Summary of A Mirror Descent Perspective Of Smoothed Sign Descent, by Shuyang Wang et al.
A Mirror Descent Perspective of Smoothed Sign Descent
by Shuyang Wang, Diego Klabjan
First submitted to arxiv on: 18 Oct 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 new framework for understanding the optimization dynamics of gradient descent-based algorithms, specifically smoothed sign descent with a stability constant ε. The framework views the optimization process as low-dimensional dual dynamics induced by a mirror map, which is applied to regression problems. By analyzing these dual dynamics, the authors show that the convergent solution is an approximate KKT point of minimizing a Bregman divergence style function. This allows for tuning of the stability constant ε to reduce the KKT error. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper explores how smoothed sign descent with a stability constant ε works and why it’s important. It shows how this algorithm can be used for regression problems and helps us understand what makes it effective. By using a mirror map, the authors create a dual dynamics framework that explains the optimization process. |
Keywords
» Artificial intelligence » Gradient descent » Optimization » Regression
