Differentially Private Linearized ADMM Algorithm for Decentralized Nonconvex Optimization

Privacy preservation is a challenging problem in decentralized nonconvex optimization containing sensitive data. Prior approaches to decentralized nonconvex optimization are either not strong enough to protect privacy or exhibit low utility under a high privacy guarantee. To address these issues, we propose a differentially private linearized alternating direction method of multipliers (DP-LADMM), which achieves fast convergence property for nonconvex objective functions while achieving saddle/maximum avoidance under differential privacy guarantee. We also apply the Analytic Gaussian Mechanism to track the cumulative privacy loss and provide a tight global differential privacy guarantee for DP-LADMM. The theoretical analysis offers an explicit convergence rate for our algorithm. To the best of our knowledge, this is the first paper to provide explicit convergence for decentralized nonconvex optimization with differential privacy and saddle/maximum avoidance. Numerical simulations and comparison studies on decentralized estimation confirm the superiority of the algorithm and the effectiveness of global privacy preservation.