Differentially private convex optimization with piecewise affine objectives

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 problems are 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 an 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.