Algorithmic Chaining and the Role of Partial Feedback in Online Nonparametric Learning

Nicolò Cesa-Bianchi 1 Pierre Gaillard 2 Claudio Gentile 3 Sébastien Gerchinovitz 4
2 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, ENS Paris - École normale supérieure - Paris, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : We investigate contextual online learning with nonparametric (Lipschitz) comparison classes under different assumptions on losses and feedback information. For full information feedback and Lipschitz losses, we design the first explicit algorithm achieving the minimax regret rate (up to log factors). In a partial feedback model motivated by second-price auctions, we obtain algorithms for Lipschitz and semi-Lipschitz losses with regret bounds improving on the known bounds for standard bandit feedback. Our analysis combines novel results for contextual second-price auctions with a novel algorithmic approach based on chaining. When the context space is Euclidean, our chaining approach is efficient and delivers an even better regret bound.
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Pré-publication, Document de travail
This document is the full version of an extended abstract accepted for presentation at COLT 2017. 2017
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Soumis le : vendredi 23 juin 2017 - 18:37:44
Dernière modification le : jeudi 18 janvier 2018 - 10:39:12
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  • HAL Id : hal-01476771, version 2
  • ARXIV : 1702.08211

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Nicolò Cesa-Bianchi, Pierre Gaillard, Claudio Gentile, Sébastien Gerchinovitz. Algorithmic Chaining and the Role of Partial Feedback in Online Nonparametric Learning. This document is the full version of an extended abstract accepted for presentation at COLT 2017. 2017. 〈hal-01476771v2〉

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