# fairfed_enabling_group_fairness_in_federated_learning__c2b65d7f.pdf

Fair Fed: Enabling Group Fairness in Federated Learning

Yahya H. Ezzeldin*, Shen Yan*, Chaoyang He, Emilio Ferrara, Salman Avestimehr

University of Southern California (USC) yessa@usc.edu, shenyan@usc.edu, chaoyang.he@usc.edu, emiliofe@usc.edu, avestime@usc.edu

Training ML models which are fair across different demographic groups is of critical importance due to the increased integration of ML in crucial decision-making scenarios such as healthcare and recruitment. Federated learning has been viewed as a promising solution for collaboratively training machine learning models among multiple parties while maintaining their local data privacy. However, federated learning also poses new challenges in mitigating the potential bias against certain populations (e.g., demographic groups), as this typically requires centralized access to the sensitive information (e.g., race, gender) of each datapoint. Motivated by the importance and challenges of group fairness in federated learning, in this work, we propose Fair Fed, a novel algorithm for fairness-aware aggregation to enhance group fairness in federated learning. Our proposed approach is server-side and agnostic to the applied local debiasing thus allowing for flexible use of different local debiasing methods across clients. We evaluate Fair Fed empirically versus common baselines for fair ML and federated learning and demonstrate that it provides fairer models, particularly under highly heterogeneous data distributions across clients. We also demonstrate the benefits of Fair Fed in scenarios involving naturally distributed real-life data collected from different geographical locations or departments within an organization.

Introduction An important notion of fairness in machine learning, group fairness (Dwork et al. 2012), concerns the mitigation of bias in the performance of a trained model against certain protected demographic groups, which are defined based on sensitive attributes within the population (e.g., gender, race). Several approaches to achieve group fairness have been studied in recent years in centralized settings. However, these approaches rely on the availability of the entire dataset at a central entity during training and are therefore unsuitable for application in Federated Learning (FL). Federated learning allows for decentralized training of large-scale models without requiring direct access to clients data, hence maintaining their privacy (Kairouz et al. 2021; Wang et al. 2021a). However, this decentralized nature makes it complicated to translate solutions for fair training

*These authors contributed equally. Copyright 2023, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.

More heterogeneous More heterogeneous

Fed Avg Local Reweighting Global Reweighting

Figure 1: Comparison of local/global debiasing under different heterogeneity levels. For the Equal Opportunity Difference (EOD) metric, values close to 0 indicate better fairness.

from centralized settings to FL, where the decentralization of data is a major cornerstone. This gives rise to the key question that we attempt to answer in this paper: How can we train a classifier using FL so as to achieve group fairness, while maintaining data decentralization?

Potential approaches for group fairness in FL. One potential solution that one may consider for training fair models in FL is for each client to apply local debiasing on its locally trained models (without sharing any additional information or data), while the FL server simply aggregates the model parameters in each round using FL aggregation algorithms such as Fed Avg (Mc Mahan et al. 2017) (or its subsequent derivatives, e.g., Fed OPT (Reddi et al. 2020), Fed Nova (Wang et al. 2020)). Although this allows for training a global model without explicitly sharing the local datasets, but the drawback is that applying a debiasing mechanism at each client in isolation on its local dataset can results in poor performance in scenarios where data distributions are highly-heterogeneous across clients (See Figure 1). Another potential solution for fair training in FL would be to adapt a debiasing technique from the rich literature of centralized fair training to be used in FL. Although this may result in reasonable fair training (see Figure 1), however, in the process of applying this debiasing globally, the clients may need to exchange additional detailed information with the server about their dataset constitution which can leak information about different subgroups in the client s dataset. For example, the server may require knowledge of the model s performance on each group in a client s dataset and/or local statistical information about each group in the dataset.

The Thirty-Seventh AAAI Conference on Artificial Intelligence (AAAI-23)

clients in FL have private data from

Fair Fed: group fairness aware aggregation

central server (aggregation)

model performance is unfair to unprivileged group

group fairness aware accuracy is achieved

diverse groups (race, sex, etc.)

Figure 2: Fair Fed: Group fairness-aware FL framework.

