WassFFed: Wasserstein Fair Federated Learning

TL;DR

Wasserstein Fair Federated Learning framework is proposed, namely WassFFed, which outperforms existing approaches in striking a balance between accuracy and fairness and conducts extensive experiments on three real-world datasets.

Abstract

Federated Learning (FL) employs a training approach to address scenarios where users' data cannot be shared across clients. Achieving fairness in FL is imperative since training data in FL is inherently geographically distributed among diverse user groups. Existing research on fairness predominantly assumes access to the entire training data, making direct transfer to FL challenging. However, the limited existing research on fairness in FL does not effectively address two key challenges, i.e., (CH1) Current methods fail to deal with the inconsistency between fair optimization results obtained with surrogate functions and fair classification results. (CH2) Directly aggregating local fair models does not always yield a globally fair model due to non Identical and Independent data Distributions (non-IID) among clients. To address these challenges, we propose a Wasserstein Fair Federated Learning framework, namely WassFFed. To tackle CH1, we ensure that the outputs of local models, rather than the loss calculated with surrogate functions or classification results with a threshold, remain independent of various user groups. To resolve CH2, we employ a Wasserstein barycenter calculation of all local models' outputs for each user group, bringing local model outputs closer to the global output distribution to ensure consistency between the global model and local models. We conduct extensive experiments on three real-world datasets, demonstrating that WassFFed outperforms existing approaches in striking a balance between accuracy and fairness.

Figures (5)

• Figure 1: The samples above the horizontal solid line are predicted to be positive samples and vice versa. (a) visualizes a fair classification but is considered unfair according to the surrogate function ($male = -0.5$, $female = 0$). (b) visualizes an unfair classification model but is considered fair according to the surrogate function ($male = 0$, $female = 0$). (c) visualizes two local fair classification models that are also considered fair with the surrogate function. (d) depicts the global model derived from aggregating the two models in (c). Upon aggregation, this global model yields fair classification results; however, when evaluated with the surrogate function, it is regarded as unfair ($male = 1$, $female = 0.67$).
• Figure 2: The overall framework of WassFFed. We give an example of three clients. Firstly, in the Client Prediction stage, all clients share their parameters ($w_t$) and model outputs for various sensitive groups ($S_{1, t}^{a_1}, S_{1, t}^{a_2}, \dots, S_{3, t}^{a_{N_A}}$) with the server. Subsequently, the server employs the Wasserstein Fair model to compute transport matrices ($T_{1, t}^{a_1}, T_{1, t}^{a_2}, \dots, T_{3, t}^{a_{N_A}}$) and aggregates parameters ($w^{t+1}$). Finally, in the Client Updation stage, the server shares these results with each client. Clients calculate the fairness loss and combine it with the model utility loss to strike a balance between accuracy and fairness.
• Figure 3: The Pareto frontier of $\mathcal{M}_{EOP}$ and $\mathcal{M}_{DP}$ on Compas, Adult, and CelebA datasets. The curve closer to the upper right corner indicates a better trade-off between accuracy and fairness.
• Figure 4: This figure demonstrates the model output distributions for various sensitive groups on the Compas dataset. The results provide evidence that WassFFed successfully achieves a model whose outputs are independent of sensitive attributes.
• Figure 5: Effect of hyperparameters.

Theorems & Definitions (4)

• Definition 1: Demographic Parity (DP) dwork2012fairness
• Definition 2: Equal Opportunity (EOP) hardt2016equality
• Definition 3: Metric of Demographic Parity ($\mathcal{M}_{DP}$)
• Definition 4: Metric of Equal Opportunity ($\mathcal{M}_{EOP}$)