Bilevel Optimization for Differentially Private Optimization in Energy Systems
This addresses privacy concerns in energy systems with sensitive customer data, offering a novel post-processing method to maintain optimization performance while ensuring differential privacy.
The paper tackles the challenge of applying differential privacy to constrained optimization problems with sensitive inputs, which often become infeasible or suboptimal due to noise, by proposing a bilevel optimization model that redistributes noise to restore feasibility and near-optimality efficiently for large-scale nonlinear nonconvex problems.
This paper studies how to apply differential privacy to constrained optimization problems whose inputs are sensitive. This task raises significant challenges since random perturbations of the input data often render the constrained optimization problem infeasible or change significantly the nature of its optimal solutions. To address this difficulty, this paper proposes a bilevel optimization model that can be used as a post-processing step: It redistributes the noise introduced by a differentially private mechanism optimally while restoring feasibility and near-optimality. The paper shows that, under a natural assumption, this bilevel model can be solved efficiently for real-life large-scale nonlinear nonconvex optimization problems with sensitive customer data. The experimental results demonstrate the accuracy of the privacy-preserving mechanism and showcases significant benefits compared to standard approaches.