Robust Constrained Consensus and Inequality-constrained Distributed Optimization with Guaranteed Differential Privacy and Accurate Convergence

TL;DR

This paper introduces a novel distributed optimization algorithm that guarantees both differential privacy and convergence to a global solution under inequality constraints, applicable even with non-separable objectives.

Contribution

It presents the first co-designed distributed constrained optimization method ensuring differential privacy and convergence without requiring strict convexity or separability.

Findings

Achieves rigorous $$-differential privacy in distributed optimization.

Ensures convergence to a global optimal solution under inequality constraints.

Validated effectiveness through smart grid demand response simulations.

Abstract

We address differential privacy for fully distributed optimization subject to a shared inequality constraint. By co-designing the distributed optimization mechanism and the differential-privacy noise injection mechanism, we propose the first distributed constrained optimization algorithm that can ensure both provable convergence to a global optimal solution and rigorous $\epsilon$-differential privacy, even when the number of iterations tends to infinity. Our approach does not require the Lagrangian function to be strictly convex/concave, and allows the global objective function to be non-separable. As a byproduct of the co-design, we also propose a new constrained consensus algorithm that can achieve rigorous $\epsilon$-differential privacy while maintaining accurate convergence, which, to our knowledge, has not been achieved before. Numerical simulation results on a demand response control problem in smart grid confirm the effectiveness of the proposed approach.