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You Get What You Give: Reciprocally Fair Federated Learning
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Proposes MShap, a budget-balanced, cost-agnostic payment mechanism for federated learning that pays each agent the gap between her Shapley share of total accuracy and her own accuracy, achieving reciprocal fairness and efficient Nash equilibria.
Problem
Strategic agents in federated learning free-ride at Nash equilibrium, producing unfair, low-data, and low-welfare outcomes; existing mechanisms are efficient but not reciprocally fair.
Approach
Payment p_i(s) = Shapley share of total accuracy minus agent i's own accuracy, which makes every agent's final benefit equal her Shapley contribution (full reciprocity), needs no cost information, and still admits Nash equilibria that match efficiency guarantees on data and welfare.
Key results
- MShap achieves reciprocity 1.00 on all five datasets, versus 0.47-0.93 for M0 and 0.02-0.95 for MBG.
- MShap gives data gains of 9.51x (MNIST), 13.43x (FashionMNIST), and 3.89x (CIFAR-10) over the no-payment baseline M0.
- Accuracy gain of 1.36x on the synthetic quadratic dataset and 1.02x-1.11x on the image datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MShap instead of M0 | Federated learning mechanism · MNIST | accuracy (%): 88.3 -> 90.4 | Helped |
| Use MShap instead of M0 | Federated learning mechanism · FashionMNIST | accuracy (%): 60.9 -> 63.3 | Helped |
| Use MShap instead of MBG | Federated learning mechanism · CIFAR-10 | accuracy (%): 44.7 -> 48.5 | Helped |
| Use MShap instead of M0 | Federated learning mechanism · Lumpy Skin Disease | accuracy (%): 94.2 -> 95.2 | Helped |
| Use MShap instead of M0 | Federated learning mechanism · Quadratic | accuracy (%): 67.2 -> 90.8 | Helped |
| Use MShap instead of MBG | Federated learning mechanism · MNIST | data gain: 1.32 -> 9.51 | Helped |
| Use MShap instead of MBG | Federated learning mechanism · FashionMNIST | data gain: 1.51 -> 13.43 | Helped |
| Use MShap instead of MBG | Federated learning mechanism · CIFAR-10 | data gain: 1.13 -> 3.89 | Helped |
| Use MShap instead of M0 | Federated learning mechanism · Lumpy Skin Disease | data gain: 1.00 -> 1.73 | Helped |
| Use MShap instead of MBG | Federated learning mechanism · Quadratic | data gain: 1.25 -> 31.18 | Helped |
| Use MShap instead of MBG | Federated learning mechanism · MNIST | reciprocity: 0.70 -> 1.00 | Helped |
| Use MShap instead of MBG | Federated learning mechanism · FashionMNIST | reciprocity: 0.75 -> 1.00 | Helped |
Surprising findings
- In the skin disease task, baseline NEs have agent 1 (with higher-quality data) contributing more than agent 2, whereas MShap reverses this so the lower-quality agent contributes more.
Limitations
- Shapley value computation is expensive and tractable mainly for moderate numbers of agents (cross-silo settings).
- Theoretical guarantees rely on concavity of payoffs and convexity of costs, and strong concavity for convergence.
- Experiments use closed-form fitted accuracy functions for the main NE results, with FedBR-Shap as a practical approximation.
Experimental setup
Datasets: MNIST FashionMNIST CIFAR-10 Lumpy Skin Disease dataset (Afshari Safavi, 2021) synthetic quadratic regression dataset
Benchmarks: MNIST FashionMNIST CIFAR-10 Lumpy Skin Disease synthetic quadratic regression
Metrics: average accuracy data share data gain accuracy gain reciprocity welfare
Baselines: M0 (no payments) MBG (welfare-maximizing mechanism, Murhekar et al. 2023)
Builds on: Karimireddy et al. 2022 data-sharing incentivization Murhekar et al. 2023 welfare-maximizing mechanism Shapley value
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