Active-Trace Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling
MYULA’s discretization cost is bounded by an “active trace” term that can avoid the usual \(d/\lambda\) curvature penalty.
Xin and Zhang analyze MYULA for nonsmooth composite targets with a strongly convex smooth part and a convex Lipschitz nonsmooth part. Their bound replaces the global Moreau-envelope curvature ceiling with \(B_{\mathrm{ref}}\), an average active trace along one heat substep. For structured penalties including lasso-type, group, and total-variation cases, they show this term can stay independent of \(\lambda\), improving the stated accuracy dependence from \(\widetilde O(\varepsilon^{-3})\) to \(\widetilde O(\varepsilon^{-2})\). They also give a Moreau-bias bound supporting an end-to-end guarantee for the original target. ArXiv · AI/CL/LG's note
Xin and Zhang analyze MYULA for nonsmooth composite targets with a strongly convex smooth part and a convex Lipschitz nonsmooth part. Their bound replaces the global Moreau-envelope curvature ceiling with \(B_{\mathrm{ref}}\), an average active trace along one heat substep. For structured penalties including lasso-type, group, and total-variation cases, they show this term can stay independent of \(\lambda\), improving the stated accuracy dependence from \(\widetilde O(\varepsilon^{-3})\) to \(\widetilde O(\varepsilon^{-2})\). They also give a Moreau-bias bound supporting an end-to-end guarantee for the original target. ArXiv · AI/CL/LG's note
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