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We consider distributed optimization problems in which a group of agents areto collaboratively seek the global optimum through peer-to-peer communicationnetworks. The problem arises in various application areas, such as resourceallocation, sensor fusion and distributed learning. We propose a generalefficient distributed algorithm--termed Distributed Forward-Backward BregmanSplitting (D-FBBS)--to simultaneously solve the above primal problem as well asits dual based on Bregman method and operator splitting. The proposed algorithmallows agents to communicate asynchronously and thus lends itself to stochasticnetworks. This algorithm belongs to the family of general proximal pointalgorithms and is shown to have close connections with some existing well-knownalgorithms when dealing with fixed networks. However, we will show that it isgenerally different from the existing ones due to its effectiveness in handlingstochastic networks. With proper assumptions, we establish a non-ergodicconvergence rate of o(1/k) in terms of fixed point residuals over fixednetworks both for D-FBBS and its inexact version (ID-FBBS) which is morecomputationally efficient and an ergodic convergence rate of O(1/k) for D-FBBSover stochastic networks respectively. We also apply the proposed algorithm tosensor fusion problems to show its superior performance compared to existingmethods.

A Bregman Splitting Algorithm for Distributed Optimization over Networks