Summary of Error Estimates Between Sgd with Momentum and Underdamped Langevin Diffusion, by Arnaud Guillin (lmbp) et al.
Error estimates between SGD with momentum and underdamped Langevin diffusion
by Arnaud Guillin, Yu Wang, Lihu Xu, Haoran Yang
First submitted to arxiv on: 22 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Probability (math.PR)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper explores the connection between stochastic gradient descent with momentum (SGDM) and the underdamped Langevin diffusion. SGDM is a widely used optimization algorithm that has been shown to be closely related to Langevin diffusion, which is a probabilistic framework for simulating Markov chains. The authors provide a quantitative error estimate between SGDM and Langevin diffusion in terms of both 1-Wasserstein distance and total variation distance. This work sheds light on the theoretical foundations of SGDM and has implications for the development of new optimization algorithms. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how an important math tool called stochastic gradient descent with momentum relates to another mathematical concept, underdamped Langevin diffusion. Both are used in machine learning and statistics. The researchers try to figure out exactly how well these two things match up by looking at the distance between them. This helps us understand why SGDM works so well for solving optimization problems. |
Keywords
» Artificial intelligence » Diffusion » Machine learning » Optimization » Stochastic gradient descent
