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.

翻译：本文研究如何将差异隐私运用于投入敏感的限制优化问题。本工作文件提出了重大挑战,因为输入数据的随机扰动往往使限制优化问题不可行,或大大改变了最佳解决方案的性质。为了解决这一困难,本文件提出一个双级优化模式,可以用作处理后步骤:在恢复可行性和近于最佳程度的同时,以最佳的方式重新分配由差异私营机制带来的噪音。本论文表明,在自然假设下,这一双级模型可以有效地解决与敏感客户数据相关的实际生活中大规模非线性非线性非线性优化问题。实验结果显示了隐私保护机制的准确性,并展示了与标准方法相比的重大效益。