Poisson-Corrector Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling
We study the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA) for $π(\,\mathrm{d} x)\propto e^{-f(x)-g(x)}\,\mathrm{d} x$, where $f\in C^2(\mathbb{R}^d)$ is $m$-strongly convex with $L_f$-Lipschitz gradient and $g:\mathbb{R}^d\to\mathbb{R}$ is convex and globally $G$-Lipschitz. For the Moreau-smoothed target $π_λ$ and the MYULA invariant law $\widehatπ_{λ,h}$, we prove \[ \sqrt m\,W_2(π_λ,\widehatπ_{λ,h}) =O(h)+\widetilde O(h^{3/4}) \] under $0<h(L_f+λ^{-1})\le c$, 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 $\sqrt m\,W_2(μ_N,...
| Authors | Yuchen Xin, Zhihua Zhang |
|---|---|
| Primary category | cs.LG |
| Published | 11 September 2026 |
| Last updated at source | 11 September 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.