A linearly Convergent Distributed Proximal Gradient Algorithm via Edge-Based Method

摘要

#$%^&*AU2020101008A420200716.pdf#####Abstract This patent focuses on the composite convex optimization problem with a non-smooth term over an undirected network, which is a generic model and has wide applications. For solving this problem, a distributed proximal strategy via edge-based method is proposed. The algorithm mainly consists of five parts including determining parameter; variable initialization; exchanging information; computing gradient; updating variable. By adjusting the parameters to the appropriate range, the proposed algorithm can linearly converge to the global optimal solution, which is comparable to centralized optimization methods. With applying the edge-based Laplacian matrix, the algorithm has adjustable edge weights, which means more flexible edge weight selections. The present invention has broad application in large-scale machine learning.1/3 Start Each agent sets k = 0 and the maximum number of iterations, k. Each agent initializes local variables Selecting edge weights, the step size and adjustable parameters Each agent sends the variables to its neighbours and receives the variables from its neighbours Each agent updates the variables and computes the gradient Each agent sets k = k +1 Y k kn ? N End Fig. 1