Push-Sum Distributed Dual Averaging for convex optimization

Recently there has been a significant amount of research on developing consensus based algorithms for distributed optimization motivated by applications that vary from large scale machine learning to wireless sensor networks. This work describes and proves convergence of a new algorithm called Push-Sum Distributed Dual Averaging which combines a recent optimization algorithm [1] with a push-sum consensus protocol [2]. As we discuss, the use of push-sum has significant advantages. Restricting to doubly stochastic consensus protocols is not required and convergence to the true average consensus is guaranteed without knowing the stationary distribution of the update matrix in advance. Furthermore, the communication semantics of just summing the incoming information make this algorithm truly asynchronous and allow a clean analysis when varying intercommunication intervals and communication delays are modelled. We include experiments in simulation and on a small cluster to complement the theoretical analysis.