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SUMMARY:Optimizing the diffusion for sampling with overdamped Langevin dyn
 amics - Gabriel Stoltz (ENPC - École des Ponts ParisTech)
DTSTART:20241125T112500Z
DTEND:20241125T121500Z
UID:TALK221470@talks.cam.ac.uk
DESCRIPTION:Overdamped Langevin dynamics are stochastic differential equat
 ions\, where gradient dynamics are perturbed by noise in order to sample h
 igh dimensional probability measures such as the ones appearing in computa
 tional statistical physics and Bayesian inference. By varying the diffusio
 n coefficient\, there are in fact infinitely many overdamped Langevin dyna
 mics which preserve the target probability measure at hand. This suggests 
 to optimize the diffusion coefficient in order to increase the convergence
  rate of the dynamics\, as measured by the spectral gap of the generator a
 ssociated with the stochastic differential equation. We analytically study
  this problem here\, obtaining in particular necessary conditions on the o
 ptimal diffusion coefficient. We also derive an explicit expression of the
  optimal diffusion in some homogenized limit. Numerical results\, both on 
 discretizations of the spectral gap problem and Monte Carlo simulations of
  the stochastic dynamics\, demonstrate the increased quality of the sampli
 ng arising from an appropriate choice of the diffusion coefficient.
LOCATION:Seminar Room 1\, Newton Institute
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