@@ -2672,14 +2672,12 @@ The appraoch is based on the following:

@InProceedings{Jezequel2020,

author={J{\'e}z{\'e}quel, R{\'e}mi and Gaillard, Pierre and Rudi, Alessandro},

booktitle={Proceedings of Thirty Third Conference on Learning Theory},

booktitle={Proceedings of Machine Learning Research},

title={Efficient improper learning for online logistic regression},

year={2020},

editor={Abernethy, Jacob and Agarwal, Shivani},

month={09--12 Jul},

pages={2085--2108},

publisher={PMLR},

series={Proceedings of Machine Learning Research},

pages={1--25},

volume={125},

abstract={We consider the setting of online logistic regression and consider the regret with respect to the $\ell_2$-ball of radius $B$. It is known (see Hazan et al. (2014)) that any proper algorithm which has logarithmic regret in the number of samples (denoted $n$) necessarily suffers an exponential multiplicative constant in $B$. In this work, we design an efficient improper algorithm that avoids this exponential constant while preserving a logarithmic regret. Indeed, Foster et al. (2018) showed that the lower bound does not apply to improper algorithms and proposed a strategy based on exponential weights with prohibitive computational complexity. Our new algorithm based on regularized empirical risk minimization with surrogate losses satisfies a regret scaling as $O(B\log(Bn))$ with a per-round time-complexity of order $O(d^2 + \log(n))$.},