Robust Constrained Consensus and Inequality-constrained Distributed Optimization with Guaranteed Differential Privacy and Accurate Convergence
<|reference_start|>Robust Constrained Consensus and Inequality-constrained Distributed Optimization with Guaranteed Differential Privacy and Accurate Convergence: 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.<|reference_end|>
@article{wang2024robust,
    title={Robust Constrained Consensus and Inequality-constrained Distributed
  Optimization with Guaranteed Differential Privacy and Accurate Convergence},
    author={Yongqiang Wang, Angelia Nedic},
    journal={arXiv preprint arXiv:2404.02327},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.02327},
    primaryClass={math.OC cs.SY eess.SY}
}