Summary of Stochastic Differential Equations Models For Least-squares Stochastic Gradient Descent, by Adrien Schertzer and Loucas Pillaud-vivien
Stochastic Differential Equations models for Least-Squares Stochastic Gradient Descent
by Adrien Schertzer, Loucas Pillaud-Vivien
First submitted to arxiv on: 2 Jul 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Probability (math.PR)
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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 studies the dynamics of Stochastic Gradient Descent (SGD) for the least-square problem using continuous-time models of Stochastic Differential Equations (SDEs). Building on previous work by Li et al. (2019), the authors analyze SDEs that model SGD in both finite sample and online settings, highlighting a perfect interpolator of data regardless of sample size. The study provides precise rates of convergence to the stationary distribution, along with estimates of mean, deviations, and heavy-tailed emergence related to step-size magnitude. Numerical simulations support these findings. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper explores how a machine learning algorithm called Stochastic Gradient Descent (SGD) works when it’s used for a specific task called the least-square problem. The authors use special mathematical equations called Stochastic Differential Equations (SDEs) to understand how SGD behaves in different situations. They find that no matter what, there is always a way to perfectly fit the data points together. The study also shows how fast the algorithm gets close to its final state and provides information about how it can get stuck or move away from its average behavior. |
Keywords
* Artificial intelligence * Machine learning * Stochastic gradient descent