The Proposed Fair Fed Approach. Motivated by the drawbacks of the two aforementioned directions, in this work, we propose Fair Fed, a strategy to train fair models via a fairness-aware aggregation method (Figure 2). In Fair Fed, each client performs local debiasing on its own local dataset, thus maintaining data decentralization and avoiding the exchange of any explicit information of its local data composition. To amplify the local debiasing performance, the clients will evaluate the fairness of the global model on their local datasets in each FL round and collectively collaborate with the server to adjust its model aggregation weights. The weights are a function of the mismatch between the global fairness measurement (on the full dataset) and the local fairness measurement at each client, favoring clients whose local measures match the global measure. We carefully design the exchange between the server and clients during weights computation, making use of the secure aggregation protocol (Bonawitz et al. 2017) to prevent the server from learning any explicit information about any single client s dataset. The server-side/local debiasing nature of Fair Fed gives it the following benefits over existing fair FL strategies: Enhancing group fairness under data heterogeneity: One of the biggest challenges to group fairness in FL is the heterogeneity of data distributions across clients, which limits the impact of local debiasing efforts on the global data distribution. Fair Fed shows significant improvement in fairness performance under highly heterogeneous distribution settings and outperforms state-ofthe-art methods for fairness in FL, indicating promising implications from applying it to real-life applications. Freedom for different debiasing across clients: As Fair Fed works at the server side and only requires evaluation metrics of the model fairness from the clients, it is more flexible to run on top of heterogeneous client debiasing strategies (we expand on this notion in Sections ). For example, different clients can adopt different local debiasing methods based on the properties (or limitations) of their devices and data partitions.

Background and Related Work Group fairness in centralized learning. In classical centralized ML, common approaches for realizing group fairness can be classified into three categories: pre-processing (Grgi c-Hlaˇca et al. 2018; Feldman et al. 2015), in-processing (Kamishima et al. 2012; Zhang, Lemoine, and Mitchell 2018; Roh et al. 2021) and post-processing (Lohia et al. 2019; Kim, Ghorbani, and Zou 2019) techniques. However,

a majority of these techniques need centralized access to the sensitive information (e.g., race) of each datapoint, making it unsuitable for FL. As a result developing effective approaches for fair FL is an important area of study.

Fairness in federated learning. New challenges in FL have introduced different notions of fairness. These new notions include for example, client-based fairness (Li et al. 2019; Mohri, Sivek, and Suresh 2019) which aims to equalize model performance across different clients or collaborative fairness (Lyu et al. 2020; Wang et al. 2021b) which aims to reward a highly-contributing participant with a better performing local model than is given to a low-contributing participant. In this paper, we instead focus on the notion of group fairness in FL, where each datapoint in the FL system belongs to particular group, and we aim to train models that do not discriminate against any group of datapoints. Several recent works have made progress on group fairness in FL. One common research direction is to distributively solve an optimization objective with fairness constraints (Zhang, Kou, and Wang 2020; Du et al. 2021; G alvez et al. 2021), which requires each client to share the statistics of the sensitive attributes of its local dataset to the server. The authors in (Abay et al. 2020) investigated the effectiveness of adopting a global reweighting mechanism. In (Zeng, Chen, and Lee 2021), an adaptation of the Fair Batch debiasing algorithm (Roh et al. 2021) is proposed for FL where clients use Fair Batch locally and the weights are updated through the server in each round. In (Papadaki et al. 2021), an algorithm is proposed to achieve minimax fairness in federated learning. In these works, the server requires each client to explicitly share the performance of the model on each subgroup separately; for example (males with +ve outcomes, females with +ve outcomes, etc). Differently from these works, our proposed Fair Fed method does not restrict the local debiasing strategy of the participating clients, thus increasing the flexibility of the system. Furthermore, Fair Fed does not share explicit information on the model performance for any specific group within a client s dataset. Finally, our empirical evaluations consider extreme cases of data heterogeneity and demonstrate that our method can yield significant fairness improvements in these situations.

Preliminaries We begin by reviewing the standard FL setup (Mc Mahan et al. 2017), and then introduce key definitions and metrics for group fairness. We then extend these to the FL setting by defining the notions of global and local fairness in FL.

