Barzilai-Borwein gradient tracking method for distributed optimization over directed networks

This paper studies the distributed optimization problem over directed networks. The global objective function of this problem is the average of all smooth and strongly convex local objective functions on the networks. Motivated by the capability of Barzilai-Borwein step sizes in improving the performance of gradient methods, a distributed Barzilai-Borwein gradient tracking method is proposed. Different from the distributed gradient algorithms using fixed step sizes in the literature, the proposed method allows each agent to calculate its step size automatically using its local gradient information. By using row- and column-stochastic weights simultaneously, the method can avoid the computation and communication on eigenvector estimation. It is proved that the iterative sequence generated by the proposed method converges linearly to the optimal solution for smooth and strongly convex functions. Simulation results on the distributed logistic regression problem show that the proposed method performs better than some advanced distributed gradient algorithms with fixed step sizes. © 2023 South China University of Technology. All rights reserved.