CORE: Common Random Reconstruction for Distributed Optimization with Provable Lower Total Communication Costs

In this paper, we propose a new compression technique named Common randOm REconstruction (CORE), which can be used to compress the information transmitted between agents to reduce the total communication costs (TCCs) without other strict conditions. Previous communication compression techniques cannot ensure the improvement of TCCs due to the additional communication rounds caused by information distortion. CORE projects the vector-valued information to a low dimensional one through common Gauss