Guaranteed privacy of distributed nonconvex optimization via mixed-monotone functional perturbations

Mohammad Khajenejad and Sonia Martínez
IEEE Control Systems Letters 7 (DOI: 10.1109/LCSYS.2022.3231223) (2022) 1081-1086

Abstract:

In this letter, we introduce a new notion of guaranteed privacy for distributed nonconvex optimization algorithms. In particular, leveraging mixed-monotone inclusion functions, we propose a privacy-preserving mechanism which is based on deterministic, but unknown affine perturbations of the local objective functions. The design requires a robust optimization method to characterize the best accuracy that can be achieved by an optimal perturbation. This is used to guide the refinement of a guaranteed-private perturbation mechanism that can achieve a quantifiable accuracy via a theoretical upper bound that is independent of the chosen optimization algorithm. Finally, simulation results illustrate the accuracy-privacy trade-off and that our approach outperforms a benchmark differentially private distributed optimization algorithm in the literature.

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Bib-tex entry:

@article{MK-SM:22-lcss,
author = {M. Khajenejad and S. Mart{\'\i}nez},
title = {Guaranteed privacy of distributed nonconvex optimization via mixed-monotone functional perturbations},
journal= {IEEE Control Systems Letters},
pages = {1081-1086},
volume = {7},
doi = {10.1109/LCSYS.2022.3231223},
year = {2022}
}