A forward-backward Bregman splitting scheme for regularized distributed optimization problems

We consider regularized distributed optimization problems over networks. The problem arises from many existing domains, such as coordinated control, sensor fusion and distributed learning. We propose a new framework based on Bregman method and operator splitting, which allows us to come up with a general distributed algorithm, termed Distributed Forward-Backward Bregman Splitting (D-FBBS). The proposed algorithm, though derived from a different perspective, is shown to have close connections with some existing algorithms. In addition, we show that the proposed algorithm is able to seek a saddle point which solves the above primal problem as well as its dual simultaneously. We also establish a non-ergodic convergence rate of o(1/k) in terms of fixed point residual. A simple example of sensor fusion problem is provided to illustrate the effectiveness of the algorithm.