Federated Learning Setup Following a standard FL setting (Mc Mahan et al. 2017), we consider a scenario where K clients collaborate with a server to find a parameter vector θ that minimizes the weighted average of the loss across all clients. In particular:

min θ f(θ) =

k=1 ωk Lk(θ), (1)

where: Lk(θ) denotes the local objective at client k; ωk 0, and P ωk = 1. The local objective Lk s can be defined by empirical risks over the local dataset Dk of size nk at client k, i.e., Lk(θ) = 1 nk P (x,y) Dk ℓ(θ, x, y). To minimize the objective in (1), the federated averaging algorithm Fed Avg, proposed in (Mc Mahan et al. 2017), samples a subset of the K clients per round to perform local training of the global model on their local datasets. The model updates are then averaged at the server, being weighted based on the size of their respective datasets. To ensure the server does not learn any information about the values of the individual transmitted updates from the clients beyond the aggregated value that it sets out to compute, Fed Avg typically employs a Secure Aggregation (Sec Agg) algorithm (Bonawitz et al. 2017). Training using Fed Avg and its subsequent improvements (e.g., Fed OPT (Reddi et al. 2020)) allows training of a highperformance global model, however, this collaborative training can result in a global model that discriminates against an underlying demographic group of datapoints (similar to biases incurred in centralized training of machine learning models (Dwork et al. 2012)). We highlight key notions of group fairness in fair ML in the following subsection.

Notions of Group Fairness In sensitive machine learning applications, a data sample often contains private and sensitive demographic information that can lead to discrimination. In particular, we assume that each datapoint is associated with a sensitive binary attribute A (e.g., gender or race). For a binary prediction model ˆY (θ, x), the fairness is evaluated with respect to its performance compared to the underlying groups defined by the sensitive attribute A. We use A = 1 to represent the privileged group (e.g., male), while A = 0 is used to represent the under-privileged group (e.g., female). For the binary model output ˆY (and similarly the label Y ), ˆY = 1 is assumed to be the positive outcome. Using these definitions, we can now define two group fairness notions that are applied in group fairness literature for centralized training: Definition 1 (Equal Opportunity) : Equal opportunity (Hardt et al. 2016) measures the performance a binary predictor ˆY with respect to A and Y . The predictor is considered fair from the equal opportunity perspective if the true positive rate is independent of the sensitive attribute A. To measure this, we use the Equal Opportunity Difference (EOD), defined as

EOD= Pr( ˆY =1|A=0,Y =1) Pr( ˆY =1|A=1,Y =1). (2)

Definition 2 (Statistical Parity) : Statistical parity (Dwork et al. 2012) rewards the classifier for classifying each group

as positive at the same rate. Thus, a binary predictor ˆY is fair from the statistical parity perspective if Pr( ˆY = 1|A = 1) = Pr( ˆY = 1|A = 0). Thus, the Statistical Parity Difference (SPD) metric is defined as

SPD = Pr( ˆY = 1|A = 0) Pr( ˆY = 1|A = 1). (3)

For the EOD and SPD metrics, values closer to zero indicate better fairness. Positive fairness metrics indicate that the unprivileged group outperform the privileged group.

Global vs Local Group Fairness in FL The fairness definitions above can be readily applied to centralized model training to evaluate the performance of the trained model. However, in FL, clients typically have non IID data distributions, which gives rise to different levels of consideration for fairness: global fairness and local fairness. The global fairness of a given model considers the full dataset D = k Dk across the K clients in FL, which is our end-goal in fair FL; to train a model that is in general nondiscriminatory to any group in the global dataset. In contrast, when only the local dataset Dk at client k is considered, we can define the local fairness performance by applying (2) or (3) on the data distribution at client k. We can highlight the difference between global and local fairness using the example of the EOD metric. For a classifier ˆY , the global fairness EOD metric Fglobal is given by

Fglobal= Pr( ˆY =1|A=0,Y =1) Pr( ˆY =1|A=1,Y =1), (4)

where the probability above is based on the full dataset distribution (a mixture of the distributions across the clients). In contrast, the local fairness metric Fk at client k is

Fk = Pr( ˆY =1|A=g, Y =1, C =k)

Pr( ˆY =1|A=g, Y =1, C =k), (5)

where the parameter C = k denotes that the k-th client (and dataset Dk) is considered in the fairness evaluation. Note that if clients have IID distributions (i.e., distributions that are independent of C), global and local fairness match. However, they can greatly differ in the non-IID case.

Fair Fed: Fairness-Aware Aggregation in FL In this section, we introduce our proposed approach Fair Fed which uses local debiasing due for its advantages for data decentralization, while addressing its challenges by adjusting how the server aggregates local model updates from clients.

