Network Dissensus via Distributed ADMM

Common approaches in distributed optimization build upon the consensus framework to enforce cooperation and consistency among the nodes. In many applications however, the inter-node relationships are better modeled via antagonistic or dissensual constraints. These relationships can generally be incorporated via non-convex constraints or penalty functions, and the resulting formulations are flexible enough to subsume a wide variety of classification and discrimination problems. This work develops a general-purpose ADMM algorithm for distributed optimization with dissensus constraints. The formulation is generalized to incorporate both consensus and dissensus relationships. The non-convex constraints are handled via appropriate first-order approximations. The proposed algorithm is tested on the discriminative dictionary learning problem, where the goal is to learn class-specific dictionaries usable for both reconstruction and discrimination tasks. Extensive tests over human activity recognition dataset demonstrate the efficacy of the proposed approach.