In federated learning (FL), a center trains a shared model from updates that clients compute on their private data. Collecting and training on data is costly, so a strategic client may contribute little data and free-ride on the model trained by the others. We study mechanisms that incentivize data contribution and learn the model at the same time. Our first mechanism, UPBReD, updates the clients ' contributions and the model jointly, and converges at a geometric rate to a Nash equilibrium of the contribution game together with the welfare-maximizing model for those contributions. This equilibrium can involve under-contribution, so our second mechanism, 2P-UPBReD, adds budget-balanced transfers that make full contribution a dominant strategy, after which training converges to the optimal model; we also give conditions under which every client prefers to participate. Both mechanisms trust what clients report about the data they use and the gradients they compute. We show that no payment rule can reward unverifiable contributions unless something the center observes depends on the data actually used. Building on this, T-2P-UPBReD checks each client's reported contribution against the other clients ' realized valuations of the trained model, and prices gradient reports with a budget-balanced charge. It elicits truthful contribution reports, makes gradient reports approximately truthful, still reaches full contribution and the optimal model, and never runs a deficit. Experiments on CIFAR-10, FEMNIST, and Twitter show that 2P-UPBReD matches the welfare of FedAvg trained on all data, while strategic clients without incentives lower the welfare of the learned model.
Figures & tables
Eq.
Learn.
Transfers
Reports
Truthful
Contrib.
Private
Procaccia et al. [42]
E
✗
BB
D
DSIC
P
✗
Bornstein et al. [3]
E
✗
✓
C
DSIC
F
✓
Blum et al. [2]
E
✗
✗
S
✗
P
✓
Murhekar et al. [38]
C
✗
BB
S,C
✗
P
✓
Karimireddy et al. [27]
E
✗
✓
S,C
✗
F
✓
UPBReD (Thm. 1 )
C
J
✗
S,G
✗
P
✓
Table 1: Comparison with incentive mechanisms for FL; our mechanisms are in the last four rows. Eq. : existence (E) of, or convergence (C) to, a Nash equilibrium. Learn. : joint convergence of the model and the contributions (J), or convergence to the optimal parameter wOPT (OPT). Transfers : budget balanced (BB), budget balanced on the truthful path and never in deficit (BB ∗ ), individually rational (IR). Reports : data distribution (D), cost (C), contribution (S), gradient (G). Truthful : guarantee for the reported quantity; ε denotes ε -truthfulness with a vanishing gain from misreporting, and † marks guarantees that rely on agents observing realized valuations ( Assumption 5 ); Proposition 2 shows that evidence of this kind is necessary. Contrib. : partial (P) or full (F) contribution at equilibrium. Private : data are not shared with the center.
Figure 1: Shaded regions show the feasible choices of γ in Theorem 1 for n=2 and L=2 : (a) as a function of λ for the values of P~ shown, and (b) as a function of P~ for the values of λ shown. Dashed lines mark the boundary γ=2(λ−P~)/(n2L2−P~2) . The region is empty when λ⩽P~ . The feasible choices of η are obtained by replacing (n,L,λ,P~) with (m,L~,λ~,P) .
Figure 2: The three rows in this figure correspond to the experiments with the datasets CIFAR-10, FEMNIST, and Twitter, respectively. The y-axis in every plot is the social welfare (computed using 10−Li(w) , where Li(w) is the test loss for agent i ). The x-axis corresponds to the number of agents in the first plot, the choice of β in the second, and the time taken (in minutes) in the third plot, respectively, in every row.
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 3: The three rows in this figure correspond to the experiments with the datasets CIFAR-10, FEMNIST, and Twitter, respectively. The y-axis in every plot is the social welfare (computed using test accuracy for each agent). The x-axis corresponds to the number of agents in the first plot, the choice of β in the second, and the time taken (in minutes) in the third plot, respectively, in every row.
Figure 4: Social welfare vs. number of clients for different CIFAR-10 dataset splits using the Flower framework.
Figure 5: Label distributions for different data partitioning strategies using Flower with 10 agents. The x-axis represents the client ID and the y-axis represents the number of data points of the given label.
Figure 6: Utilities and payments received by agents for 2P-UPBReD based on their data contributions for FEMNIST (averaged over 10 runs).
