Differentially Private Distributed Constrained Optimization (1411.4105v1)

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.

• The paper introduces a differentially private optimization algorithm that perturbs coordination signals to safeguard sensitive constraints.
• It employs a modified stochastic gradient descent approach to quantify the trade-off between privacy (controlled by ε) and performance suboptimality.
• Empirical evaluations, including an EV charging coordination case, demonstrate the method's practical application in secure distributed systems.

Differentially Private Distributed Constrained Optimization

The paper "Differentially Private Distributed Constrained Optimization" by Shuo Han, Ufuk Topcu, and George J. Pappas explores the integration of differential privacy into distributed optimization algorithms, particularly for problems where constraints are sensitive and potentially revealing of user-specific information. The authors address scenarios where standard distributed optimization techniques, typically involving a central entity broadcasting coordination signals, fall short in preserving user privacy.

Problem and Approach

The optimization problems under consideration involve constraints that encapsulate the sensitive data of individual participants. In traditional settings, coordination signals might expose this sensitive information to adversaries, especially when they have access to auxiliary data. To counteract this, the authors propose a modified distributed optimization algorithm that implements differential privacy by perturbing coordination signals with noise. The magnitude of this noise is derived from the sensitivity of the constraint projections, aligning with the requirements of differential privacy.

This approach is articulated as a differentially private variant of stochastic gradient descent, which introduces perturbative noise to maintain privacy without severely compromising the optimization's performance. The algorithm is thoroughly analyzed, quantifying privacy guarantees using the adaptive composition theorem. A specific instance of the algorithm is illustrated through the electric vehicle (EV) charging coordination problem, a practical case where users’ charging schedules carry sensitive information.

Numerical Analysis

The authors provide both a theoretical characterization and numerical simulations to substantiate the efficacy of their algorithm. The theoretical discourse includes bounding the suboptimality of the differentially private method, equating performance loss to that of stochastic gradient methods affected by inherent noise. Empirical evaluations in the context of EV charging demonstrate the trade-off between privacy (controlled by parameter ε) and performance (captured by suboptimality). Notably, as the ε parameter decreases, indicating stronger privacy, there is an observable increase in suboptimality, explicitly balancing privacy with practical optimization outcomes.

Implications and Future Directions

This research introduces significant implications for privacy-preserving optimization in decentralized systems, particularly those reliant on user-supplied constraints that are adversary targets. Integrating differential privacy ensures robustness against auxiliary information, a common vector for privacy infringement in decentralized systems, such as smart grid applications.

The paper hints at the broader applicability of the proposed method, encouraging exploration in fields where distributed decision-making intersects with privacy-sensitive data. Future work might engage in refining the bounds of suboptimality in strongly convex settings or extending the approach to multi-agent systems beyond EV charging, with potential considerations for adaptive consensus models.

In summary, "Differentially Private Distributed Constrained Optimization" contributes an insightful methodology to the confluence of privacy-preserving techniques and distributed optimization, offering a scalable solution in the wake of increasing demands for algorithmic transparency and privacy protection in networked systems.