A Method to Improve Consensus Averaging using Quantized ADMM

In this paper, a method is proposed to overcome the consensus error in an average consensus problem, under a distributed setting and with finite-bit communications between the network agents. Previous works have illustrated that the average consensus problem can be solved under a distributed setting, using the Alternating Direction Method of Multipliers (ADMM) method, in which consensus can be attained by using locally available information along with information from neighboring nodes. This holds true even under finite-bit exchanges between neighbouring nodes, but suffers from consensus errors and cyclic states due to the introduced quantization schemes. This work deals with achieving perfect consensus with finite-bit communications between neighboring nodes. We propose an algorithm which leads to perfect consensus in an asymptotic sense, without the need to increase the per-exchange communication rate of the network.