Differentially private distributed convex optimization via objective perturbation

Erfan Nozari, Pavankumar Tallapragada, Jorge Cortés

Abstract: This paper studies the problem of differentially private distributed convex unconstrained optimization for multi-agent systems. A group of agents seek to minimize the aggregate sum of their individual objective functions. Each agent only knows its own objective function and wants to keep it private from other agents or eavesdroppers listening to the network communications. Our design strategy consists of perturbing the objective functions with Laplace noise so that any query on the functions or their attributes is differentially private. This, together with the fact that differential privacy is immune to post-processing, allows us to employ any distributed algorithm that solves the unconstrained convex optimization problem on the perturbed objective functions. Our technical approach carefully describes how these perturbations can be selected so that the resulting functions retain the requirements on smoothness and convexity critical to many optimization algorithms. We quantify the magnitude of the expected deviation of the algorithm output from the true optimizer. The specific choice of distributed optimization algorithm determines the requirements on the network communication graph. Simulations illustrate the strengths of the proposed approach.