Summary of Anytime Acceleration Of Gradient Descent, by Zihan Zhang et al.
Anytime Acceleration of Gradient Descent
by Zihan Zhang, Jason D. Lee, Simon S. Du, Yuxin Chen
First submitted to arxiv on: 26 Nov 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Systems and Control (eess.SY); 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 This paper explores the acceleration of gradient descent using stepsize schedules that provide “anytime” convergence guarantees. For smooth, non-strongly convex optimization problems, the authors propose a stepsize schedule that achieves convergence rates of O(T^(-1.119)) for any stopping time T. This result resolves an open problem in COLT (Conference on Learning Theory) regarding whether stepsize-based acceleration can achieve anytime convergence rates of o(T^(-1)). The authors also extend their theory to yield anytime convergence guarantees for smooth and strongly convex optimization problems, with a condition number κ. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand how gradient descent works better. It shows that we can make it work faster by adjusting the “stepsize” – the amount it moves each time. This is important because sometimes we don’t know exactly when to stop the algorithm. The authors found a way to make it work well even if we stop at any point, and this is useful for many real-world problems. |
Keywords
» Artificial intelligence » Gradient descent » Optimization
