  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.
