Summary of A Conversion Theorem and Minimax Optimality For Continuum Contextual Bandits, by Arya Akhavan et al.
A conversion theorem and minimax optimality for continuum contextual bandits
by Arya Akhavan, Karim Lounici, Massimiliano Pontil, Alexandre B. Tsybakov
First submitted to arxiv on: 9 Jun 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Statistics Theory (math.ST)
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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 studies the contextual continuum bandits problem, where a learner must choose an action from a convex set based on a side information vector and a context. The goal is to minimize the cumulative regret for different contexts, which is stronger than standard static regret. The authors demonstrate that any algorithm achieving sub-linear static regret can be extended to achieve sub-linear contextual regret. They also prove a static-to-contextual regret conversion theorem and study three cases of dependency between objective functions: Lipschitz bandits, convex bandits, and strongly convex and smooth bandits. For Lipschitz bandits, the authors prove that the minimax optimal contextual regret is achieved in the noise-free setting, while for convex bandits and strongly convex and smooth bandits, the algorithms proposed achieve the minimax optimal rate of contextual regret up to a logarithmic factor. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper studies how to make better choices based on context. Imagine you’re trying to decide what to eat at a restaurant, and you get information about the menu and your preferences. The goal is to find the best choice that works for all situations. The authors show that if an algorithm does well in one situation, it can be adapted to do well in others too. They also study three different cases where this algorithm performs well: when the options are very different, when they’re similar but not identical, and when they’re extremely varied. |
