Inference Attack in Distributed Optimization via Interpolation and Manipulation

We study the problem of inference attack in distributed optimization, with adversarial agents aiming to obtain the sensitive information of some critical agent in a network. Different from existing privacy-preserving and resilient distributed optimization algorithms, we propose inference algorithms from the perspective of launching well-designed attacks to help infer sensitive local information. The key idea is that by utilizing the critical agent’s neighborhood information and the predefined update protocol, adversarial agents can not only interpolate the gradient of its local objective function, but also manipulate it to converge to its own local minimizer. The proposed algorithms can thus obtain approximations of the gradient or the minimizer of the local objective of this critical agent. We characterize the performance through interpolation errors, as well as distances to the optimal value and optimal point of the local objective. Numerical simulations are presented to verify the effectiveness of these algorithms.