Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Related Works 2 Related Works 3 Preliminaries 3.1 Fair Supervised Learning and 3.2 Fairness Criteria 3.1 Fair Supervised Learning and 3.2 Fairness Criteria 3.3 Dependence Measures for Fair Supervised Learning 3.3 Dependence Measures for Fair Supervised Learning 4 Inductive Biases of DP-based Fair Supervised Learning 4 Inductive Biases of DP-based Fair Supervised Learning 4.1 Extending the Theoretical Results to Randomized Prediction Rule 4.1 Extending the Theoretical Results to Randomized Prediction Rule 5 A Distributionally Robust Optimization Approach to DP-based Fair Learning 5 A Distributionally Robust Optimization Approach to DP-based Fair Learning 6 Numerical Results 6.1 Experimental Setup 6.1 Experimental Setup 6.2 Inductive Biases of Models trained in DP-based Fair Learning 6.2 Inductive Biases of Models trained in DP-based Fair Learning 6.3 DP-based Fair Classification in Heterogeneous Federated Learning 6.3 DP-based Fair Classification in Heterogeneous Federated Learning 7 Conclusion and References 7 Conclusion and References Appendix A Proofs Appendix A Proofs Appendix B Additional Results for Image Dataset Appendix B Additional Results for Image Dataset 6.2 Inductive Biases of Models trained in DP-based Fair Learning DRO-based Fair Learning. We tested Algorithm 1 utilizing a sensitive attribute-based distributional robust optimization (SA-DRO) to DP-based fair learning algorithms. In our experiments, we applied the SA-DRO algorithm to the DDP-based KDE fair learning algorithm proposed by [11], and RFI proposed by [13]. We kept the fairness regularization penalty coefficient to be λ = 0.9. The DRO regularization coefficient can take over the range [0, 1], in this table, we set ϵ = 0.9 for SA-DRO case. In these figures 4, we applied the SA-DRO algorithm to the DDP-based KDE fair learning algorithm by [11], and RFI by [13]. We kept the fairness regularization penalty coefficient to be λ = 0.9. The DRO regularization coefficient can take over the range [0, 1]. DRO-based Fair Learning. As Table 1 shows, we observed that the proposed SA-DRO reduces the tendency of the fair learning algorithm toward the majority sensitive attribute, and the resulting negative prediction rates conditioned to sensitive attribute outcomes became closer to the midpoint between the majority and minority conditional accuracies. On the other hand, the SA-DRO-based algorithms still achieve a low DDP value while the accuracy drop is less than 1%. Moreover, we visualize the prediction shifting in Figure 4 by applying the SA-DRO algorithm to the DDP-based KDE fair learning algorithm by [11], and RFI by [13]. We kept the fairness regularization penalty coefficient to be λ = 0.9. The DRO regularization coefficient takes over the range [0, 1]. 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. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv Authors:
(1) Haoyu LEI, Department of Computer Science and Engineering, The Chinese University of Hong Kong (hylei22@cse.cuhk.edu.hk);
(2) Amin Gohari, Department of Information Engineering, The Chinese University of Hong Kong (agohari@ie.cuhk.edu.hk);
(3) Farzan Farnia, Department of Computer Science and Engineering, The Chinese University of Hong Kong (farnia@cse.cuhk.edu.hk). Authors: Authors: (1) Haoyu LEI, Department of Computer Science and Engineering, The Chinese University of Hong Kong (hylei22@cse.cuhk.edu.hk); (2) Amin Gohari, Department of Information Engineering, The Chinese University of Hong Kong (agohari@ie.cuhk.edu.hk); (3) Farzan Farnia, Department of Computer Science and Engineering, The Chinese University of Hong Kong (farnia@cse.cuhk.edu.hk).

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