Summary of An Equivalence Between Static and Dynamic Regret Minimization, by Andrew Jacobsen and Francesco Orabona
An Equivalence Between Static and Dynamic Regret Minimization
by Andrew Jacobsen, Francesco Orabona
First submitted to arxiv on: 3 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: 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 tackles the problem of dynamic regret minimization in online convex optimization. The goal is to minimize the difference between an algorithm’s cumulative loss and that of an arbitrary sequence of comparators. While there is a rich literature on this topic, a unifying framework for analysis and design has been missing. The authors show that for linear losses, dynamic regret minimization is equivalent to static regret minimization in an extended decision space. They use this observation to establish a frontier of lower bounds trading off penalties due to loss variance and comparator sequence variability. They also provide a framework for achieving any guarantee along this frontier. Furthermore, they prove that adapting to the squared path-length of an arbitrary comparator sequence is impossible. However, they introduce an alternative notion of variability based on locally-smoothed comparators and develop an algorithm that guarantees dynamic regret while matching worst-case path-length dependencies up to polylogarithmic terms. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how to make online optimization work better when the goal changes over time. It’s like trying to get a computer program to learn from its mistakes without getting stuck in a pattern. The researchers show that some problems are harder than others, and they develop new ways to measure these difficulties. They also prove that there’s no one-size-fits-all solution, but instead offer tools for solving specific types of optimization problems. |
Keywords
» Artificial intelligence » Optimization
