Summary of Quantitative Convergences Of Lie Group Momentum Optimizers, by Lingkai Kong et al.
Quantitative Convergences of Lie Group Momentum Optimizers
by Lingkai Kong, Molei Tao
First submitted to arxiv on: 30 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA); Optimization and Control (math.OC); Machine Learning (stat.ML)
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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 abstract presents a novel approach to constructing optimization algorithms that can be used on Lie groups. The authors develop explicit, momentum-based dynamics that optimize functions defined on these groups using variational optimization and momentum trivialization. They then investigate two types of structure-preserving time discretizations: the Lie Heavy-Ball method and the newly proposed Lie NAG-SC algorithm. Both methods are shown to be computationally efficient and easy to implement, thanks to their utilization of group structure. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper introduces a new way to optimize functions on special groups called Lie groups. It uses a technique called variational optimization and momentum trivialization to create an “optimizer” that can be used on these groups. The authors then test two different ways to discretize this optimizer, which are called Lie Heavy-Ball and Lie NAG-SC. Both of these methods work well and are easy to use because they take advantage of the special properties of the Lie group. |
Keywords
* Artificial intelligence * Optimization
