  We consider nonconvex stochastic optimization problems in the asynchronous
centralized distributed setup where the communication times from workers to a
server can not be ignored, and the computation and communication times are
potentially different for all workers. Using an unbiassed compression
technique, we develop a new method-Shadowheart SGD-that provably improves the
time complexities of all previous centralized methods. Moreover, we show that
the time complexity of Shadowheart SGD is optimal in the family of centralized
methods with compressed communication. We also consider the bidirectional
setup, where broadcasting from the server to the workers is non-negligible, and
develop a corresponding method.
