  Due to the explosion in size and complexity of modern data sets and privacy
concerns of data holders, it is increasingly important to be able to solve
machine learning problems in distributed manners. The Alternating Direction
Method of Multipliers (ADMM) through the concept of consensus variables is a
practical algorithm in this context where its diverse variations and its
performance have been studied in different application areas. In this paper, we
study the effect of the local data sets of users in the distributed learning of
ADMM. Our aim is to deploy variational inequality (VI) to attain an unified
view of ADMM variations. Through the simulation results, we demonstrate how
more general definitions of consensus parameters and introducing the uncertain
parameters in distribute approach can help to get the better results in
learning processes.
