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

arXiv · AI, language, vision and robotics · article · Sep 11, 2026 · UTC

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 appr

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