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Design of Two-Level Incentive Mechanisms for Hierarchical Federated Learning

Shunfeng Chu, Jun Li, Kang Wei, Yuwen Qian, Kunlun Wang, Feng Shu, Wen Chen

TL;DR

This work tackles incentivizing participation in Hierarchical Federated Learning across device-edge-cloud layers under wireless resource constraints. It introduces a two-level mechanism: a lower-level coalition formation game with altruistic preferences to optimize device-edge association and bandwidth, and an upper-level Stackelberg game to determine edge aggregations and cloud rewards. The lower-level game is shown to be an exact potential game with a stable coalition partition and is solved via a gradient projection-based bandwidth allocation; the upper-level game is analyzed through a variational-inequality framework to yield Stackelberg equilibria. Numerical results on real datasets demonstrate performance gains over benchmarks, including accuracy improvements up to 3% on FashionMNIST and CIFAR-10.

Abstract

Hierarchical Federated Learning (HFL) is a distributed machine learning paradigm tailored for multi-tiered computation architectures, which supports massive access of devices' models simultaneously. To enable efficient HFL, it is crucial to design suitable incentive mechanisms to ensure that devices actively participate in local training. However, there are few studies on incentive mechanism design for HFL. In this paper, we design two-level incentive mechanisms for the HFL with a two-tiered computing structure to encourage the participation of entities in each tier in the HFL training. In the lower-level game, we propose a coalition formation game to joint optimize the edge association and bandwidth allocation problem, and obtain efficient coalition partitions by the proposed preference rule, which can be proven to be stable by exact potential game. In the upper-level game, we design the Stackelberg game algorithm, which not only determines the optimal number of edge aggregations for edge servers to maximize their utility, but also optimize the unit reward provided for the edge aggregation performance to ensure the interests of cloud servers. Furthermore, numerical results indicate that the proposed algorithms can achieve better performance than the benchmark schemes.

Design of Two-Level Incentive Mechanisms for Hierarchical Federated Learning

TL;DR

This work tackles incentivizing participation in Hierarchical Federated Learning across device-edge-cloud layers under wireless resource constraints. It introduces a two-level mechanism: a lower-level coalition formation game with altruistic preferences to optimize device-edge association and bandwidth, and an upper-level Stackelberg game to determine edge aggregations and cloud rewards. The lower-level game is shown to be an exact potential game with a stable coalition partition and is solved via a gradient projection-based bandwidth allocation; the upper-level game is analyzed through a variational-inequality framework to yield Stackelberg equilibria. Numerical results on real datasets demonstrate performance gains over benchmarks, including accuracy improvements up to 3% on FashionMNIST and CIFAR-10.

Abstract

Hierarchical Federated Learning (HFL) is a distributed machine learning paradigm tailored for multi-tiered computation architectures, which supports massive access of devices' models simultaneously. To enable efficient HFL, it is crucial to design suitable incentive mechanisms to ensure that devices actively participate in local training. However, there are few studies on incentive mechanism design for HFL. In this paper, we design two-level incentive mechanisms for the HFL with a two-tiered computing structure to encourage the participation of entities in each tier in the HFL training. In the lower-level game, we propose a coalition formation game to joint optimize the edge association and bandwidth allocation problem, and obtain efficient coalition partitions by the proposed preference rule, which can be proven to be stable by exact potential game. In the upper-level game, we design the Stackelberg game algorithm, which not only determines the optimal number of edge aggregations for edge servers to maximize their utility, but also optimize the unit reward provided for the edge aggregation performance to ensure the interests of cloud servers. Furthermore, numerical results indicate that the proposed algorithms can achieve better performance than the benchmark schemes.
Paper Structure (13 sections, 3 theorems, 35 equations, 11 figures, 1 table, 3 algorithms)

This paper contains 13 sections, 3 theorems, 35 equations, 11 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Hierarchical Federated Learning Model
  4. Participant Utility Function of Edge FL
  5. Low-Level Coalition Formation Game Formulation
  6. Game Model and Analysis
  7. Coalition Game Based Algorithm
  8. Upper-Level Stackelberg Game
  9. Problem Formulation of Upper-Level Game
  10. Stackelberg Game Approach
  11. Simulation Results and Discussion
  12. Conclusion
  13. Proof of Theorem \ref{['theorem 3']}

Key Result

Theorem 1

Given a coalition partition $\boldsymbol{\mathcal{S}} = \{ \mathcal{S}_1, ...,\mathcal{S}_L \}$, the Nash equilibrium strategy for the amount of local training data of the device $i \in \mathcal{S}_l$ in the coalition $l \in \{1, ..., L\}$ is and the Nash equilibrium strategy profile of the coalition $l$ is $\boldsymbol{D^{l*}}= \{D_{1}^{l*}, ..., D_{i}^{l*}, ..., D_{|\mathcal{S}_l|}^{l*}\}$, $\f

Figures (11)

  • Figure 1: An HFL system with a two-tiered computing structure, consisting of multiple devices and multiple edge servers. In the HFL process, the devices first transmit their local models to edge servers for edge aggregation, and then the edge servers send the edge models to the cloud server for global aggregation.
  • Figure 2: An example of the final stable coalition in edge FL network.
  • Figure 3: The converge behavior of proposed algorithm based on three preference rules.
  • Figure 4: The total coalition utilities versus the time interval of global aggregation.
  • Figure 5: The total coalition utilities versus the number of devices with low communication overhead.
  • ...and 6 more figures

Theorems & Definitions (14)

  • Definition 1
  • Theorem 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Definition 8
  • Definition 9
  • ...and 4 more