Private and Accurate Decentralized Optimization via Encrypted and Structured Functional Perturbation

We propose a decentralized optimization algorithm that preserves the privacy of agents' cost functions without sacrificing accuracy, termed EFPSN. The algorithm adopts Paillier cryptosystem to construct zero-sum functional perturbations. Then, based on the perturbed cost functions, any existing decentralized optimization algorithm can be utilized to obtain the accurate solution. We theoretically prove that EFPSN is (epsilon, delta)-differentially private and can achieve nearly perfect privacy under deliberate parameter settings. Numerical experiments further confirm the effectiveness of the algorithm.