We developed new paper Distributed Second Order Methods with Fast Rates and Compressed Communication. Our goal was to unite feature of Newton's method - doesn't suffer from condition number - with communication efficiency. We created three learning schemes for solving $L_2$ regularized ERM problem. Two of them have local superlinear rate (${\sf NL1}$ and ${\sf NL2}$), and one of them has global linear and local superlinear rate (${\sf CNL}$). You can find more information about the paper by clicking on the link.
