Non-asymptotic convergence of discretized NALD and NRALD

Establish non-asymptotic convergence guarantees for discretizations of non-reversible anchored Langevin dynamics (NALD) for unconstrained sampling and non-reversible reflected anchored Langevin dynamics (NRALD) for constrained sampling, despite the state-dependent diffusion coefficients and the reflections present in NRALD.

Background

The paper develops finite-time convergence results for the continuous-time NALD and NRALD diffusions, including total-variation bounds, but does not analyze the corresponding discrete-time algorithms. The discretizations inherit technical difficulties from the state-dependent diffusion coefficient in both dynamics and from the boundary reflection in NRALD.

A resolution would provide theoretical guarantees for the practical Euler-type and projected schemes used in the numerical experiments, linking their computational performance and discretization bias to the continuous-time acceleration results.

References

It will be interesting to obtain non-asymptotic convergence guarantees for the algorithms based on the discretization of the continuous-time NALD for unconstrained sampling and NRALD for constrained sampling in the paper. The analysis can be challenging due to the state-dependent diffusion coefficient in NALD and NRALD as well as the presence of reflections in NRALD. This will be left for future investigations.

— Accelerating Non-Smooth and Heavy-Tailed Sampling  (2610.11139 - Ali et al., 8 Oct 2026) in Conclusion, Section 6