Our Proposed Approach (Fair Fed) Recall that in the t-th round in Fed Avg (Mc Mahan et al. 2017), local model updates {θt k}K k=1 are weight-averaged to get the new global model parameter θt as: θt+1 = PK k=1 ωt k θt k, where the weights ωt k = nk/ P k nk depend only on the number of datapoints at each client. As a result, a fairness-oblivious aggregation would favor clients with more datapoints. If the training at these clients results in locally biased models, then the global model can potentially be biased since the weighted averaging exaggerates the contribution of model update from these clients.

Algorithm 1: Fair Fed Algorithm (tracking EOD)

Initialize: global model parameter θ0 and weights {ω0 k} as ω0 k = nk/ PK i=1 ni, k [K]; Dataset statistics: Aggregate statistics S ={ Pr(A=1, Y =1), Pr(A=0, Y =1)} from clients using Secure Aggregation (Sec Agg) and send it to clients; for each round t = 1, 2, do

F t global , Acct Sec Agg Client Local Metrics k, θt 1 K k=1

; // Sec Agg to get Acct and global fairness F t global as in (7);

i i Sec Agg Client Metric Gap k, θt 1, F t global, Acct K

; // Sec Agg to compute mean of metric gaps;

// Compute aggregation weights locally at clients based on (6) then use Sec Agg to aggregate weighted local model updates; PK k=1 ωt kθt k , PK k=1 ωt k Sec Agg Client Weighted Model Update k, θt 1, ωt k, 1

θt+1 PK k=1 ωt kθt k / PK k=1 ωt k ;

Based on this observation, in Fair Fed, we propose a method to optimize global group fairness Fglobal via adaptively adjusting the aggregation weights of different clients based on their local fairness metric Fk. In particular, given the current global fairness metric F t global (we will discuss later in the section, how the server can compute this value), then in the next round, the server gives a slightly higher weight to clients that have a similar local fairness F t k to the global fairness metric, thus relying on their local debiasing to steer the next model update towards a fair global model. Next, we detail how Fair Fed computes the aggregation weights in each round. The steps performed while tracking the EOD metric in Fair Fed are shown in Algorithm 1.

Computing Aggregation Weights for Fair Fed At the beginning of training, we start with the default Fed Avg weights ω0 k = nk/ PK k=1 nk. Next, in each round t, we update the weight assigned to the k-th client based on the current gap between its local fairness metric F t k and the global fairness metric Fglobal. In particular, the weight update follows this formula k [K]:

( Acct k Acct if F t k is undefined,

|F t global F t k| otherwise ,

ωt k= ωt 1 k β

, ωt k = ωt k PK i=1 ωt i . (6)

where: (i) Acct k represents the local accuracy at client k, and Acct = PK k=1 Acck nk/ PK k=1 nk, is global accuracy across the full dataset, respectively; (ii) β is a parameter that controls the fairness budget for each update, thus impacting the trade-off between model accuracy and fairness. Higher values of β result in fairness metrics having a higher impact on the model optimization, while a lower β results in a reduced perturbation to the default Fed Avg weights due to fair training; note that at β = 0, Fair Fed is equivalent to Fed Avg, as the initial weights ω0 k are unchanged.

Intuition for weight update. The intuition behind the update in (6) is to effectively rank the clients in the FL system based on how far their local view of fairness (measured through their local metric) compares to the global fairness

metric; closer views to the global metric get assigned higher weights while clients with local metrics that significantly deviate from the global metric will have their weights reduced. The significance is decided based on whether the gap from the global metric is above the average gap (across clients) or vice versa. Note that, whenever, the client distribution makes the local metric Fk undefined1, Fair Fed relies on the discrepancy between the local and global accuracy metric as a proxy to compute the fairness metric gap k. Thus, so far, the training process of Fair Fed at each iteration follows the following conceptual steps:

1. Each client computes its updated local model parameters; 2. The server computes the global fairness metric value F t global and global accuracy Acct using secure aggregation and broadcasts them back to the clients; 3. Each client computes its metric gap t k and from it, it calculates its aggregation weight ωt k with the help of the server as defined in (6); 4. The server next aggregates the weighted local updates ωt kθt k using secure aggregation to compute the new global model and broadcasts it to the clients.

