Summary of Stochastic Zeroth-order Optimization Under Strongly Convexity and Lipschitz Hessian: Minimax Sample Complexity, by Qian Yu et al.
Stochastic Zeroth-Order Optimization under Strongly Convexity and Lipschitz Hessian: Minimax Sample Complexity
by Qian Yu, Yining Wang, Baihe Huang, Qi Lei, Jason D. Lee
First submitted to arxiv on: 28 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Information Theory (cs.IT); 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 investigates optimization of convex functions using noisy evaluations. It focuses on strongly convex functions with second-order smoothness, where the algorithm only has access to noisy feedback. The authors provide tight bounds for simple regret and propose an algorithm combining bootstrapping and mirror-descent stages. They also develop a novel characterization for spherical-sampling gradient estimators under higher-order smoothness conditions. This allows the algorithm to balance bias-variance tradeoff optimally. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper solves a tricky problem in online learning: optimizing convex functions with noisy feedback. It helps us better understand how algorithms can learn and improve when they don’t have perfect information. The authors develop new methods for optimizing these kinds of problems, which is important for many real-world applications where data might be incomplete or unreliable. |
Keywords
» Artificial intelligence » Bootstrapping » Online learning » Optimization
