Séminaire de Probabilités et Statistique
lundi 13 septembre 2021 à 13:45 - UM - Bât 09 - Salle 430
Geneviève Robin (CNRS - Laboratoire de Mathématiques et Modélisation d'Évry)
Optimizing the diffusion function of overdamped Langevin dynamics sampling algorithms
Overdamped Langevin dynamics are often used as building blocks to propose new states in MCMC sampling algorithms; an important example is the Metropolis Adjusted Langevin Algorithm (MALA). In Langevin dynamics, new states are produced following a noisy pre-conditioned gradient step. A crucial parameter is the diffusion function (or tensor) which sets the variance of the noise and the pre-conditioning of the gradient step and may depend on the spatial position.
In this talk, I will present a new approach to optimize the choice of diffusion function in order to accelerate convergence towards the invariant measure. I will introduce the optimization problem, provide theoretical results and a numerical scheme. I will also discuss the asymptotic behaviour of the optimal diffusion in the homogenized limit, and present numerical illustrations in simple examples.
Séminaire en salle 430 (IMAG, bâtiment 9), en présentiel.
Également retransmis sur zoom (attention, nouveau lien) :
https://umontpellier-fr.zoom.us/j/94087408185