Gossip-based asynchronous algorithms for distributed composite optimization

The distributed composite optimization problem associated a multi-agent network is investigated in this paper. Different from conventional optimization issues, the cost function of composite optimization consists of a convex function and a regularization function (possibly nonsmooth). The gossip protocol is also introduced to enhance the robustness of the network, and a gossip-based distributed composite mirror descent algorithm is presented to deal with the previous problem, which adopts the asynchronous communication method. Moreover, the algorithm performance is analyzed and the theoretical results on the corresponding error bounds are obtained. Finally, the distributed logistic regression is provided as an example to validate the practicability of the proposed algorithm.