DC-LA: Difference-of-Convex Langevin Algorithm

• URL: http://arxiv.org/abs/2601.22932v1
• Date: Fri, 30 Jan 2026 12:49:05 GMT
• Title: DC-LA: Difference-of-Convex Langevin Algorithm
• Authors: Hoang Phuc Hau Luu, Zhongjian Wang,
• Abstract summary: We study a sampling problem where the data term $prop(-f-r)$ is distant.<n>Our results show that the term.<n>DC-LA produces accurate fidelity in.<n>settings and provides in a real-d To application.
• Score: 5.184108122340349
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study a sampling problem whose target distribution is $π\propto \exp(-f-r)$ 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 of 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 $π$, 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 reliably provides uncertainty quantification in a real-world Computed Tomography application.

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