On the Communication Latency of Wireless Decentralized Learning

We consider a wireless network comprising n nodes located within a circular area of radius R, which are participating in a decentralized learning algorithm to optimize a global objective function using their local datasets. To enable gradient exchanges across the network, we assume each node communicates only with a set of neighboring nodes, which are within a distance R n-β of itself, where β∈(0,frac12). We use tools from network information theory and random geometric graph theory to show that the communication delay for a single round of exchanging gradients on all the links throughout the network scales as Oleft(fracn2-3ββlog nright), increasing (at different rates) with both the number of nodes and the gradient exchange threshold distance.