Summary of Non-convergence Of Adam and Other Adaptive Stochastic Gradient Descent Optimization Methods For Non-vanishing Learning Rates, by Steffen Dereich and Robin Graeber and Arnulf Jentzen
Non-convergence of Adam and other adaptive stochastic gradient descent optimization methods for non-vanishing learning rates
by Steffen Dereich, Robin Graeber, Arnulf Jentzen
First submitted to arxiv on: 11 Jul 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC); Probability (math.PR)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| 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 properties of deep learning algorithms, specifically focusing on the limitations of standard stochastic gradient descent (SGD) methods. The authors show that plain vanilla standard SGD fails to converge in certain situations, even when the learning rates are bounded away from zero. To address this issue, adaptive SGD methods like RMSprop and Adam optimizers were developed, which modify the learning rates during training. However, the paper reveals that these adaptive optimizers also fail to converge if the learning rates remain non-vanishing. The authors’ proof of non-convergence relies on establishing pathwise a priori bounds for accelerated and adaptive SGD methods, which has implications for various AI applications, including large language models (LLMs) like ChatGPT and Gemini, generative AI text-to-image creation models like Midjourney, DALL-E, and Stable Diffusion, as well as optimal control and stopping problems from engineering. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper explores the limitations of deep learning algorithms used in many AI systems. Researchers discovered that plain vanilla standard SGD methods can fail to converge if the learning rates are not zero. To fix this issue, adaptive methods like RMSprop and Adam were developed, which adjust the learning rates during training. However, these adaptive optimizers also have their own limitations. The authors proved that even adaptive SGD methods will not converge if the learning rates remain non-zero. This work is important for understanding how AI systems learn and can inform the development of new AI models and applications. |
Keywords
» Artificial intelligence » Deep learning » Diffusion » Gemini » Stochastic gradient descent
