d x, where f∈ C2(ℝd) is m-strongly convex with Lf-Lipschitz gradient and g:ℝd→ℝ is convex and globally G-Lipschitz. For the Moreau-smoothed target πλ and the MYULA invariant law widehatπλ,h, we prove [ √ m,W2(πλ,widehatπλ,h) =O(h)+widetilde O(h3/4) ] under 0<h(Lf+λ-1)≤ c, with only logarithmic dependence on λ-1 in the error coefficients. Combining this estimate with the Moreau approximation bias yields widetilde O(varepsilon-4/3) iterations to achieve √ m,W2(μN,π)≤varepsilon, for fixed model parameters and initialization. The proof combines a discrete Poisson corrector with active-trace estimates and a shared-noise bound for the exact--Euler two-point curvature.