Graph-Homomorphic Perturbations for Private Decentralized Learning

TL;DR

This paper introduces a novel privacy-preserving perturbation scheme for decentralized learning that maintains privacy without significantly affecting performance, applicable to complex nonconvex problems like deep learning.

Contribution

It proposes graph-homomorphic perturbations that are invisible to the network centroid, enhancing privacy while preserving learning accuracy in decentralized algorithms.

Findings

Perturbations are invisible to the network centroid, ensuring privacy.

The scheme applies to nonconvex loss functions, including deep learning.

Performance loss is minimized compared to traditional independent perturbations.

Abstract

Decentralized algorithms for stochastic optimization and learning rely on the diffusion of information as a result of repeated local exchanges of intermediate estimates. Such structures are particularly appealing in situations where agents may be hesitant to share raw data due to privacy concerns. Nevertheless, in the absence of additional privacy-preserving mechanisms, the exchange of local estimates, which are generated based on private data can allow for the inference of the data itself. The most common mechanism for guaranteeing privacy is the addition of perturbations to local estimates before broadcasting. These perturbations are generally chosen independently at every agent, resulting in a significant performance loss. We propose an alternative scheme, which constructs perturbations according to a particular nullspace condition, allowing them to be invisible (to first order in the step-size) to the network centroid, while preserving privacy guarantees. The analysis allows for general nonconvex loss functions, and is hence applicable to a large number of machine learning and signal processing problems, including deep learning.