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

• Published in: IEEE transactions on automatic control Vol. 69; no. 11; pp. 7463 - 7478
• Main Authors: Wang, Yongqiang, Nedic, Angelia
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Co-design; Consensus protocol; Constrained consensus; Constraints; Convergence; Differential equations; differential privacy; distributed optimization; Lagrangian function; Linear programming; Noise measurement; Optimization; Privacy; Protection; shared inequality constraints; Smart grid
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2024.3385546

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 <inline-formula><tex-math notation="LaTeX">\epsilon</tex-math></inline-formula>-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 nonseparable. As a byproduct of the co-design, we also propose a new constrained consensus algorithm that can achieve rigorous <inline-formula><tex-math notation="LaTeX">\epsilon</tex-math></inline-formula>-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.