Summary of Gradient-variation Online Learning Under Generalized Smoothness, by Yan-feng Xie et al.
Gradient-Variation Online Learning under Generalized Smoothness
by Yan-Feng Xie, Peng Zhao, Zhi-Hua Zhou
First submitted to arxiv on: 17 Aug 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 This paper extends the classic optimistic mirror descent algorithm to achieve regret guarantees that scale with variations in gradient norms, which is crucial for attaining fast convergence in games and robustness in stochastic optimization. The authors systematically study gradient-variation online learning under generalized smoothness conditions, allowing smoothness to correlate with gradient norms. They design a universal online learning algorithm that achieves optimal gradient-variation regrets for convex and strongly convex functions simultaneously without requiring prior knowledge of curvature. This algorithm adopts a two-layer structure with a meta-algorithm running over a group of base-learners. To ensure favorable guarantees, the authors propose a new Lipschitz-adaptive meta-algorithm capable of handling potentially unbounded gradients while ensuring a second-order bound to effectively ensemble the base-learners. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about making computers learn better when they play games or optimize things. It’s trying to find a way for computers to adapt to changing situations and still make good choices. The authors are proposing new ways to do this by allowing the computer to adjust how it learns based on the size of the changes it sees. They’re also designing special algorithms that can handle different types of problems, like finding the shortest path or maximizing rewards. This could lead to faster learning times and better performance in games and optimization tasks. |
Keywords
» Artificial intelligence » Online learning » Optimization
