Safety
Poisson-Corrector Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling
arXiv:2609.12594v1 Announce Type: new Abstract: We study the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA) for pi(,d x)propto e^{-f(x)-g(x)},d x, where fin C^2(R^d) is m-strongly conv
arXiv:2609.12594v1 Announce Type: new Abstract: We study the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA) for pi(,d x)propto e^{-f(x)-g(x)},d x, where fin C^2(R^d) is m-strongly convex with L_f-Lipschitz gradient and g:R^doR is convex and globally G-Lipschitz. For the Moreau-smoothed target pi_lambda and the MYULA invariant law widehatpi_{lambda,h}, we prove [ sqrt m,W_2(pi_lambda,widehatpi_{lambda,h}) =O(h)+widetilde O(h^{3/4}) ] under 0<h(L_f+lambda^{-1})le c, with only logarithmic dependence on lambda^{-1} in the error coefficients. Combining this estimate with the Moreau approximation bias yields widetilde O(arepsilon^{-4/3}) iterations to achieve sqrt m,W_2(mu_N,pi)learepsilon, 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.
Related
- Active-Trace Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling
- Wasserstein mixing time of the unadjusted Langevin algorithm
Source: arXiv cs.LG | 2026-09-14