Local Graph-homomorphic Processing for Privatized Distributed Systems
This work addresses privacy concerns in distributed systems for networked agents, offering an incremental improvement over previous methods by better aligning noise addition with graph topology.
The paper tackles the problem of generating dependent random numbers for privatized distributed learning by networked agents, proposing local graph-homomorphic processing to add structured noise that ensures differential privacy without affecting model performance, as demonstrated in a linear regression example.
We study the generation of dependent random numbers in a distributed fashion in order to enable privatized distributed learning by networked agents. We propose a method that we refer to as local graph-homomorphic processing; it relies on the construction of particular noises over the edges to ensure a certain level of differential privacy. We show that the added noise does not affect the performance of the learned model. This is a significant improvement to previous works on differential privacy for distributed algorithms, where the noise was added in a less structured manner without respecting the graph topology and has often led to performance deterioration. We illustrate the theoretical results by considering a linear regression problem over a network of agents.