DC-LA: Difference-of-Convex Langevin Algorithm

arXiv:2601.22932v2 Announce Type: replace 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 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.

Source: arXiv cs.LG | 2026-05-21