Abstract:We study a sampling problem whose target distribution is $\pi \propto \exp(-f-r)$ where the data fidelity term $f$ is Lipschitz smooth while the regularizer term $r=r_1-r_2$ is a non-smooth difference-of-convex (DC) function, i.e., $r_1,r_2$ are convex. By leveraging the DC structure of $r$, we can smooth out $r$ by applying Moreau envelopes to $r_1$ and $r_2$ separately. In line with DC programming, we then redistribute the concave part of the regularizer to the data fidelity and study its corresponding proximal Langevin algorithm (termed DC-LA). We establish convergence of DC-LA to the target distribution $\pi$, up to discretization and smoothing errors, in the $q$-Wasserstein distance for all $q \in \mathbb{N}^*$, under the assumption that $V$ is distant dissipative. Our results improve previous work on non-log-concave sampling in terms of a more general framework and assumptions. Numerical experiments show that DC-LA produces accurate distributions in synthetic settings and provides qualitatively reasonable uncertainty quantification in a real-world Computed Tomography application.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2601.22932 [cs.LG] |
| (or arXiv:2601.22932v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2601.22932 arXiv-issued DOI via DataCite |
From: Hoang Phuc Hau Luu [view email]
[v1]
Fri, 30 Jan 2026 12:49:05 UTC (6,515 KB)
[v2]
Wed, 20 May 2026 09:11:24 UTC (6,675 KB)
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