# Penalized Langevin dynamics with vanishing penalty for smooth and log-concave targets

arXiv: https://arxiv.org/abs/2006.13998 · HTML: https://mlsanity.com/paper/2006.13998/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2020.

## Built on by (most cited first, 2 of 2)

- [Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Condition](https://mlsanity.com/paper/2206.00508/) (2022)
- [ELF: Federated Langevin Algorithms with Primal, Dual and Bidirectional Compression](https://mlsanity.com/paper/2303.04622/) (2023)

## Abstract (arXiv)

We study the problem of sampling from a probability distribution on mathbb Rp 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 influence 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.