Fair Bayesian Stackelberg Federated Learning Under Strategic and Heterogeneous Client Participation

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Federated learning must accommodate statistical heterogeneity, costly client participation, and distinct fairness objectives for model performance and participation frequency. We introduce Fair Bayesian Stackelberg Federated Learning (FBS-FL), in which a server maintains beliefs over private client cost types and selects stochastic inclusion probabilities and incentives under an expected client-inclusion constraint. The framework combines an analytical cost-threshold response model with a scalable PPO–EXP3 behavioral implementation using approximate belief tracking. We evaluate FBS-FL over five seeds on CIFAR-10, FEMNIST, and Shakespeare. FBS-FL obtains Jain indices from 0.91 to 0.93 and KL divergences to uniform participation from 0.07 to 0.09, compared with 0.81 to 0.86 and 0.16 to 0.22 for the strongest baseline values on the same participation metrics. The evaluation jointly examines participation fairness, mean accuracy, and worst-client performance. The results indicate improved participation balance with small accuracy variation under the reported protocol.