Summary of A Stochastic Quasi-newton Method For Non-convex Optimization with Non-uniform Smoothness, by Zhenyu Sun and Ermin Wei
A Stochastic Quasi-Newton Method for Non-convex Optimization with Non-uniform Smoothness
by Zhenyu Sun, Ermin Wei
First submitted to arxiv on: 22 Mar 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 The paper proposes a fast stochastic quasi-Newton method for optimization problems with non-uniform smoothness, where the smoothness factor grows with respect to the gradient norm along the training trajectory. This type of non-uniform smoothness is different from traditional uniform smoothness assumptions, which are commonly used in classical convergence analyses. The authors leverage gradient clipping and variance reduction techniques to design a stochastic quasi-Newton method that achieves the best-known (^{-3}) sample complexity for finding an -approximate first-order stationary solution. This approach outperforms existing state-of-the-art methods, demonstrating the effectiveness of using non-uniform smoothness assumptions in optimization problems. The proposed algorithm also enjoys convergence speedup with simple hyperparameter tuning. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper solves a problem in machine learning called optimization. Usually, people assume that the data is “smooth” and follows certain rules. However, some problems don’t follow these rules, making it harder to solve them. The authors propose a new way to solve these hard problems by using a different type of smoothness. This method is faster and more accurate than existing methods. It also requires less effort to set up the algorithm correctly. The results show that this method performs better than other state-of-the-art approaches. |
Keywords
* Artificial intelligence * Hyperparameter * Machine learning * Optimization
