Distributed Mismatch Tracking Algorithm for Constraint-Coupled Resource Allocation: Optimality and Differential Privacy

This paper considers constraint-coupled distributed resource allocation problems (DRAPs), where each agent holds a private cost function and obtains the solution via only local communication. In this paper, we propose a novel distributed algorithm (termed DMAC) to achieve optimality for DRAPs based on mismatch tracking scheme. We show that the proposed algorithm converges at a sublinear rate for strongly convex cost functions and a linear convergence rate for smooth and strongly convex cost functions, respectively. With privacy concerns, the exchanged information is masked with independent Laplace noise against potential attackers with access to even all network communication. We further propose a differentially private version (termed diff-DMAC) to achieve cost-optimal distribution of resources while preserving privacy. Adopting constant stepsizes, the linear convergence property of diff-DMAC in mean square is established. Moreover, it is proven that the algorithm is differentially private. We also characterize and improve the trade-off between convergence accuracy and privacy level. Finally, a numerical example is provided for verification.