Summary of Coupling-based Convergence Diagnostic and Stepsize Scheme For Stochastic Gradient Descent, by Xiang Li and Qiaomin Xie
Coupling-based Convergence Diagnostic and Stepsize Scheme for Stochastic Gradient Descent
by Xiang Li, Qiaomin Xie
First submitted to arxiv on: 15 Dec 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 The paper investigates the convergence behavior of Stochastic Gradient Descent (SGD) with constant stepsize, proposing a novel coupling-based diagnostic procedure for stationarity detection. The authors aim to develop an effective dynamic stepsize scheme, comparing their method against existing approaches. Their proposed diagnostic statistic tracks the transition from transient to stationary states theoretically. Numerical experiments demonstrate superior performance across various convex and non-convex problems, showcasing robustness to hyperparameter variations. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper studies how Stochastic Gradient Descent (SGD) works when you use a constant stepsize. They find that SGD gets stuck in an oscillating pattern around the best solution after initially moving quickly towards it. To fix this, they create a new way to check if SGD has reached stationarity by monitoring two connected versions of itself. This helps them develop a better system for adjusting the stepsize on-the-fly. The authors test their method with many different problems and show that it performs well across a wide range of scenarios. |
Keywords
» Artificial intelligence » Hyperparameter » Stochastic gradient descent
