Error estimates between SGD with momentum and underdamped Langevin diffusion

Arnaud Guillin; Yu Wang; Lihu Xu; Haoran Yang

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arXiv · 2410.17297

Error estimates between SGD with momentum and underdamped Langevin diffusion

Arnaud Guillin·Yu Wang·Lihu Xu·Haoran Yang

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Abstract

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.

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Arnaud Guillin, Yu Wang, Lihu Xu, Haoran Yang. 2024-10-22. Error estimates between SGD with momentum and underdamped Langevin diffusion. https://arxiv.org/abs/2410.17297

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