Summary of Improving Implicit Regularization Of Sgd with Preconditioning For Least Square Problems, by Junwei Su et al.
Improving Implicit Regularization of SGD with Preconditioning for Least Square Problems
by Junwei Su, Difan Zou, Chuan Wu
First submitted to arxiv on: 13 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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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 investigates the generalization performance of stochastic gradient descent (SGD) with preconditioning for the least squared problem. Prior research has shown that SGD can exhibit worse generalization performance than ridge regression in certain cases due to uneven optimization along different dimensions. The study proposes a comprehensive approach to understanding and improving SGD with preconditioning, including establishing excess risk bounds for both preconditioned SGD and ridge regression, constructing a simple preconditioned matrix that makes SGD comparable to ridge regression, and demonstrating the feasibility of robust estimation from finite samples. The results suggest that preconditioned SGD can achieve improved regularization effects, bridging the gap with ridge regression. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how well a type of machine learning algorithm called stochastic gradient descent (SGD) does when it’s used to solve a specific problem called the least squared problem. Sometimes, SGD doesn’t do as well as another method called ridge regression because it optimizes differently along different dimensions. The researchers tried to fix this by using something called preconditioning. They studied how well preconditioned SGD and ridge regression work and found that there’s a special way to use preconditioning that makes SGD just as good as ridge regression. They also showed that their method is reliable even when working with limited data. |
Keywords
* Artificial intelligence * Generalization * Machine learning * Optimization * Regression * Regularization * Stochastic gradient descent
