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Adaptive and Optimal Online Linear Regression on L1-balls

Sébastien Gerchinovitz 1, 2 Jia Yuan Yu 1, 2, 3
2 CLASSIC - Computational Learning, Aggregation, Supervised Statistical, Inference, and Classification
DMA - Département de Mathématiques et Applications - ENS Paris, ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt
Abstract : 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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https://hal.archives-ouvertes.fr/hal-00594399
Contributor : Sébastien Gerchinovitz <>
Submitted on : Thursday, May 19, 2011 - 8:32:33 PM
Last modification on : Thursday, September 17, 2020 - 12:29:54 PM
Long-term archiving on: : Saturday, August 20, 2011 - 2:31:47 AM

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  • HAL Id : hal-00594399, version 1
  • ARXIV : 1105.4042

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Sébastien Gerchinovitz, Jia Yuan Yu. Adaptive and Optimal Online Linear Regression on L1-balls. 2011. ⟨hal-00594399v1⟩

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