  In this paper, we propose a communication-efficiently decentralized machine
learning framework that solves a consensus optimization problem defined over a
network of inter-connected workers. The proposed algorithm, Censored and
Quantized Generalized GADMM (CQ-GGADMM), leverages the worker grouping and
decentralized learning ideas of Group Alternating Direction Method of
Multipliers (GADMM), and pushes the frontier in communication efficiency by
extending its applicability to generalized network topologies, while
incorporating link censoring for negligible updates after quantization. We
theoretically prove that CQ-GGADMM achieves the linear convergence rate when
the local objective functions are strongly convex under some mild assumptions.
Numerical simulations corroborate that CQ-GGADMM exhibits higher communication
efficiency in terms of the number of communication rounds and transmit energy
consumption without compromising the accuracy and convergence speed, compared
to the censored decentralized ADMM, and the worker grouping method of GADMM.
