Summary of The Dimension Strikes Back with Gradients: Generalization Of Gradient Methods in Stochastic Convex Optimization, by Matan Schliserman and Uri Sherman and Tomer Koren
The Dimension Strikes Back with Gradients: Generalization of Gradient Methods in Stochastic Convex Optimization
by Matan Schliserman, Uri Sherman, Tomer Koren
First submitted to arxiv on: 22 Jan 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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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 generalization performance of gradient methods in stochastic convex optimization, focusing on their dimension dependence. It presents a construction for full-batch gradient descent to converge with constant probability to an approximate empirical risk minimizer in high-dimensional spaces, answering an open question raised by Feldman (2016) and Amir et al. (2021b). The study also shows that one-pass stochastic gradient descent requires an exponential improvement in the sample complexity compared to previous work, resolving another open question. The findings have implications for understanding the fundamental limits of gradient-based optimization methods. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at how well a type of computer learning called gradient methods works when trying to find the best answer to a problem. It shows that these methods can get stuck if they’re dealing with really big sets of data, and it takes a lot more examples to make sure they’re doing a good job. This is important because it helps us understand how these methods work and how we can improve them. |
Keywords
* Artificial intelligence * Generalization * Gradient descent * Optimization * Probability * Stochastic gradient descent
