Summary of Error Dynamics Of Mini-batch Gradient Descent with Random Reshuffling For Least Squares Regression, by Jackie Lok et al.
Error dynamics of mini-batch gradient descent with random reshuffling for least squares regression
by Jackie Lok, Rishi Sonthalia, Elizaveta Rebrova
First submitted to arxiv on: 6 Jun 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Optimization and Control (math.OC)
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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 The paper explores the discrete dynamics of mini-batch gradient descent with random reshuffling for least squares regression. It reveals that training and generalization errors depend on a sample cross-covariance matrix Z between original features X and modified features tildeX, where each feature is influenced by previous mini-batches during learning. The study finds that while mini-batch gradient descent agrees with full-batch gradient descent up to leading order using the linear scaling rule, it exhibits subtle step-size dependence not detectable through gradient flow analysis. Furthermore, batching affects dynamics by inducing shrinkage on the spectrum. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary In this paper, researchers look at how mini-batch gradient descent works for a type of regression problem called least squares regression. They discover that the way the algorithm performs depends on a special kind of matrix that combines original data with modified versions. The study finds that while mini-batching agrees with full-batching most of the time, it has some subtle differences depending on how small steps are taken during learning. Overall, the paper shows how batching affects how the algorithm works and why. |
Keywords
» Artificial intelligence » Generalization » Gradient descent » Regression