A detailed description on performing these steps using secure aggregation (Sec Agg) is shown in Algorithm 1, where Sec Agg({bi}K i=1) computes P i bi using secure aggregation.

Flexibility of Fair Fed with heterogeneous debiasing. Note that the Fair Fed weights ωt k in (6) rely only on the global and local fairness metrics and are not tuned towards a specific local debiasing method. Thus, Fair Fed is flexible to be applied with different debiasing methods at each client, and the server will incorporate the effects of these different methods by reweighting their respective clients based on their local/global metrics and the weight computation in (6).

How the Server Gets the Global Metric Fglobal One central ingredient for computing weights in Fair Fed is the server s ability to calculate the global metric Fglobal in each round (recall equation (6)) without the clients having to share their datasets with the server or any explicit information about their local group distribution. If the metric of

1For instance, in the case of the EOD metric, this happens whenever Pr(A = 1, Y = 1) = 0 or Pr(A = 0, Y = 1) = 0.

interest is EOD, we next show how the server can compute Fglobal from the clients using secure aggregation. Similar computations follow for SPD and are presented in (Ezzeldin et al. 2021, Appendix A). Let n = PK k=1 nk; the EOD metric in (4) can be rewritten as:

Fglobal =Pr( ˆY =1|A=0, Y =1) Pr( ˆY =1|A=1,Y =1)

Pr( ˆY =1|A=0,Y =1,C=k) Pr(A=0,Y =1|C=k)

Pr(Y =1,A=0)

Pr( ˆY =1|A=1,Y =1,C=k) Pr(A=1,Y =1|C=k)

Pr(Y =1,A=1)

| {z } mglobal,k

where mglobal,k is the summation component that each client k computes locally. Thus, the global EOD metric Fglobal can be computed at the server by applying secure aggregation (Bonawitz et al. 2017) to get the sum of the mglobal,k values from the K clients without the server learning any information about the individual mglobal,k values. Note that the conditional probabilities defining mglobal,k in (7) are all local performance metrics that can easily be computed locally by client k using its local dataset Dk. The only non-local terms in mglobal,k are the full dataset statistics S = {Pr(Y =1, A=0), Pr(Y =1, A=1)}. These statistics S can be aggregated at the server using a single round of secure aggregation (e.g., (Bonawitz et al. 2017)) at the start of training, then be shared with the clients to enable them to compute their global fairness component mglobal,k.

Experimental Evaluation In this section, we investigate the performance of Fair Fed under different system settings. In particular, we explore how the performance changes with different heterogeneity levels in data distributions across clients. We also evaluate how the trade-off between fairness and accuracy changes with the fairness budget β in Fair Fed (see equation (6)). Additional experiments in (Ezzeldin et al. 2021, Appendix C) investigate how the performance of Fair Fed changes when different local debiasing approaches are used across clients.

Experimental Setup Implementation. We developed Fair Fed using Fed ML (He et al. 2020), which is a research-friendly FL library for exploring new algorithms. We use a server with AMD EPYC 7502 32-Core CPU Processor, and use a parallel training paradigm, where each client is handled by an independent process using MPI (message passing interface).

Datasets. In this section, we demonstrate the performance of different debiasing methods using two binary decision datasets that are widely investigated in fairness literature: the Adult (Dua and Graff 2017) dataset and Pro Publica COMPAS dataset (Larson et al. 2016). In the Adult dataset (Dua and Graff 2017), we predict the yearly income (with binary label: over or under $50,000) using twelve categorical or continuous features. The gender (defined as male or female) of each subject is considered the sensitive attribute. The

Pro Publica COMPAS dataset relates to recidivism, which is to assess if a criminal defendant will commit an offense within a certain future time. Features in this dataset include the number of prior offenses, the age of the defendant, etc. The race (classified as white or non-white) of the defendant is the sensitive attribute of interest.

Configurable data heterogeneity for diverse sensitive attribute distributions. To understand the performance of our method and the baselines, under different distributions of the sensitive attribute across clients, a configurable data synthesis method is needed. In our context, we use a generic non-IID synthesis method based on the Dirichlet distribution proposed in (Hsu, Qi, and Brown 2019) but apply it in a novel way for configurable sensitive attribute distribution: for each sensitive attribute value a, we sample pa Dir(α) and allocate a portion pa,k of the datapoints with A = a to client k. The heterogeneity across clients is controlled via α, where α results in IID distributions. Examples of these heterogeneous distributions for the Adult and COMPAS are shown in (Ezzeldin et al. 2021, Appendix B).

