The paper introduces a new underdamped Langevin system for sampling Gibbs distributions on matrix spaces where the potential energy is neither convex nor globally gradient‑Lipschitz. By employing non‑quadratic kinetic energies, the authors achieve momentum preconditioning that smooths the momentum via a spectral taming of its gradient. They prove that this dynamics preserves the target Gibbs measure, converges exponentially fast in a weighted total variation distance, and that its Euler–Maruyama discretization remains stable with uniform moment bounds over time.
By Nikolaos Makras, Sotirios Sabanis
We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex. We introduce the Subgradient Tamed Unadjusted Langevin Algorithm (SG-TULA), a discretisation of the Langevin diffusion that operates directly on subgradients, without relying on computationally demanding smoothing procedures.
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