Privacy-Preserving Convex Optimization: When Differential Privacy Meets Stochastic Programming

Convex optimization finds many applications where optimization results may expose private data (e.g., health records, commercial information). To guarantee privacy to optimization data owners, we develop a new privacy-preserving perturbation strategy for convex optimization programs by combining stochastic (chance-constrained) programming and differential privacy. Unlike standard noise-additive strategies, which perturb either optimization data or result, we formulate optimization variables as functions of a random perturbation using linear decision rules; we then optimize these rules to accommodate the perturbation within the feasible region using chance constraints. The perturbation becomes feasible and makes adjacent—in the sense of some distance function—optimization datasets statistically similar in randomized optimization results, thereby enabling privacy guarantees.