On the role of cooperation in private multi-agent systems

Abstract

We consider a distributed quadratic optimization problem for multi-agent systems, where the agents wish to maintain privacy of their states over time. To this aim, the agents add noise to their communicated states using the differential privacy framework. We characterize the performance degradation due to the noise and show that depending on the desired level of privacy (and thus noise), the system performance is optimized by reducing the level of cooperation among the agents. The notion of cooperation level, which is formally introduced and defined in the chapter, models the trust of an agent towards the information received from neighboring agents. We characterize the optimum cooperation level and show that under certain conditions, it is always beneficial for the agents to reduce their cooperation level when the privacy level increases.We illustrate our results using the average consensus problem.