Baselines. We adopt the following state-of-the-art solutions as baselines:

Fed Avg (Mc Mahan et al. 2017): the original FL algorithm for distributed training of private data. It does not consider fairness for different demographic groups.

Fed Avg + Local reweighting [Local / RW]: Each client adopts the reweighting strategy (Kamiran and Calders 2012) to debias its local training data, then trains local models based on the pre-processed data. Fed Avg is used to aggregate the local model updates at the server.

Fed Avg + Fair Batch [Local / Fair Batch]: Each client adopts the state-of-the-art Fair Batch in-processing debiasing strategy (Roh et al. 2021) to debias its local training data and then aggregation uses Fed Avg.

Fed Avg + Fair Linear Representation [Local / Fair Rep]: Each client adopts the Fair Linear Representations pre-processing debiasing strategy (He, Burghardt, and Lerman 2020) locally and aggregates using Fed Avg.

Fed Avg + Global reweighting [Global RW] (Abay et al. 2020): A differential-privacy approach to collect noisy statistics such as the number of samples with privileged attribute values (A=1) and favorable labels (Y =1) from clients. Server computes global weights based on the collected statistics and shares them with the clients, which assign them to their data samples during FL training 2.

Fed FB (Zeng, Chen, and Lee 2021): An in-processing debiasing approach in FL based on Fair Batch (Roh et al. 2021). The server computes new weights for each group based on information from the clients in each round and broadcasts them back to the clients. For fair comparison, we use Fed FB that is optimized w.r.t EOD as in Fair Fed.

2We apply the global reweighting approach in (Abay et al. 2020) without differential-privacy noise in order to compare with the optimal debiasing performance of global reweighting.

Adult (β = 1) COMPAS (β = 1) Heterogeneity Level α Heterogeneity Level α 0.1 0.2 0.5 10 5000 0.1 0.2 0.5 10 5000

Fed Avg 0.835 0.836 0.835 0.836 0.837 0.674 0.673 0.675 0.674 0.675 Local / [Best] 0.831 0.833 0.834 0.831 0.829 0.666 0.659 0.665 0.663 0.664 Global RW 0.834 0.833 0.831 0.829 0.829 0.673 0.671 0.672 0.676 0.675 Fed FB 0.825 0.825 0.829 0.832 0.832 0.674 0.673 0.675 0.677 0.677 Fair Fed / RW 0.830 0.834 0.832 0.829 0.829 0.672 0.670 0.669 0.669 0.673 Fair Fed / Fair Rep 0.824 0.833 0.834 0.834 0.834 0.661 0.655 0.663 0.663 0.660 Fair Fed / Fair Batch 0.829 0.833 0.830 0.830 0.831 0.659 0.664 0.665 0.661 0.661

Fed Avg -0.174 -0.173 -0.176 -0.179 -0.180 -0.065 -0.071 -0.067 -0.076 -0.078 Local / [Best] 0.052 -0.009 -0.006 -0.013 0.014 -0.055 -0.051 -0.054 -0.038 -0.035 Global RW -0.030 0.019 0.022 0.017 0.010 -0.060 -0.065 -0.066 -0.076 -0.077 Fed FB -0.019 0.015 0.015 -0.012 -0.012 -0.062 -0.061 -0.063 -0.077 -0.072 Fair Fed / RW -0.017 0.001 0.018 0.016 0.013 -0.057 -0.065 -0.053 -0.067 -0.061 Fair Fed / Fair Rep 0.023 -0.009 -0.071 -0.174 -0.187 0.037 0.023 0.043 0.046 0.039 Fair Fed / Fair Batch -0.020 0.001 0.000 -0.005 -0.004 -0.048 -0.048 -0.049 -0.035 -0.031

Table 1: Performance comparison under different heterogeneity levels α. Smaller α indicates more heterogeneous client distributions. We report the average of 20 random seeds. For EOD, values closer to zero indicate better fairness. For brevity, we report the values achieved by the best local debiasing baseline (without Fair Fed) as Local / [Best] in the table. An extended version of this table is reported in (Ezzeldin et al. 2021, Appendix C).

