Asymptotically Optimal Secure Aggregation for Wireless Federated Learning with Multiple Servers

TL;DR

This paper introduces a secure, coded aggregation scheme for wireless federated learning with multiple servers, optimizing transmission latency while ensuring privacy, and proves its near-optimality across various system configurations.

Contribution

The paper proposes a novel privacy-preserving coded aggregation scheme for wireless federated learning with multiple servers, achieving near-optimal transmission latency bounds.

Findings

The scheme guarantees information-theoretic privacy.

The normalized delivery time decreases with more servers.

The scheme is within a factor of 4 of optimal for arbitrary parameters.

Abstract

In this paper, we investigate the transmission latency of the secure aggregation problem in a \emph{wireless} federated learning system with multiple curious servers. We propose a privacy-preserving coded aggregation scheme where the servers can not infer any information about the distributed users' local gradients, nor the aggregation value. In our scheme, each user encodes its local gradient into $\sK$ confidential messages intended exclusively for different servers using a multi-secret sharing method, and each server forwards the summation of the received confidential messages, while the users sequentially employ artificial noise alignment techniques to facilitate secure transmission. Through these summations, the user can recover the aggregation of all local gradients. We prove the privacy guarantee in the information-theoretic sense and characterize the uplink and downlink communication latency measured by \emph{normalized delivery time} (NDT), both of which decrease monotonically with the number of servers $\sK$ while increasing over most of the range of the number of users $\sM$. Finally, we establish a lower bound on the NDT of the considered system and theoretically prove that the scheme achieves the optimal uplink and downlink NDT under the conditions $\sK \gg \sM \gg 0$ and $\sK \gg \sM$, respectively. For arbitrary $\sK$ and $\sM$, the proposed scheme achieves the optimal uplink NDT within a multiplicative gap of $4$.