Distributed Optimization with Noisy Information Sharing

This paper considers distributed optimization where multiple agents cooperatively solve a global optimization problem. This paper proposes a distributed gradient method that is applicable to general directed network topologies without requiring participating agents to maintain or share any extra variables besides the decision variable. Furthermore, by incorporating a decaying factor in inter-agent interactions, the proposed approach can gradually eliminate the influence of information-sharing noise and ensure the almost sure convergence of all agents to a same optimal solution even in the presence of persistent information-sharing noise. Numerical simulation results confirm the effectiveness of the proposed approach.