Recycled ADMM: Improving the Privacy and Accuracy of Distributed Algorithms
This work addresses privacy concerns in distributed optimization for applications like federated learning, though it is incremental as it builds on existing ADMM methods.
The paper tackles the problem of data privacy leakage in distributed ADMM algorithms by proposing Recycled ADMM (R-ADMM), which reduces privacy loss and computational cost by using linear approximations in half the iterations, and shows significant improvement in the privacy-accuracy tradeoff compared to conventional ADMM.
Alternating direction method of multiplier (ADMM) is a powerful method to solve decentralized convex optimization problems. In distributed settings, each node performs computation with its local data and the local results are exchanged among neighboring nodes in an iterative fashion. During this iterative process the leakage of data privacy arises and can accumulate significantly over many iterations, making it difficult to balance the privacy-accuracy tradeoff. We propose Recycled ADMM (R-ADMM), where a linear approximation is applied to every even iteration, its solution directly calculated using only results from the previous, odd iteration. It turns out that under such a scheme, half of the updates incur no privacy loss and require much less computation compared to the conventional ADMM. Moreover, R-ADMM can be further modified (MR-ADMM) such that each node independently determines its own penalty parameter over iterations. We obtain a sufficient condition for the convergence of both algorithms and provide the privacy analysis based on objective perturbation. It can be shown that the privacy-accuracy tradeoff can be improved significantly compared with conventional ADMM.