Reviews: GIANT: Globally Improved Approximate Newton Method for Distributed Optimization

The paper introduces GIANT, a distributed variant of Newton algorithm. The considered problem is important and the paper gives a nice contribution to the field of distributed optimisation. The paper is very clear and nice to read, and propose nice theoretical contributions and experiments, with a detailed bibliography and positioning with respect to priori work. Here is my main criticism: * Authors acknowledge that their approach is close to previous works, namely DANE, for which GIANT seem to coincide to DANE in the least-squares loss case. However, the rate obtained in the paper is much better, certainly thanks to the introduction of the incoherence assumption, which is well known in the field of compressed sensing and randomized linear algebra.