Multi-Message Shuffled Privacy in Federated Learning

TL;DR

This paper introduces a communication-efficient, differentially private distributed optimization method using multi-message shuffled privacy, achieving near-optimal privacy-communication-performance tradeoffs in federated learning.

Contribution

It develops a novel private distributed mean estimation scheme with multi-message shuffled privacy, resolving open questions on optimal tradeoffs in privacy and communication.

Findings

Achieves order-optimal privacy-communication-performance tradeoff.

Introduces a non-uniform privacy allocation mechanism.

Provides numerical evaluation of private DME algorithms.

Abstract

We study differentially private distributed optimization under communication constraints. A server using SGD for optimization aggregates the client-side local gradients for model updates using distributed mean estimation (DME). We develop a communication-efficient private DME, using the recently developed multi-message shuffled (MMS) privacy framework. We analyze our proposed DME scheme to show that it achieves the order-optimal privacy-communication-performance tradeoff resolving an open question in [1], whether the shuffled models can improve the tradeoff obtained in Secure Aggregation. This also resolves an open question on the optimal trade-off for private vector sum in the MMS model. We achieve it through a novel privacy mechanism that non-uniformly allocates privacy at different resolutions of the local gradient vectors. These results are directly applied to give guarantees on private distributed learning algorithms using this for private gradient aggregation iteratively. We also numerically evaluate the private DME algorithms.