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Fair Allocation of Bandwidth At Edge Servers For Concurrent Hierarchical Federated Learning

Md Anwar Hossen, Fatema Siddika, Wensheng Zhang

TL;DR

The paper tackles uplink bandwidth bottlenecks in concurrent three-tier Hierarchical Federated Learning by modeling the interaction between edge servers and multiple FL servers as a Stackelberg game. It develops both a distributed heuristic and a centralized algorithm to approximate a Nash Equilibrium, aiming for full utilization of edge uplink capacity $b_j$ and fairness across FL servers with funds $f_i$. Key contributions include the formal three-tier architecture, the Stackelberg formulation with allocations $x_{i,j}$ and prices $p_j$, and extensive MNIST-based evaluations showing that the proposed schemes achieve fair client allocation and competitive FL accuracy versus a centralized baseline, while outperforming a naive proportional baseline. The results demonstrate practical potential for scalable, privacy-preserving FL with multiple concurrent processes by leveraging edge mediation to balance efficiency and fairness under heterogeneity of client distributions, funds, and bandwidth needs.

Abstract

This paper explores concurrent FL processes within a three-tier system, with edge servers between edge devices and FL servers. A challenge in this setup is the limited bandwidth from edge devices to edge servers. Thus, allocating the bandwidth efficiently and fairly to support simultaneous FL processes becomes crucial. We propose a game-theoretic approach to model the bandwidth allocation problem and develop distributed and centralized heuristic schemes to find an approximate Nash Equilibrium of the game. We proposed the approach mentioned above using centralized and entirely distributed assumptions. Through rigorous analysis and experimentation, we demonstrate that our schemes efficiently and fairly assign the bandwidth to the FL processes for centralized and distributed solutions and outperform a baseline scheme where each edge server assigns bandwidth proportionally to the FL servers' requests that it receives. The proposed distributed and centralized schemes have comptetive performance.

Fair Allocation of Bandwidth At Edge Servers For Concurrent Hierarchical Federated Learning

TL;DR

The paper tackles uplink bandwidth bottlenecks in concurrent three-tier Hierarchical Federated Learning by modeling the interaction between edge servers and multiple FL servers as a Stackelberg game. It develops both a distributed heuristic and a centralized algorithm to approximate a Nash Equilibrium, aiming for full utilization of edge uplink capacity and fairness across FL servers with funds . Key contributions include the formal three-tier architecture, the Stackelberg formulation with allocations and prices , and extensive MNIST-based evaluations showing that the proposed schemes achieve fair client allocation and competitive FL accuracy versus a centralized baseline, while outperforming a naive proportional baseline. The results demonstrate practical potential for scalable, privacy-preserving FL with multiple concurrent processes by leveraging edge mediation to balance efficiency and fairness under heterogeneity of client distributions, funds, and bandwidth needs.

Abstract

This paper explores concurrent FL processes within a three-tier system, with edge servers between edge devices and FL servers. A challenge in this setup is the limited bandwidth from edge devices to edge servers. Thus, allocating the bandwidth efficiently and fairly to support simultaneous FL processes becomes crucial. We propose a game-theoretic approach to model the bandwidth allocation problem and develop distributed and centralized heuristic schemes to find an approximate Nash Equilibrium of the game. We proposed the approach mentioned above using centralized and entirely distributed assumptions. Through rigorous analysis and experimentation, we demonstrate that our schemes efficiently and fairly assign the bandwidth to the FL processes for centralized and distributed solutions and outperform a baseline scheme where each edge server assigns bandwidth proportionally to the FL servers' requests that it receives. The proposed distributed and centralized schemes have comptetive performance.
Paper Structure (32 sections, 5 theorems, 12 equations, 7 figures, 3 tables, 3 algorithms)

This paper contains 32 sections, 5 theorems, 12 equations, 7 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem Description
  3. System Model
  4. Federated Learning Processes
  5. Design Goals
  6. Game-Theoretic Formulation and Analysis
  7. Assumption: Competing System
  8. Rules and Strategies of The Game
  9. Constraints
  10. Utility Functions
  11. Nash Equilibrium
  12. Properties of Nash Equilibrium
  13. Solution of Nash Equilibrium
  14. Game-Theoretic Heuristic Schemes
  15. Distributed Scheme
  16. ...and 17 more sections

Key Result

Theorem 1

For any Nash Equilibrium of the game, as denoted by (eq:sp-ne), it must hold that $p^*_0=\cdots=p^*_{e-1}$.

Figures (7)

  • Figure 1: Proposed Three-Tier FL Architecture.
  • Figure 2: Numbers of clients acquired by FL servers with Client Heterogeneity (Baseline Scheme).
  • Figure 3: Numbers of clients acquired by FL servers with Client Heterogeneity (Proposed Centralized Scheme).
  • Figure 4: Numbers of clients acquired by FL servers with Client Heterogeneity (Proposed Distributed Scheme).
  • Figure 5: Numbers of clients acquired by FL servers (Heterogeneity of Funds).
  • ...and 2 more figures

Theorems & Definitions (11)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • proof
  • Corollary 5
  • ...and 1 more