Penalized Langevin dynamics with vanishing penalty for smooth and log-concave targets [article]

Avetik Karagulyan, Arnak S. Dalalyan
2020 arXiv   pre-print
We study the problem of sampling from a probability distribution on R^p defined via a convex and smooth potential function. We consider a continuous-time diffusion-type process, termed Penalized Langevin dynamics (PLD), the drift of which is the negative gradient of the potential plus a linear penalty that vanishes when time goes to infinity. An upper bound on the Wasserstein-2 distance between the distribution of the PLD at time t and the target is established. This upper bound highlights the
more » ... nfluence of the speed of decay of the penalty on the accuracy of the approximation. As a consequence, considering the low-temperature limit we infer a new nonasymptotic guarantee of convergence of the penalized gradient flow for the optimization problem.
arXiv:2006.13998v1 fatcat:ffkgkl4pfbed3larncmr5sx2jq