Convex optimization-based Privacy-Preserving Distributed Least Squares via Subspace Perturbation

Over the past decades, privacy-preservation has received considerable attention, not only as a consequence of regulations such as the General Data Protection Regulation in the EU, but also from the fact that people are more concerned about data abuse as the world is becoming increasingly digitized. In this paper we propose a convex optimization-based subspace perturbation approach to solve privacy-preserving distributed least squares problems. Based on the primal-dual method of multipliers, the introduced dual variables will only converge in a subspace determined by the graph topology and do not converge in its orthogonal complement. We, therefore, propose to exploit this property for privacy-preservation by using the nonconverging part of the dual variables to perturb the private data, thereby protecting it from being revealed. Moreover, we prove that the proposed approach is secure under both eavesdropping and passive adversaries. Computer simulations are conducted to demonstrate the benefits of the proposed approach through its convergence properties and accuracy.