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Performative Federated Learning: A Solution to Model-Dependent and Heterogeneous Distribution Shifts
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Formalizes performative federated learning where clients' data shift in response to the deployed model, and proposes P-FedAvg with O(1/T) convergence to the performative stable solution under full and partial participation.
Problem
Federated learning when each client's data distribution is reshaped by the deployed decision model (model-dependent, heterogeneous distribution shifts), so standard FL converges to a biased solution.
Approach
Extends performative prediction to federated settings by modeling per-client shift mappings D_i(theta) and proposing P-FedAvg with multi-step local updates and partial participation, with convergence analysis based on a relaxed heterogeneity assumption (local gradient bound) instead of bounded gradients.
Key results
- P-FedAvg converges to the performative stable solution at O(1/T) under full, Scheme I and Scheme II partial participation.
- Scheme II converges fastest in the Gaussian mean estimation experiment, consistent with the theoretical bound B1 > B2.
- On FMNIST, the average total variation distance between consecutive aggregation steps decreases over rounds, indicating convergence to a PS solution.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use P-FedAvg with full participation | Performative FL · Performative FL | convergence rate to PS solution: O(1/T) | Helped |
| Use partial participation Scheme I | P-FedAvg · Performative FL | convergence rate to PS solution: O(1/T) | Helped |
| Use partial participation Scheme II | P-FedAvg · Performative FL | convergence rate to PS solution: O(1/T) | Helped |
| Use static FedAvg instead of accounting for performative shifts | Federated learning · Performative Gaussian mean estimation | distance to PS solution | Hurt |
| Increase the aggregation interval E | P-FedAvg · Performative Gaussian mean estimation | time to reach ε-accuracy | Mixed |
| Increase the number of participating clients K | P-FedAvg with partial participation · Performative Gaussian mean estimation | convergence time | Mixed |
| Use Scheme II rather than Scheme I with uniformly sampled clients | P-FedAvg · Performative Gaussian mean estimation | convergence rate | Helped |
| Increase K in the partial participation experiment | P-FedAvg · Performative Gaussian mean estimation | convergence time | No clear effect |
| Use P-FedAvg for performative image classification | P-FedAvg · FMNIST | total variation distance between aggregation steps | Helped |
Surprising findings
- Empirically, the three participation schemes behave very similarly and weakly depend on K, despite the full-participation scheme having the lowest theoretical upper bound.
Limitations
- Convergence requires the average sensitivity to satisfy epsilon < mu/L, so strong distribution shifts can break the guarantee.
- Assumptions such as strong convexity of the averaged objective and smoothness restrict applicability to deep models.
- Image experiments are empirical only without convergence guarantees for the non-convex setting.
Experimental setup
Datasets: Kaggle GiveMeSomeCredit FMNIST CIFAR-10 synthetic Gaussian
Benchmarks: FMNIST CIFAR-10 GiveMeSomeCredit
Metrics: distance to performative stable solution loss total variation distance between aggregation steps
Baselines: static FedAvg multi-agent performative prediction (Li, Yau, and Wai 2022) performative SGD
Builds on: performative prediction (Perdomo et al. 2020) FedAvg multi-agent performative prediction (Li, Yau, and Wai 2022)
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