  In decentralized learning, operator splitting methods using a primal-dual
formulation (e.g., the Edge-Consensus Learning (ECL)) has been shown to be
robust to heterogeneous data and has attracted significant attention in recent
years. However, in the ECL, a node needs to exchange dual variables with its
neighbors. These exchanges incur significant communication costs. For the
Gossip-based algorithms, many compression methods have been proposed, but these
Gossip-based algorithm do not perform well when the data distribution held by
each node is statistically heterogeneous. In this work, we propose the novel
framework of the compression methods for the ECL, called the Communication
Compressed ECL (C-ECL). Specifically, we reformulate the update formulas of the
ECL, and propose to compress the update values of the dual variables. We
demonstrate experimentally that the C-ECL can achieve a nearly equivalent
performance with fewer parameter exchanges than the ECL. Moreover, we
demonstrate that the C-ECL is more robust to heterogeneous data than the
Gossip-based algorithms.
