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How Can Incentives and Cut Layer Selection Influence Data Contribution in Split Federated Learning?

Joohyung Lee, Jungchan Cho, Wonjun Lee, Mohamed Seif, H. Vincent Poor

TL;DR

This work addresses data contribution incentives in Split Federated Learning under privacy and computation constraints by modeling the interaction between an SFL model owner (leader) and clients (followers) as a two-stage Stackelberg game. The model owner chooses the cut layer and incentive budget, while clients decide how much data to contribute, with client incentives allocated proportionally to data contributions. The authors derive a closed-form Nash equilibrium for clients, prove the existence of a Stackelberg equilibrium, and solve for optimal incentives and cut-layer settings using CVX coupled with an exhaustive search over feasible cut layers. Empirical results on CIFAR-10/100 and F-MNIST show incentives substantially boost data contributions and model accuracy, with the price of anarchy decreasing as the client pool grows and as the cut layer becomes more burdensome, indicating improved efficiency in larger, well-incentivized settings. The paper also discusses privacy implications of cut-layer choices and how differential privacy can interact with cut-layer settings to balance privacy and utility in practical deployments.

Abstract

To alleviate the training burden in federated learning while enhancing convergence speed, Split Federated Learning (SFL) has emerged as a promising approach by combining the advantages of federated and split learning. However, recent studies have largely overlooked competitive situations. In this framework, the SFL model owner can choose the cut layer to balance the training load between the server and clients, ensuring the necessary level of privacy for the clients. Additionally, the SFL model owner sets incentives to encourage client participation in the SFL process. The optimization strategies employed by the SFL model owner influence clients' decisions regarding the amount of data they contribute, taking into account the shared incentives over clients and anticipated energy consumption during SFL. To address this framework, we model the problem using a hierarchical decision-making approach, formulated as a single-leader multi-follower Stackelberg game. We demonstrate the existence and uniqueness of the Nash equilibrium among clients and analyze the Stackelberg equilibrium by examining the leader's game. Furthermore, we discuss privacy concerns related to differential privacy and the criteria for selecting the minimum required cut layer. Our findings show that the Stackelberg equilibrium solution maximizes the utility for both the clients and the SFL model owner.

How Can Incentives and Cut Layer Selection Influence Data Contribution in Split Federated Learning?

TL;DR

This work addresses data contribution incentives in Split Federated Learning under privacy and computation constraints by modeling the interaction between an SFL model owner (leader) and clients (followers) as a two-stage Stackelberg game. The model owner chooses the cut layer and incentive budget, while clients decide how much data to contribute, with client incentives allocated proportionally to data contributions. The authors derive a closed-form Nash equilibrium for clients, prove the existence of a Stackelberg equilibrium, and solve for optimal incentives and cut-layer settings using CVX coupled with an exhaustive search over feasible cut layers. Empirical results on CIFAR-10/100 and F-MNIST show incentives substantially boost data contributions and model accuracy, with the price of anarchy decreasing as the client pool grows and as the cut layer becomes more burdensome, indicating improved efficiency in larger, well-incentivized settings. The paper also discusses privacy implications of cut-layer choices and how differential privacy can interact with cut-layer settings to balance privacy and utility in practical deployments.

Abstract

To alleviate the training burden in federated learning while enhancing convergence speed, Split Federated Learning (SFL) has emerged as a promising approach by combining the advantages of federated and split learning. However, recent studies have largely overlooked competitive situations. In this framework, the SFL model owner can choose the cut layer to balance the training load between the server and clients, ensuring the necessary level of privacy for the clients. Additionally, the SFL model owner sets incentives to encourage client participation in the SFL process. The optimization strategies employed by the SFL model owner influence clients' decisions regarding the amount of data they contribute, taking into account the shared incentives over clients and anticipated energy consumption during SFL. To address this framework, we model the problem using a hierarchical decision-making approach, formulated as a single-leader multi-follower Stackelberg game. We demonstrate the existence and uniqueness of the Nash equilibrium among clients and analyze the Stackelberg equilibrium by examining the leader's game. Furthermore, we discuss privacy concerns related to differential privacy and the criteria for selecting the minimum required cut layer. Our findings show that the Stackelberg equilibrium solution maximizes the utility for both the clients and the SFL model owner.

Paper Structure

This paper contains 17 sections, 6 theorems, 30 equations, 10 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. System Model
  4. Utility Function of SFL Model Owner
  5. Utility Function of Clients
  6. Overall computation energy of the client
  7. Overall communication energy of the client
  8. Overall energy consumption
  9. Shared incentives and utility function design
  10. Game-Theoretic Analysis
  11. Stage 1: Noncooperative Game Among Clients
  12. Stage 2: Utility Maximization for SFL Model Owner
  13. Performance Evaluation
  14. Discussion
  15. Impact of Cut Layer Selection on Privacy
  16. ...and 2 more sections

Key Result

Theorem 1

The utility function $U_n(d_n, \mathbf{d}_{-n}, R, L_c)$ of client $n$ is strictly concave in $d_n$. Thus, a Nash equilibrium exists in the noncooperative game among the clients.

Figures (10)

  • Figure 1: Concept of the proposed Split Federated Learning: It considers interactions between the model owner and clients. The SFL model owner determines the cut layer and incentives, while the clients manage data contribution, considering their energy consumption.
  • Figure 2: Timeline of the Overall SFL Process.
  • Figure 3: Regression analysis of computation load and the number of model parameters with varying $L_c$.
  • Figure 4: A diagram of a two-stage Stackelberg game in SFL where the SFL model owner is a leader and clients are followers.
  • Figure 5: Data contribution at NE for various ($f_n$, $\psi_n$ ) pairs.
  • ...and 5 more figures

Theorems & Definitions (15)

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