Recycled ADMM: Improving the Privacy and Accuracy of Distributed Algorithms

TL;DR

Recycled ADMM (R-ADMM) enhances distributed convex optimization by reducing privacy leakage and computational costs through linear approximation, with proven convergence and improved privacy-accuracy tradeoff.

Contribution

Introduction of R-ADMM and MR-ADMM algorithms that reduce privacy loss and computation in distributed optimization, with convergence guarantees and privacy analysis.

Findings

R-ADMM halves privacy loss compared to standard ADMM.

R-ADMM requires less computation per iteration.

The algorithms improve the privacy-accuracy tradeoff significantly.

Abstract

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.