A distributed optimization algorithm with guaranteed optimality subject to lossy information-sharing over directed networks - Liu, Shuai; Wang, Dong; Chen, Mingfei (Journal of the Franklin Institute, 2025)
This paper addresses the distributed optimization problem subject to lossy information-sharing. In the setting, each agent is assumed to have an individual cost function that is strongly convex and smooth. The goal of agents is to cooperatively minimize the sum of the local cost functions associated with each agent through information-sharing over unbalanced directed networks. Unfortunately, inherent additive noise in communication networks makes the diffused information no longer accurate. Such lossy information-sharing poses a fundamental challenge to the cooperation mechanism among agents, and it destroys the process of seeking the optimal solution if not adequately regarded. Inspired by the robust gradient tracking strategy, a distributed optimization algorithm with guaranteed optimality is proposed to cope with such difficulty. Also, the heavy-ball momentum and uncoordinated step sizes are integrated into the algorithm to improve convergence and flexibility. After theoretical analysis, the designed algorithm converges almost surely to the optimal solution at a linear rate. Finally, the performance of the proposed approach is verified with numerical simulations.