In Orabona and P\'al [2016], we introduced the shifted KT potentials, to remove the lnlnT factor in the parameter-free learning with expert bound. In this short technical note, I show that this is equivalent to changing the prior in the Krichevsky--Trofimov algorithm. Then, I show how to use the same idea to remove the lnlnT factor in the data-independent bound for the Squint algorithm.
@article{arxiv.2604.26926,
title = {A Note on How to Remove the $\ln\ln T$ Term from the Squint Bound},
author = {Francesco Orabona},
journal= {arXiv preprint arXiv:2604.26926},
year = {2026}
}