Graph-Homomorphic Perturbations for Private Decentralized Learning
This addresses privacy concerns in decentralized learning for agents hesitant to share raw data, offering a method to reduce performance loss compared to independent perturbations.
The paper tackles the performance loss in private decentralized learning by proposing a perturbation scheme that satisfies a nullspace condition, making perturbations invisible to the network centroid while preserving privacy, applicable to nonconvex functions including deep learning.
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.