tldr: We propose the first asynchronous decentralized optimization algorithm that utilizes the primal-dual framework on random graph and randomly sparsified communications. This algorithm operates in practical scenario such as decentralized systems with unstable pairwise communication and asynchronous gradient computation.
This figure demonstrates how FSPDA tolerates different levels of sparse communication on sparse random graph while converging to the same magnitude of stationarity, due to the transient effect of sparsity error. Only consensus error is dominantly affected by the sparsity error.