Summary of From Logistic Regression to the Perceptron Algorithm: Exploring Gradient Descent with Large Step Sizes, by Alexander Tyurin
From Logistic Regression to the Perceptron Algorithm: Exploring Gradient Descent with Large Step Sizes
by Alexander Tyurin
First submitted to arxiv on: 11 Dec 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 classic machine learning problem of classification with separable datasets, focusing on the standard approach using logistic regression with gradient descent (LR+GD). Recent studies have shown that LR+GD can find solutions with arbitrarily large step sizes, contradicting conventional optimization theory. The authors make three key observations about LR+GD with large step sizes: its reduction to a batch version of the perceptron algorithm, the relationship between step size and logistic loss, and the suboptimal iteration complexity required for solution convergence. To address these issues, the authors propose a new method, Normalized LR+GD, which offers better theoretical guarantees. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper explores how machine learning models can solve classification problems with large steps sizes, which is important because it helps us understand how to make our models work better. The researchers found that using big step sizes makes the model reduce to a simpler algorithm called perceptron, and that this can actually help the model converge faster, even if the loss function values get higher. However, they also found that the number of iterations needed to reach a solution is not as good as it could be. To fix this, they came up with a new method called Normalized LR+GD that works better. |
Keywords
» Artificial intelligence » Classification » Gradient descent » Logistic regression » Loss function » Machine learning » Optimization
