Differentially Private Convex Optimization with Piecewise Affine Objectives

TL;DR

This paper develops differentially private algorithms for convex optimization problems with piecewise affine objectives, balancing privacy guarantees with solution accuracy, and evaluates their practical performance.

Contribution

It introduces new privacy-preserving mechanisms tailored for piecewise affine convex optimization and analyzes their privacy-utility trade-offs.

Findings

Proposed mechanisms ensure differential privacy in convex optimization.

Trade-offs between privacy level and solution optimality are characterized.

Numerical experiments demonstrate practical effectiveness of the methods.

Abstract

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.