Summary of The Optimality Of (accelerated) Sgd For High-dimensional Quadratic Optimization, by Haihan Zhang et al.
The Optimality of (Accelerated) SGD for High-Dimensional Quadratic Optimization
by Haihan Zhang, Yuanshi Liu, Qianwen Chen, Cong Fang
First submitted to arxiv on: 15 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC)
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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 This paper investigates the effectiveness of stochastic gradient descent (SGD) and its accelerated variants in high-dimensional learning problems. Recent studies have shown that SGD can achieve good generalization under suitable conditions, but it remains unclear for what types of problems SGD can attain optimality. The authors establish a convergence upper bound for momentum-accelerated SGD (ASGD) and identify concrete classes of learning problems where SGD or ASGD achieves optimal convergence rates. They also provide insights into the learning bias of SGD, showing that it is efficient in learning “dense” features, avoiding saturation effects in easy problems, and accelerating convergence with momentum when problems are harder. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how a popular machine learning algorithm called stochastic gradient descent (SGD) works on really big datasets. They want to know what kinds of problems SGD can solve quickly and accurately. The authors find that SGDs can do well in certain situations, but they don’t work for all types of problems. They also discover some patterns about how SGDs learn new information. |
Keywords
» Artificial intelligence » Generalization » Machine learning » Stochastic gradient descent
