Adaptive and Optimal Online Linear Regression on L1-balls

05/20/2011
by   Sébastien Gerchinovitz, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/29/2018

Uniform regret bounds over R^d for the sequential linear regression problem with the square loss

We consider the setting of online linear regression for arbitrary determ...
research
01/05/2011

Sparsity regret bounds for individual sequences in online linear regression

We consider the problem of online linear regression on arbitrary determi...
research
11/02/2021

Stochastic Online Linear Regression: the Forward Algorithm to Replace Ridge

We consider the problem of online linear regression in the stochastic se...
research
02/11/2014

Online Nonparametric Regression

We establish optimal rates for online regression for arbitrary classes o...
research
05/23/2018

Efficient online algorithms for fast-rate regret bounds under sparsity

We consider the online convex optimization problem. In the setting of ar...
research
02/13/2019

Distributed Online Linear Regression

We study online linear regression problems in a distributed setting, whe...
research
05/19/2021

L1 Regression with Lewis Weights Subsampling

We consider the problem of finding an approximate solution to ℓ_1 regres...

Please sign up or login with your details

Forgot password? Click here to reset