Stochastic zeroth-order discretizations of Langevin diffusions for Bayesian inference

Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation the gradient potential function. In several real-world scenarios, obtaining evaluations might either be computationally expensive, or simply impossible. this work, we propose analyze stochastic zeroth-order algorithms discretizing overdamped underdamped diffusions. Our approach is based on estimating gradients, Gaussian Stein’s identities, widely used in optimization literature. We comprehensive oracle complexity analysis – number noisy function to made obtain an ϵ-approximate sample Wasserstein distance both diffusions, under various noise models. theoretical contributions extend applicability black-box settings arising practice.