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 infinitesimally small
$\epsilon,\delta $
under deliberate parameter settings. Numerical experiments further confirm the effectiveness of the algorithm.