Summary of Large Stepsize Gradient Descent For Logistic Loss: Non-monotonicity Of the Loss Improves Optimization Efficiency, by Jingfeng Wu et al.
Large Stepsize Gradient Descent for Logistic Loss: Non-Monotonicity of the Loss Improves Optimization Efficiency
by Jingfeng Wu, Peter L. Bartlett, Matus Telgarsky, Bin Yu
First submitted to arxiv on: 24 Feb 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 We examine the behavior of gradient descent (GD) with a constant stepsize when applied to logistic regression with linearly separable data. The constant stepsize η is so large that the loss initially oscillates. Our findings show that GD rapidly exits this initial oscillatory phase in O(η) steps and subsequently achieves an Õ(1/(ηt)) convergence rate after t additional steps. Given a budget of T steps, our results imply that GD can achieve an accelerated loss of Õ(1/T^2) with an aggressive stepsize η:= Θ(T), without using momentum or variable stepsize schedulers. Our proof technique is versatile and also handles general classification loss functions, nonlinear predictors in the neural tangent kernel regime, and online stochastic gradient descent (SGD) with a large stepsize under suitable separability conditions. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Researchers studied how a popular machine learning algorithm called gradient descent works when it’s used to solve simple problems. They found that even when the algorithm is set up to be very aggressive, it can still work well and get better over time. This is important because it means we can use this algorithm to quickly solve certain types of problems without having to make it more complicated. The researchers’ method for proving this works for many different types of problems, not just simple ones. |
Keywords
* Artificial intelligence * Classification * Gradient descent * Logistic regression * Machine learning * Stochastic gradient descent
