Differentially Private Distributed Constrained Optimization

TL;DR

This paper introduces a distributed optimization algorithm that ensures user privacy through differential privacy by adding noise to public signals, with theoretical analysis and a case study on electric vehicle charging.

Contribution

It proposes a novel differentially private distributed optimization method that maintains privacy while providing suboptimality bounds and practical implementation insights.

Findings

The algorithm guarantees differential privacy against adversaries.

Numerical simulations demonstrate the trade-off between privacy and suboptimality.

Case study on electric vehicle charging illustrates practical application.

Abstract

Many resource allocation problems can be formulated as an optimization problem whose constraints contain sensitive information about participating users. This paper concerns solving this kind of optimization problem in a distributed manner while protecting the privacy of user information. Without privacy considerations, existing distributed algorithms normally consist in a central entity computing and broadcasting certain public coordination signals to participating users. However, the coordination signals often depend on user information, so that an adversary who has access to the coordination signals can potentially decode information on individual users and put user privacy at risk. We present a distributed optimization algorithm that preserves differential privacy, which is a strong notion that guarantees user privacy regardless of any auxiliary information an adversary may have. The algorithm achieves privacy by perturbing the public signals with additive noise, whose magnitude is determined by the sensitivity of the projection operation onto user-specified constraints. By viewing the differentially private algorithm as an implementation of stochastic gradient descent, we are able to derive a bound for the suboptimality of the algorithm. We illustrate the implementation of our algorithm via a case study of electric vehicle charging. Specifically, we derive the sensitivity and present numerical simulations for the algorithm. Through numerical simulations, we are able to investigate various aspects of the algorithm when being used in practice, including the choice of step size, number of iterations, and the trade-off between privacy level and suboptimality.