Layer (type:depth-idx)
Output Shape
Param #
Cifar10ResNet
[1, 10]
–
Conv2d: 1-1
[1, 64, 32, 32]
1,728
BatchNorm2d: 1-2
[1, 64, 32, 32]
128
ReLU: 1-3
[1, 64, 32, 32]
–
Identity: 1-4
[1, 64, 32, 32]
–
Sequential (layer1): 1-5
[1, 64, 32, 32]
147,968
Appendix
Table 2: Layer-wise Summary of Cifar10ResNet for CIFAR-10
Layer (type:depth-idx)
Output Shape
Param #
FemnistCNN
[1, 62]
–
Conv2d: 1-1
[1, 32, 28, 28]
832
MaxPool2d: 1-2
[1, 32, 14, 14]
–
Conv2d: 1-3
[1, 64, 14, 14]
51,264
MaxPool2d: 1-4
[1, 64, 7, 7]
–
Linear: 1-5
[1, 2048]
6,424,576
Appendix
Table 3: Layer-wise Summary of the CNN for FEMNIST
Figure 7: Ratio of social welfare with adversaries and without adversaries.
Federated learning (FL) is a communication-efficient collaborative learning framework that enables model training across multiple agents with private local datasets. While the benefits of FL in improving global model performance are well established, individual agents may behave strategically, balancing the learning payoff against the cost of contributing their local data. Motivated by the need for FL frameworks that successfully retain participating agents, we propose an incentive-aware federated averaging method in which, at each communication round, clients transmit both their local model parameters and their updated training dataset sizes to the server. The dataset sizes are dynamically adjusted via a Nash equilibrium (NE)-seeking update rule that captures strategic data participation. We analyze the proposed method under convex and nonconvex global objective settings and establish performance guarantees for the resulting incentive-aware FL algorithm. Furthermore, under a merely monotone game setting, we consider a welfare loss minimization framework and establish asymptotic convergence of the scheme. Numerical experiments on the MNIST and CIFAR-10 datasets demonstrate that agents achieve competitive global model performance while converging to stable data participation strategies.
Federated learning has become a popular paradigm for privacy protection and edge-based machine learning. However, defending against differential attacks and devising incentive strategies remain significant bottlenecks in this field. Despite recent works on privacy-aware incentive mechanism design for federated learning, few of them consider both data volume and noise level. In this paper, we propose a novel federated learning system called FEDBUD, which combines privacy and economic concerns together by considering the joint influence of data volume and noise level on incentive strategy determination. In this system, the cloud server controls monetary payments to edge nodes, while edge nodes control data volume and noise level that potentially impact the model performance of the cloud server. To determine the mutually optimal strategies for both sides, we model FEDBUD as a two-stage Stackelberg Game and derive the Nash Equilibrium using the mean-field estimator and virtual queue. Experimental results on real-world datasets demonstrate the outstanding performance of FEDBUD.
Tao Liu, Xuehe Wang
School of Artificial Intelligence, Sun Yat-sen University, Zhuhai 519082, China
Participation in federated learning (FL) comes at a cost. Clients trade off privacy, communication, and compute costs for potentially greater gains in model efficacy. This paper explores this tradeoff under the aegis of individual rationality (IR) versus autarky, the basic game-theoretic requirement that the federation provide utility no worse than local training. Using the above as the design target, we examine pathwise performance of FL, as a per-round bound on cumulative surplus rather than only an asymptotic equilibrium guarantee under different degrees of client data heterogeneity. Along the learning path, clients can remain below their local-training baseline for hundreds of rounds. The natural remedy is to cap each client's per-round contribution so that this shortfall stays bounded. We prove that such a cap drives all contributions to zero, with high probability, when its tolerance is small relative to the warm-up deficit, and we observe learning collapse under it even at low heterogeneity. We then propose a design that combines a short-term participation guarantee, enforced after an announced grace window, with personalized model evaluation, while preserving the incentive properties of the underlying mechanism. We provide a theoretical basis for this approach and empirically demonstrate that, after the grace window, clients meet IR on nearly all rounds without harming overall performance under low to moderate heterogeneity; under severe heterogeneity, the design shows promising outcomes for clients compared to their local baseline at some cost in accuracy.
Amin Meghrazi, Srinivasan Parthasarathy, Andrew Perrault