Privacy-Preserving Distributed Optimization via Obfuscated Gradient Tracking

As the modern world becomes increasingly digitized and interconnected, distributed systems have proven to be effective in the processing of large volumes of data. In this context, optimization techniques have become essential in an extensive range of domains. However, a major concern, regarding the privacy issue in handling sensitive data, has recently emerged. To address this privacy issue we propose a novel consensus-based privacy-preserving distributed optimization algorithm called Obfuscated Gradient Tracking. The algorithm is characterized by a balanced noise insertion method which protects private data from being revealed to others, while not affecting the result’s accuracy. Indeed, we theoretically prove that the introduced perturbations do not condition the convergence properties of the algorithm, which is proven to reach the optimal solution without compromises. Moreover, security against the widely-used honest-but-curious adversary model, is shown. Furthermore, numerical tests are performed to show the effectiveness of the novel algorithm, both in terms of privacy and convergence properties. Numerical results highlight the Obfuscated Gradient Tracking attractiveness, against standard distributed algorithms, when privacy issues are involved. Finally, we present a privacy-preserving distributed Deep Learning application developed using our novel algorithm, with the aim of demonstrating its general applicability.