Summary of A Methodology Establishing Linear Convergence Of Adaptive Gradient Methods Under Pl Inequality, by Kushal Chakrabarti and Mayank Baranwal
A Methodology Establishing Linear Convergence of Adaptive Gradient Methods under PL Inequality
by Kushal Chakrabarti, Mayank Baranwal
First submitted to arxiv on: 17 Jul 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Optimization and Control (math.OC); 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 investigates the convergence properties of adaptive gradient-descent optimizers, specifically AdaGrad and Adam, two popular methods used for training neural network models. While these methods exhibit faster convergence than vanilla gradient-descent and impressive performance in practice, their analysis is intricate due to the dynamic update of the learning rate. In contrast, simple gradient-descent methods have a theoretical guarantee of linear convergence for certain optimization problems. The paper proves that AdaGrad and Adam converge linearly when the cost function is smooth and satisfies the Polyak-Łojasiewicz (PL) inequality. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary AdaGrad and Adam are two popular adaptive gradient methods used to train neural networks. This paper shows that these methods can be proven to work effectively, even though they don’t have a straightforward explanation. The main idea is that when the cost function is nice and follows certain rules, these methods will get close to the answer quickly. |
Keywords
» Artificial intelligence » Gradient descent » Neural network » Optimization
