Distributed Second-Order Method with Diffusion Strategy

Within the realm of distributed optimization, each node in the network possesses computational capabilities. Nodes perform local calculations on their own data, and by communicating local information (e.g., local gradients) with neighboring nodes, agents collectively achieve a globally optimal solution. In recent years, distributed optimization has garnered interest across diverse disciplines, particularly in situations where communication abilities are limited or data are private. In this paper, a distributed second-order algorithm, based on an augmented Lagrangian function, is proposed with an enhanced diffusion communication strategy. An R-linear convergence rate is established under a relaxed locally restricted strong convexity assumption, along with a widely employed L-smoothness assumption. Finally, the superiority of the algorithm is showcased by a distributed logistic regression example utilizing a synthetic dataset with various parameter settings.