Differentially Private Convex Optimization with Piecewise Affine Objectives
This work addresses privacy concerns in optimization for applications with sensitive user information, but it appears incremental as it builds on existing differential privacy frameworks for convex problems.
The paper tackles the problem of computing differentially private solutions for convex optimization with piecewise affine objectives, motivated by protecting sensitive user data in the objective functions, and proposes mechanisms with analysis on privacy-optimality trade-offs and numerical evaluations.
Differential privacy is a recently proposed notion of privacy that provides strong privacy guarantees without any assumptions on the adversary. The paper studies the problem of computing a differentially private solution to convex optimization problems whose objective function is piecewise affine. Such problem is motivated by applications in which the affine functions that define the objective function contain sensitive user information. We propose several privacy preserving mechanisms and provide analysis on the trade-offs between optimality and the level of privacy for these mechanisms. Numerical experiments are also presented to evaluate their performance in practice.