Differentially Private ADMM for Convex Distributed Learning: Improved Accuracy via Multi-Step Approximation

Alternating Direction Method of Multipliers (ADMM) is a popular algorithm for distributed learning, where a network of nodes collaboratively solve a regularized empirical risk minimization by iterative local computation associated with distributed data and iterate exchanges. When the training data is sensitive, the exchanged iterates will cause serious privacy concern. In this paper, we aim to propose a new differentially private distributed ADMM algorithm with improved accuracy for a wide range of convex learning problems. In our proposed algorithm, we adopt the approximation of the objective function in the local computation to introduce calibrated noise into iterate updates robustly, and allow multiple primal variable updates per node in each iteration. Our theoretical results demonstrate that our approach can obtain higher utility by such multiple approximate updates, and achieve the error bounds asymptotic to the state-of-art ones for differentially private empirical risk minimization.