Differentially Private Distributed Optimization

TL;DR

This paper introduces a class of iterative algorithms for differentially private distributed optimization, balancing privacy guarantees with convergence to the optimal solution in multi-agent systems.

Contribution

It proposes novel algorithms that ensure differential privacy in distributed optimization while maintaining convergence to the optimal value.

Findings

Achieves $ ext{O}(1/ ext{epsilon}^2)$ accuracy for $ ext{epsilon}$-differential privacy.

Analyzes the trade-off between privacy levels and optimization accuracy.

Provides convergence guarantees under privacy constraints.

Abstract

In distributed optimization and iterative consensus literature, a standard problem is for $N$ agents to minimize a function $f$ over a subset of Euclidean space, where the cost function is expressed as a sum $\sum f_i$. In this paper, we study the private distributed optimization (PDOP) problem with the additional requirement that the cost function of the individual agents should remain differentially private. The adversary attempts to infer information about the private cost functions from the messages that the agents exchange. Achieving differential privacy requires that any change of an individual's cost function only results in unsubstantial changes in the statistics of the messages. We propose a class of iterative algorithms for solving PDOP, which achieves differential privacy and convergence to the optimal value. Our analysis reveals the dependence of the achieved accuracy and the privacy levels on the the parameters of the algorithm. We observe that to achieve $\epsilon$-differential privacy the accuracy of the algorithm has the order of $O(\frac{1}{\epsilon^2})$.