Differentially Private Distributed Constrained Optimization
This work provides a method for privacy-preserving distributed optimization, which is important for applications like smart grids where user data must be protected, but the approach is incremental as it applies differential privacy to existing distributed optimization frameworks.
The paper presents a differentially private distributed optimization algorithm for resource allocation problems where constraints contain sensitive user information. The algorithm achieves privacy by adding noise to public coordination signals, and the authors derive a suboptimality bound and demonstrate the trade-off between privacy and accuracy via electric vehicle charging simulations.
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.