  Modern applied optimization problems become more and more complex every day.
Due to this fact, distributed algorithms that can speed up the process of
solving an optimization problem through parallelization are of great
importance. The main bottleneck of distributed algorithms is communications,
which can slow down the method dramatically. One way to solve this issue is to
use compression of transmitted information. In the current literature on
theoretical distributed optimization, it is generally accepted that as much as
we compress information, so much we reduce communication time. But in reality,
the communication time depends not only on the size of the transmitted
information, but also, for example, on the message startup time. In this paper,
we study distributed optimization algorithms under the assumption of a more
complex and closer-to-reality dependence of transmission time on compression.
In particular, we describe the real speedup achieved by compression, analyze
how much it makes sense to compress information, and present an adaptive way to
select the power of compression depending on unknown or changing parameters of
the communication process.
