Distributed Empirical Risk Minimization With Differential Privacy

TL;DR

This paper introduces a private distributed dual averaging algorithm for empirical risk minimization under differential privacy, which activates only a subset of nodes to improve utility and achieves near-centralized privacy guarantees.

Contribution

The paper proposes a novel subsampling-based distributed dual averaging method that amplifies differential privacy guarantees and maintains optimal convergence rates.

Findings

Achieves comparable utility to centralized private algorithms.

Provides provable privacy amplification through node subsampling.

Demonstrates effectiveness on benchmark datasets.

Abstract

This work studies the distributed empirical risk minimization (ERM) problem under differential privacy (DP) constraint. Standard distributed algorithms achieve DP typically by perturbing all local subgradients with noise, leading to significantly degenerated utility. To tackle this issue, we develop a class of private distributed dual averaging (DDA) algorithms, which activates a fraction of nodes to perform optimization. Such subsampling procedure provably amplifies the DP guarantee, thereby achieving an equivalent level of DP with reduced noise. We prove that the proposed algorithms have utility loss comparable to centralized private algorithms for both general and strongly convex problems. When removing the noise, our algorithm attains the optimal O(1/t) convergence for non-smooth stochastic optimization. Finally, experimental results on two benchmark datasets are given to verify the effectiveness of the proposed algorithms.