Summary of Relationship Between Batch Size and Number Of Steps Needed For Nonconvex Optimization Of Stochastic Gradient Descent Using Armijo Line Search, by Yuki Tsukada et al.
Relationship between Batch Size and Number of Steps Needed for Nonconvex Optimization of Stochastic Gradient Descent using Armijo Line Search
by Yuki Tsukada, Hideaki Iiduka
First submitted to arxiv on: 25 Jul 2023
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 The paper explores the performance of stochastic gradient descent (SGD) in non-convex optimization, particularly when using line search methods to determine learning rates. The authors analyze the convergence properties of SGD with Armijo-line-search learning rates and demonstrate that the number of steps needed for optimization decreases as the batch size increases. Additionally, they show that the stochastic first-order oracle complexity, which measures gradient computation cost, is a convex function of the batch size, indicating a critical batch size that minimizes complexity. The authors provide numerical results supporting their theoretical findings, highlighting the benefits of increasing batch sizes in deep neural network training. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary SGD helps machines learn by adjusting how much they move at each step. Researchers tested different ways to decide how big those steps should be and found that using “line search” methods makes SGD work better for really complex problems. They also showed that as you gather more information (like a bigger “batch size”), the number of steps needed to solve the problem gets smaller. This means it could take less time and effort to train artificial intelligence models. |
Keywords
* Artificial intelligence * Neural network * Optimization * Stochastic gradient descent
