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arXiv · 1902.09803

Logarithmic Regret for parameter-free Online Logistic Regression

Joseph De Vilmarest·Olivier Wintenberger
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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.

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Joseph De Vilmarest, Olivier Wintenberger. 2019-02-26. Logarithmic Regret for parameter-free Online Logistic Regression. https://arxiv.org/abs/1902.09803

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