DP-based Fair Classification in Heterogeneous Federated Learning

Table of Links

Abstract and 1 Introduction

2 Related Works

3 Preliminaries

3.1 Fair Supervised Learning and 3.2 Fairness Criteria

3.3 Dependence Measures for Fair Supervised Learning

4 Inductive Biases of DP-based Fair Supervised Learning

4.1 Extending the Theoretical Results to Randomized Prediction Rule

5 A Distributionally Robust Optimization Approach to DP-based Fair Learning

6 Numerical Results

6.1 Experimental Setup

6.2 Inductive Biases of Models trained in DP-based Fair Learning

6.3 DP-based Fair Classification in Heterogeneous Federated Learning

7 Conclusion and References

Appendix A Proofs

Appendix B Additional Results for Image Dataset

6.3 DP-based Fair Classification in Heterogeneous Federated Learning

To numerically show the implications of the inductive biases of DP-based fair learning algorithms, we simulated a heterogeneous federated learning setting with multiple clients where the sensitive attribute has different distributions across clients. To do this, we split the Adult dataset into 4 subsets of 3k samples to be distributed among 4 clients in the federated learning. While 80% of the training data in Client 1 (minority subgroup in the network) had Female as sensitive attribute, only 20% of Clients 2-4 were female samples. We used the same male/female data proportion to assign 750 test samples to the clients.

For the baseline federated learning method with no fairness regularization, we utilized the FedAvg algorithm [29]. For the DP-based fair federated learning algorithms, we attempted the DDP-based KDE and FACL algorithms which result in single-level optimization problem and hence can be optimized in a distributed learning problem by averaging as in FedAvg. We refer to the extended federated learning version of these algorithms as FedKDE and FedFACL. We also tested our SA-DRO implementations of FedKDE and FedFACL, as well as the localized ERM, KDE, FACL models where each client trained a separate model only on her own data.

As our numerical results in Table 2 and Table 3 indicate, the inductive biases of DP-based federated learning could considerably lower the accuracy of Client 1 with a different majority sensitive attribute compared to the other clients. The accuracy drop led to a lower accuracy compared to Client 1’s locally fair trained model without any collaboration with the other clients, which may affect the client’s incentive to participate in the federated learning process. On the other hand, the SA-DRO implementations of the KDE and FACL methods achieved a better accuracy than Client 1’s local model while preserving the accuracy for the majority clients.