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| HAL : hal-00594399, version 3 |
| arXiv : 1105.4042 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (20-05-2011) | v2 (25-05-2011) | v3 (23-01-2012) |
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| Adaptive and Optimal Online Linear Regression on L1-balls |
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| Sébastien Gerchinovitz 1, 2Jia Yuan Yu 3 |
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| (19/05/2011) |
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| We consider the problem of online linear regression on individual sequences. The goal in this paper is for the forecaster to output sequential predictions which are, after T time rounds, almost as good as the ones output by the best linear predictor in a given L1-ball in R^d. We consider both the cases where the dimension d is small and large relative to the time horizon T. We first present regret bounds with optimal dependencies on the sizes U, X and Y of the L1-ball, the input data and the observations. The minimax regret is shown to exhibit a regime transition around the point d = sqrt(T) U X / (2 Y). Furthermore, we present efficient algorithms that are adaptive, i.e., they do not require the knowledge of U, X, and Y, but still achieve nearly optimal regret bounds. |
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| 1 : | Département de Mathématiques et Applications (DMA) |
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CNRS : UMR8553 – Ecole normale supérieure de Paris - ENS Paris |
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| 2 : | CLASSIC (INRIA Paris - Rocquencourt) |
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Ecole normale supérieure de Paris - ENS Paris – INRIA |
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| 3 : | IBM Research and Development - Ireland |
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IBM |
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| Domaine | : | Statistiques/Machine Learning Mathématiques/Statistiques Statistiques/Théorie Informatique/Apprentissage |
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| online learning – linear regression – adaptive algorithms – minimax regret |
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| hal-00594399, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00594399 | |
| oai:hal.archives-ouvertes.fr:hal-00594399 | |
| Contributeur : Sébastien Gerchinovitz | |
| Soumis le : Lundi 23 Janvier 2012, 15:29:02 | |
| Dernière modification le : Lundi 23 Janvier 2012, 20:32:15 | |
