A Note on How to Remove the $\ln\ln T$ Term from the Squint Bound
For researchers in online learning, this provides a technical improvement to remove a logarithmic factor from a known bound, but is incremental.
This note shows that shifting KT potentials is equivalent to changing the prior in the Krichevsky–Trofimov algorithm, and uses this idea to remove the ln ln T factor from the data-independent bound for the Squint algorithm.
In Orabona and Pál [2016], we introduced the shifted KT potentials, to remove the $\ln \ln T$ 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 $\ln \ln T$ factor in the data-independent bound for the Squint algorithm.