Differentially private cloud-based multi-agent optimization with constraints

We present an optimization framework that solves constrained multi-agent optimization problems while keeping each agent´s state differentially private. The agents in the network seek to optimize a local objective function in the presence of global constraints. Agents communicate only through a trusted cloud computer and the cloud also performs computations based on global information. The cloud computer modifies the results of such computations before they are sent to the agents in order to guarantee that the agents´ states are kept private. We show that under mild conditions each agent´s optimization problem converges in mean-square to its unique solution while each agent´s state is kept differentially private. A numerical simulation is provided to demonstrate the viability of this approach.