Logarithmic Regret for parameter-free Online Logistic Regression
Machine Learning
2019-02-27 v1 Statistics Theory
Statistics Theory
Abstract
We consider online optimization procedures in the context of logistic regression, focusing on the Extended Kalman Filter (EKF). We introduce a second-order algorithm close to the EKF, named Semi-Online Step (SOS), for which we prove a O(log(n)) regret in the adversarial setting, paving the way to similar results for the EKF. This regret bound on SOS is the first for such parameter-free algorithm in the adversarial logistic regression. We prove for the EKF in constant dynamics a O(log(n)) regret in expectation and in the well-specified logistic regression model.
Keywords
Cite
@article{arxiv.1902.09803,
title = {Logarithmic Regret for parameter-free Online Logistic Regression},
author = {Joseph De Vilmarest and Olivier Wintenberger},
journal= {arXiv preprint arXiv:1902.09803},
year = {2019}
}