Approximation to stochastic variance reduced gradient Langevin dynamics by stochastic delay differential equations (Q2128624)

The authors consider the stochastic variance reduced gradient Langevin dynamics algorithm, and show that its output can be approximated by the solution of a stochastic differential equations with delay. Uniform error bounds are obtained using the Wasserstein distance under assumptions that cover both convex and non-convex minimization problems. The proof arguments rely on the Lindeberg principle and on semigroup gradient bounds obtained by the Malliavin calculus.