Incentivizing Truthful Collaboration in Heterogeneous Federated Learning

TL;DR

This work addresses incentive issues in heterogeneous federated learning by modeling client behavior as a game and introducing a budget-balanced payment mechanism. It proves that the FedSGD protocol with the proposed payments is $\varepsilon$-Bayesian Incentive Compatible and yields $\varepsilon$-approximately truthful reporting, while maintaining convergence under $m$-strongly convex and $H$-smooth objectives. Theoretical results provide explicit bounds on payments and convergence rates as functions of heterogeneity parameters and learning dynamics, elucidating the trade-offs between heterogeneity, payments, and efficiency. Empirically, the mechanism consistently deters gradient manipulation across FedSGD, median-based FedSGD, and FedAvg on FeMNIST, Shakespeare, and Twitter datasets, demonstrating both robustness and adaptability to different FL paradigms and non-convex tasks. Overall, the paper contributes a principled mechanism-design approach to securing FL against manipulation arising from heterogeneity, with practical implications for reliable, scalable collaborative learning in distributed settings.

Abstract

Federated learning (FL) is a distributed collaborative learning method, where multiple clients learn together by sharing gradient updates instead of raw data. However, it is well-known that FL is vulnerable to manipulated updates from clients. In this work we study the impact of data heterogeneity on clients' incentives to manipulate their updates. First, we present heterogeneous collaborative learning scenarios where a client can modify their updates to be better off, and show that these manipulations can lead to diminishing model performance. To prevent such modifications, we formulate a game in which clients may misreport their gradient updates in order to "steer" the server model to their advantage. We develop a payment rule that provably disincentivizes sending modified updates under the FedSGD protocol. We derive explicit bounds on the clients' payments and the convergence rate of the global model, which allows us to study the trade-off between heterogeneity, payments and convergence. Finally, we provide an experimental evaluation of the effectiveness of our payment rule in the FedSGD, median-based aggregation FedSGD and FedAvg protocols on three tasks in computer vision and natural language processing. In all cases we find that our scheme successfully disincentivizes modifications.

Figures (8)

• Figure 1: The plot follows Proposition \ref{['proposition:sgd-example']}. Clients are represented by colors, and their respective loss functions (variants of quadratic loss) are shown next to their color in the legend. The black curve is the average loss function over all clients, and the legend shows the optimum. The red client scales their gradients by a constant, in this case $3 \times$; the dotted red line is their new loss function, and the dotted black line is the new average loss. The new global optimum is better for the red client, while it's worse for the green client.
• Figure 2: The three plots illustrate the result of applying our payment scheme to the FedSGD protocol. Each line is the average of 10 runs of FedSGD, and the error bars show standard error. The constant $C$ controls the magnitude of the payment; smaller $C$ corresponds to smaller payment. The success of our mechanism is particularly prominent for the FeMNIST and Shakespeare datasets. For the Twitter dataset, the scaling factor is marginally beneficial to begin with. In all three experiments the misreporting client is only amplifying their gradient, without adding noise (so $b_A = 0.0$). For experiments with various levels of noise see Appendix \ref{['appendix:experiments']}.
• Figure 3: Experiments with other federated learning protocols
• Figure 4: Experiments with FedSGD with coordinate-wise median aggregation. The $x$ axis is the scaling factor $a_A$, and the $y$ axis is the utility for the client who misreports. Noise level is set to zero. All other clients are truthful.
• Figure 5: Experiments with FedAvg. The $x$ axis is the scaling factor $a_A$, and the $y$ axis is the utility for the misreporting client in group $A$. Noise level is set to zero. All other clients are truthful.

Theorems & Definitions (51)

• Definition 2.1: Strong convexity
• Definition 2.2: Smoothness
• Proposition 3.1
• Remark
• Example 3.2
• Definition 4.1: Lipschitzness
• Definition 4.2: $\varepsilon$-Bayesian Incentive Compatibility
• Definition 4.3: $\varepsilon$-Approximately truthful reporting
• Theorem 5.1: Properties of the payment scheme
• Theorem 5.2: Bound on individual payments