Twin Sorting Dynamic Programming Assisted User Association and Wireless Bandwidth Allocation for Hierarchical Federated Learning

TL;DR

This work tackles the challenge of minimizing the round length in hierarchical federated learning by optimally assigning mobile users to edge servers under equal bandwidth sharing. It introduces the Twin Sorting Dynamic Programming (TSDP) algorithm, which provably yields a globally optimal user association when there are two edge servers, and a TSDP-assisted framework for scenarios with three or more edge servers. Given an association, the paper formulates a convex optimization for optimal wireless bandwidth allocation and enhances latency reduction through a five-phase pipeline that includes DBA and Critical Path Reduction (CPR). Empirical results show significant latency improvements over several baselines and demonstrate the method’s scalability and potential to accelerate convergence in real-world HFL deployments. The approach offers a principled, polynomial-time path to near-optimal resource coordination in large-scale wireless HFL systems, with practical implications for scalable privacy-preserving learning at the network edge.

Abstract

In this paper, we study user association and wireless bandwidth allocation for a hierarchical federated learning system that consists of mobile users, edge servers, and a cloud server. To minimize the length of a global round in hierarchical federated learning with equal bandwidth allocation, we formulate a combinatorial optimization problem. We design the twin sorting dynamic programming (TSDP) algorithm that obtains a globally optimal solution in polynomial time when there are two edge servers. In addition, we put forward the TSDP-assisted algorithm for user association when there are three or more edge servers. Furthermore, given a user association matrix, we formulate and solve a convex optimization problem for optimal wireless bandwidth allocation. Simulation results show that the proposed approach outperforms a number of alternative schemes.

Figures (8)

• Figure 1: A hierarchical federated learning system in round $t$.
• Figure 2: Advantages of the TSDP algorithm, $(M,N)=(16,2)$.
• Figure 3: $|A_{2}(t)|$ for four algorithms, $(M,N)=(16,2)$.
• Figure 4: The HFL latency for four algorithms, $(M,N)=(20,2)$.
• Figure 5: Advantages of the TSDP-assisted algorithm when $(M,N)=(8,4)$.