Paper ID: 2410.17297

Error estimates between SGD with momentum and underdamped Langevin diffusion

Arnaud Guillin (LMBP), Yu Wang, Lihu Xu, Haoran Yang

Stochastic gradient descent with momentum is a popular variant of stochastic gradient descent, which has recently been reported to have a close relationship with the underdamped Langevin diffusion. In this paper, we establish a quantitative error estimate between them in the 1-Wasserstein and total variation distances.

Submitted: Oct 22, 2024