Implicit Langevin Algorithms for Sampling From Log-concave Densities [article]

Liam Hodgkinson, Robert Salomone, Fred Roosta
2021 arXiv   pre-print
For sampling from a log-concave density, we study implicit integrators resulting from θ-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the resulting sampling methods for θ∈ [0,1] and a range of step sizes are established. Our results generalize and extend prior works in several directions. In particular, for θ≥1/2, we prove geometric ergodicity and stability of the resulting methods for all step sizes. We
more » ... w that obtaining subsequent samples amounts to solving a strongly-convex optimization problem, which is readily achievable using one of numerous existing methods. Numerical examples supporting our theoretical analysis are also presented.
arXiv:1903.12322v2 fatcat:taby5mkhf5cjpcdkgc6h4op6wq