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On Resilient and Efficient Linear Secure Aggregation in Hierarchical Federated Learning

Shudi Weng, Xiang Zhang, Yizhou Zhao, Giuseppe Caire, Ming Xiao, Mikael Skoglund

TL;DR

The paper addresses resilient and efficient secure aggregation in hierarchical federated learning under unreliable communication. It introduces an information-theoretic HSA problem, derives a complete rate region with explicit lower bounds, and presents a ComEffGC-inspired, linear-encoding achievability scheme that attains these bounds with a matching converse. A key contribution is a one-to-one mapping between finite-field and real-field sums, enabling practical applicability to real-valued model updates. The results provide both a rigorous theoretical foundation for secure aggregation in HFL with imperfections and a concrete scheme with provable optimality, bridging theory and practice for edge learning systems.

Abstract

In this paper, we study the fundamental limits of hierarchical secure aggregation under unreliable communication. We consider a hierarchical network where each client connects to multiple relays, and both client-to-relay and relay-to-server links are intermittent. Under this setting, we characterize the minimum communication and randomness costs required to achieve robust secure aggregation. We then propose an optimal protocol that attains these minimum costs, and establish its optimality through a matching converse proof. In addition, we introduce an improved problem formulation that bridges the gap between existing information-theoretic secure aggregation protocols and practical real-world federated learning problems.

On Resilient and Efficient Linear Secure Aggregation in Hierarchical Federated Learning

TL;DR

The paper addresses resilient and efficient secure aggregation in hierarchical federated learning under unreliable communication. It introduces an information-theoretic HSA problem, derives a complete rate region with explicit lower bounds, and presents a ComEffGC-inspired, linear-encoding achievability scheme that attains these bounds with a matching converse. A key contribution is a one-to-one mapping between finite-field and real-field sums, enabling practical applicability to real-valued model updates. The results provide both a rigorous theoretical foundation for secure aggregation in HFL with imperfections and a concrete scheme with provable optimality, bridging theory and practice for edge learning systems.

Abstract

In this paper, we study the fundamental limits of hierarchical secure aggregation under unreliable communication. We consider a hierarchical network where each client connects to multiple relays, and both client-to-relay and relay-to-server links are intermittent. Under this setting, we characterize the minimum communication and randomness costs required to achieve robust secure aggregation. We then propose an optimal protocol that attains these minimum costs, and establish its optimality through a matching converse proof. In addition, we introduce an improved problem formulation that bridges the gap between existing information-theoretic secure aggregation protocols and practical real-world federated learning problems.
Paper Structure (18 sections, 1 theorem, 31 equations)

This paper contains 18 sections, 1 theorem, 31 equations.

Table of Contents

  1. Introduction
  2. Hierarchical Federated Learning (HFL)
  3. Information-Theoretic Secure Aggregation
  4. Our Contributions
  5. Problem Formulation
  6. Main Results
  7. Achievability
  8. Example
  9. General Scheme
  10. Rationale
  11. General Scheme
  12. Achievability Proof
  13. Converse
  14. Proof of $R_1\geq \frac{d}{d-s}$
  15. Proof of $R_2\geq \max\left\{\frac{1}{d-s},\frac{1}{K-1} \right\}$
  16. ...and 3 more sections

Key Result

Theorem 1

In the resilient, secure HFL protocol under unreliable communication, as described in Section sec: prob_formu, the optimal rate region $\mathcal{C}^*$ is characterized by where $p$ is a primeNotably, modulo equations over finite fields admit unique solutions and support flexible algebraic operations, owing to the prime field size. In contrast, modulo equations over other groups (or e.g., real-fie

Theorems & Definitions (2)

  • Theorem 1
  • Remark 1