A Chaining Algorithm for Online Nonparametric Regression
- EDF R&D（法国电力研发中心）
- HEC Paris（巴黎高等商学院）
- CNRS（法国国家科学研究中心）
- Institut de Mathématiques de Toulouse, Université Paul Sabatier（保罗·萨巴捷大学图卢兹数学研究所）
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英文摘要：
We consider the problem of online nonparametric regression with arbitrary deterministic sequences. Using ideas from the chaining technique, we design an algorithm that achieves a Dudley-type regret bound similar to the one obtained in a non-constructive fashion by Rakhlin and Sridharan (2014). Our regret bound is expressed in terms of the metric entropy in the sup norm, which yields optimal guarantees when the metric and sequential entropies are of the same order of magnitude. In particular our algorithm is the first one that achieves optimal rates for online regression over H{ö}lder balls. In addition we show for this example how to adapt our chaining algorithm to get a reasonable computational efficiency with similar regret guarantees (up to a log factor).
