Contraction and Convergence Rates for Discretized Kinetic Langevin Dynamics (Peter Whalley, Edinburgh)
25.04.2023 14:00
Underdamped (Kinetic) Langevin dynamics is becoming a popular tool for sampling in statistical machine learning and molecular dynamics due to the fact that it has desirable non-asymptotic properties. For some target measure a continuous Langevin diffusion can be constructed to have the target as the invariant measure. In MCMC, Langevin diffusions are discretised to generate samples from the target. The choice of discretisation is very important for the quality of the samples. Popular numerical integrators include Euler-Maruyama, BAOAB and the Stochastic Euler scheme. The quality of a numerical scheme is measured through its bias and its convergence rate. This talk will focus on a framework to provide Wasserstein convergence rates for many different discretisations from machine learning and molecular dynamics which hold for a large range of stepsizes. We will also discuss the property “γ-limit convergent” (GLC) to characterise underdamped Langevin schemes that converge to the overdamped dynamics in the high friction limit and which have stepsize restrictions that are independent of the friction parameter; we show that this property is not generic by exhibiting methods from both the class and its complement.
Lieu
Bâtiment: Conseil Général 7-9
Room 1-05, Séminaire d'analyse numérique
Organisé par
Section de mathématiquesIntervenant-e-s
Peter Whalley, University of Edinburghentrée libre