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arXiv · 1903.12322

Implicit Langevin Algorithms for Sampling From Log-concave Densities

Liam Hodgkinson·Robert Salomone·Fred Roosta
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Abstract

For sampling from a log-concave density, we study implicit integrators resulting from $\theta$-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the resulting sampling methods for $ \theta \in [0,1] $ and a range of step sizes are established. Our results generalize and extend prior works in several directions. In particular, for $\theta\ge1/2$, we prove geometric ergodicity and stability of the resulting methods for all step sizes. We show 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.

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Liam Hodgkinson, Robert Salomone, Fred Roosta. 2019-03-29. Implicit Langevin Algorithms for Sampling From Log-concave Densities. https://arxiv.org/abs/1903.12322

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