Summary of Convergence Guarantees For Rmsprop and Adam in Generalized-smooth Non-convex Optimization with Affine Noise Variance, by Qi Zhang et al.
Convergence Guarantees for RMSProp and Adam in Generalized-smooth Non-convex Optimization with Affine Noise Variance
by Qi Zhang, Yi Zhou, Shaofeng Zou
First submitted to arxiv on: 1 Apr 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); 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 presents a tight convergence analysis for two popular optimization algorithms, RMSProp and Adam, in non-convex optimization problems. The authors demonstrate that these algorithms converge to an epsilon-stationary point with iteration complexity of O(epsilon^(-4)) under relaxed assumptions of coordinate-wise generalized smoothness and affine noise variance. This is achieved by analyzing the first-order term in the descent lemma and developing new upper bounds on its value. The results are generalizable to both RMSProp and Adam, providing a comprehensive understanding of their convergence properties. This work has implications for the design and evaluation of optimization algorithms in machine learning. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand how two important computer programs, RMSProp and Adam, solve tricky math problems called non-convex optimization. It shows that these programs can find a good solution after a certain number of tries, even if the problem is hard to solve. The authors used clever math tricks to prove this, and their results match what we already knew about how well these programs work. This research helps us make better computer programs for solving math problems. |
Keywords
» Artificial intelligence » Machine learning » Optimization
