Differentially Private Distributed Optimization
This addresses privacy concerns in distributed systems for applications like federated learning, though it appears incremental as it builds on existing distributed optimization frameworks.
The paper tackles the problem of distributed optimization with differential privacy, where agents aim to minimize a sum of cost functions while keeping individual functions private from adversaries. It proposes iterative algorithms that achieve differential privacy and convergence to the optimal value, with accuracy scaling as O(1/ε²) for ε-differential privacy.
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 $ε$-differential privacy the accuracy of the algorithm has the order of $O(\frac{1}{ε^2})$.