0.01 0.05 0.1 1.0 2.0 5.0 0.15

Fairness Metrics

EOD SPD Accuracy

Figure 3: Effects of fairness budget β for 5 clients and heterogeneity α = 0.2 on Fair Fed with local reweighting.

Experimental Results Performance under heterogeneous sensitive attribute distributions. We compared the performance of Fair Fed when used with three local debiasing methods (reweighting, Fair Rep (He, Burghardt, and Lerman 2020) and Fair Batch (Roh et al. 2021)) against the baselines described in the previous subsection, under different heterogeneity levels. The results are summarized in Table 1. Fair Fed outperforms the baselines at different heterogeneity levels, but at highly homogeneous data distributions (i.e., a large α value), Fair Fed does not provide significant gains in fairness performance compared to local debiasing methods (except when using Fair Batch). This is due to the fact that under homogeneous sampling, the distributions of the local datasets are statistically similar (and reflect the original distribution with enough samples), resulting in similar debiasing effect being applied across all clients when using the pre-processing methods (reweighting and Fair Rep). For a higher level of heterogeneity (i.e., at lower α = 0.1), Fair Fed can improve EOD in Adult and COMPAS data by

93% and 50%, respectively. This is done at the expense of only a 0.3% decrease in accuracy for both Adult and COMPAS datasets. In contrast, at the same heterogeneity level, local strategies can only improve EOD by 65% and 15% for Adult and COMPAS datasets, respectively. Global reweighting only improves EOD by 73% and 2% for Adult and COMPAS datasets, respectively. On average, across different heterogeneity levels, improving EOD by 87% and 1.5% for Adult and COMPAS, respectively, at α = 0.1. Note, however, that Fed FB requires the clients to share explicit information about the performance of the model on each local subgroup in order to update the weights in Fari Batch (Zeng, Chen, and Lee 2021), which can potentially leak information about the clients local datasets.

Performance with different fairness budgets (β). In Fair Fed, we introduced a fairness budget parameter β, which controls how much the aggregation weights can change due to fairness adaptation at the server in each round (refer to (6) for the explanation of β). Figure 3 shows the effects of β using heterogeneity level α = 0.2. As the value of β increases, the fairness constraint has a bigger impact on the aggregation weights, yielding better fairness (EOD closer to zero) at the cost of a decrease in model accuracy.

Cases Studies for Fair Training in FL In the previous section, we evaluated Fair Fed on heterogeneous distributions synthesized from standard benchmark datasets in fair ML. In order to validate the effectiveness of Fair Fed in FL scenarios with naturally heterogeneous distributions, we consider two FL case studies in this section.

Case Study 1: Predicting Individual Income from US Census across States In this case study, we use the US Census data to present the performance of our Fair Fed approach in a distributed learn-

ing application with a natural data partitioning. Our experiments are performed on the ACSIncome dataset (Ding et al. 2021) with the task of predicting whether an individual s income is above $50,000 (or not) based on the features collected during the Census which include employment type, education, martial status, etc.

Race Distribution (% White) by State

Data Size by State

50k 150k 100k 0.6

Figure 4: Demographic distribution of ACSIncome dataset.

Data Distribution. ACSIncome dataset is constructed from American Community Survey (ACS) Public Use Microdata Sample (PUMS) over all 50 states and Puerto Rico in 2018 with a total of 1,664,500 datapoints. In our experiments, we treat each state as one participant in the FL system (i.e., 51 participants). Due to the demographic distribution of different states, clients share different data sizes and sensitive attributes distribution. For example, Wyoming has the smallest dataset size with 3,064 users compared to California that has 195,665 users. We choose the race information (white/non-white) of the users as the sensitive attribute of interest in our experiments. Hawaii is the state with the lowest ratio (26%) of white population. , while Vermont has the highest ratio (96%) of its dataset as white population. Figure 4 provides a visualization for the data distributions across the different states.

Performance of Fair Fed. Table 3 compares the performance of Fair Fed on ACSIncome dataset. Table 3 shows that adopting local reweighting yields worse group fairness performance than simply applying Fed Avg (without any debiasing) due to the heterogeneity across states. Fair Fed with reweighting overcomes this issue and improves the EOD by 20% (-0.062 to -0.050).

