Differentially Private Distributed Resource Allocation via Deviation Tracking

This paper studies the distributed resource allocation problem where all the agents cooperatively minimize the sum of their cost functions. To prevent private information from being disclosed, agents need to keep their cost functions private against potential adversaries and other agents. We first propose a completely distributed algorithm via deviation tracking that deals with constrained resource allocation problem and preserve differential privacy for cost functions by masking states and directions with decaying Laplace noise. Adopting constant stepsizes, we prove that the proposed algorithm converges linearly in mean square. The linear convergence is established under the standard assumptions of Lipschitz gradients and strong convexity instead of the assumption of bounded gradients that is usually imposed in most existing works. Moreover, we show that the algorithm preserves differential privacy for every agent's cost function and establish the trade-off between privacy and convergence accuracy. Furthermore, we apply the proposed algorithm to economic dispatch problem in IEEE 14-bus system to verify the theoretical results.