Forward-KL Convergence of Time-Inhomogeneous Langevin Diffusions
This work offers a unified theoretical analysis for practitioners using annealing or tempering in Langevin sampling, but the results are theoretical and incremental in nature.
The paper provides non-asymptotic convergence bounds for time-inhomogeneous Langevin diffusions and their Euler-Maruyama discretization in forward-KL divergence, under abstract conditions on the time-dependent drift. The results apply to practical annealing schemes like geometric tempering and annealed Langevin sampling.
Many practical samplers rely on time-dependent drifts -- often induced by annealing or tempering schedules -- to improve exploration and stability. This motivates a unified non-asymptotic analysis of the corresponding Langevin diffusions and their discretizations. We provide a convergence analysis that includes non-asymptotic bounds for the continuous-time diffusion and its Euler--Maruyama discretization in the forward-Kullback--Leibler divergence under a single set of abstract conditions on the time-dependent drift. The results apply to many practically-relevant annealing schemes, including geometric tempering and annealed Langevin sampling. In addition, we provide numerical experiments comparing the annealing schemes covered by our theory in low- and high-dimensional settings.