This work contributed to solve the average consensus problem of switching topology networks with privacy protection. Starting from the well-known average consensus algorithm and considering the impact of uncertain environment on communication topology, we propose a simple but effective privacy protection mechanism, which can reach an accurate average consensus even if the communication link between agents changes. By dividing the initial state of the agent, a linear combination of explicit state and implicit state is obtained. The explicit state of agents interacts with each other, while the implicit state is only stored in itself. This algorithm does not need the assistance of any third party and has low computational complexity. Theoretical analysis and numerical simulation show that the true state of agents is not only protected, but also can reach an accurate average consensus.

Distributed optimization allows a separate set of data owners to collaboratively optimize a learning model, wherein information exchange between agents is usually explicit, and hence it is easy to cause the leakage of sensitive information. In order to address the critical issue of data privacy, a distributed online optimization algorithm with privacy protection is proposed in this paper. With the weight between two connected agents being decomposed into weight pairs, the homomorphic encryption mechanism (Paillier Cryptosystem) and the online distributed dual averaging algorithm are combined to propose an online distributed dual averaging privacy-protection algorithm. We prove that the sublinear regret bound and privacy protection can be guaranteed for the strongly connected undirected network. Finally, theoretical analysis and numerical simulations show that the adversaries can not steal the sensitive information of neighboring agents when collecting the multi-step intermediate information, therefore the algorithm can effectively protect the agents’ privacy of the network.