A Related Work on Compression Techniques in Distributed Optimization and Learning

The analysis in this section follows the techniques introduced in [8]. The proof of Proposition 2 follows roughly the same steps as the proof of Proposition 1. In this section, we will compile some results that will prove to be useful later in our analysis. With this in mind, we will assume throughout this section that all clients perform the same number of local updates, i.e., To that end, we will make use of the following lemma. To prove Theorem 5, we will construct an example involving two clients.