Summary of On the Last-iterate Convergence Of Shuffling Gradient Methods, by Zijian Liu et al.
On the Last-Iterate Convergence of Shuffling Gradient Methods
by Zijian Liu, Zhengyuan Zhou
First submitted to arxiv on: 12 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: 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 Shuffling gradient methods, such as Random Reshuffle (RR), Shuffle Once (SO), and Incremental Gradient (IG), are essential in modern machine learning. Despite their empirical success, the theoretical guarantees of these methods were unclear until recent studies established convergence rates for convex functions and strongly convex problems using squared distance as the metric. However, existing theories cannot explain the good performance of the last iterate when using function value gap as the criterion, even in constrained optimization settings. This paper bridges the gap by proving the first last-iterate convergence rates for shuffling gradient methods with respect to objective values without strong convexity. Our results either match or outperform existing lower and upper bounds for average iterates. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about a type of machine learning method called “shuffling gradient methods.” These methods are used in many different tasks, like image recognition and natural language processing. For a long time, it wasn’t clear why these methods worked well even though they didn’t follow the rules of traditional math. This paper helps to fill that gap by showing that these methods can actually be proven to work correctly, even when we’re not sure what’s happening inside the computer. |
Keywords
* Artificial intelligence * Machine learning * Natural language processing * Optimization
