Convergence of Adaptive Langevin using hypocoercivity

This lecture covers the convergence of Adaptive Langevin dynamics, focusing on hypocoercive techniques. It reviews the convergence of Langevin type dynamics, demonstrates convergence rates, and discusses the Central Limit Theorem. The instructor presents the structure of Adaptive Langevin dynamics, the removal of mini-batching bias, and the Hamiltonian and overdamped limits. The lecture also explores Fokker-Planck equations, ergodicity results, and the direct L² approach. It delves into the sharpness of scaling, elements of proof, and the Central Limit Theorem. Some numerical results and the normalization of dynamics for Bayesian inference in the large data context are also discussed.