Skip to Main content Skip to Navigation

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.
Complete list of metadatas
Contributor : Sébastien Gerchinovitz <>
Submitted on : Monday, May 23, 2011 - 4:29:37 PM
Last modification on : Thursday, September 17, 2020 - 12:29:54 PM
Long-term archiving on: : Wednesday, August 24, 2011 - 2:26:32 AM


Files produced by the author(s)


  • HAL Id : hal-00594399, version 2
  • ARXIV : 1105.4042


Sébastien Gerchinovitz, Jia Yuan Yu. Adaptive and Optimal Online Linear Regression on L1-balls. 2011. ⟨hal-00594399v2⟩



Record views


Files downloads