Case Study 2: Predicting Daily Stress Level from Wearable Sensor Signals

In this case study, we use the human behavior dataset TILES (Mundnich et al. 2020). Tracking Individual Performance with Sensors (TILES) is a 10 weeks longitudinal study with hospital worker volunteers in a large Los Angeles hospital, where 30% of the participants are male and 70% are female. We use this dataset to estimate users daily stress levels based on physiological and physical activity signals collected through wearable sensors (e.g., Fitbit) . The target is a binary label indicating whether the person s stress level is above individual average (i.e., 1) or not (i.e., 0), which are collected from daily surveys sent to the participants phones.

Client Size Gender Stress F M y = 0 y = 1 RN-day shift 707 82% 18% 45% 55% RN-night shift 609 77% 23% 57% 43% CNA 244 61% 39% 65% 35%

Table 2: Data distribution of TILES dataset.

Method ACSIncome TILES Acc. EOD SPD Acc. EOD SPD Fed Avg 0.800 -0.062 -0.102 0.567 -0.199 -0.166 Local / RW 0.800 -0.066 -0.106 0.567 -0.064 -0.041 Fair Fed / RW 0.799 -0.050 -0.089 0.556 0.004 0.004

Table 3: Performance on ACSIncome and TILES datasets.

Data Distribution. We focus on the nurse population in the dataset. Each client represents the data from one occupation group day-shift registered nurse (RNday shift), night-shift registered nurse (RN-night shift), and certified nursing assistant (CNA). The three clients vary by data size, the distributions of gender (the sensitive attribute) and target stress variable. In general, the client of day-shift registered nurse population has the most datapoints, more female, and higher stress levels. The detailed data distribution of each clients is shown in Table 2.

Performance of Fair Fed. Table 3 reports the performance on TILES dataset. Both Fair Fed and local reweighting improve the EOD metric as compared to Fed Avg. Fair Fed improves EOD from -0.199 to 0.004 with only 2.6% accuracy decrease (from 0.567 to 0.556).

Conclusion and Future Works

In this work, motivated by the importance and challenges of group fairness in federated learning, we propose the Fair Fed algorithm to enhance group fairness via a fairness-aware aggregation method, aiming to provide fair model performance across different sensitive groups (e.g., racial, gender groups) while maintaining high utility. Though our proposed method outperforms the state-of-the-art fair federated learning frameworks under high data heterogeneity, limitations still exist. As such, we plan to further improve Fair Fed from these perspectives: 1) We report the empirical results on binary classification tasks in this work. We will extend the work to various application scenarios (e.g., regression tasks, NLP tasks); 2) We will extend our study to scenarios of heterogeneous application of different local debiasing methods and understand how the framework can be tuned to incorporate updates from these different debiasing schemes; 3) We focused on group fairness in FL, but we plan to integrate Fair Fed with other fairness notions in FL, such as collaborative fairness and client-based fairness. We give an example of how Fair Fed can provide both group-fairness and clientbased fairness in (Ezzeldin et al. 2021, Appendix D), which sets promising preliminary steps for future exploration.

Acknowledgments

This material is based upon work supported by NSF grants 1763673, CNS-2002874, ARO grant W911NF2210165, a gift from Intel via the Private AI institute, and gifts from Qualcomm, Cisco, and Konica-Minolta, and support from USC-Amazon Center on trustworthy AI.

Abay, A.; Zhou, Y.; Baracaldo, N.; Rajamoni, S.; Chuba, E.; and Ludwig, H. 2020. Mitigating bias in federated learning. ar Xiv preprint ar Xiv:2012.02447.

Bonawitz, K.; Ivanov, V.; Kreuter, B.; Marcedone, A.; Mc Mahan, H. B.; Patel, S.; Ramage, D.; Segal, A.; and Seth, K. 2017. Practical secure aggregation for privacypreserving machine learning. In proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, 1175 1191.

Ding, F.; Hardt, M.; Miller, J.; and Schmidt, L. 2021. Retiring Adult: New Datasets for Fair Machine Learning. Advances in Neural Information Processing Systems, 34.

Du, W.; Xu, D.; Wu, X.; and Tong, H. 2021. Fairness-aware Agnostic Federated Learning. In Proceedings of the 2021 SIAM International Conference on Data Mining (SDM), 181 189. SIAM.

Dua, D.; and Graff, C. 2017. UCI Machine Learning Repository. http://archive.ics.uci.edu/ml.

Dwork, C.; Hardt, M.; Pitassi, T.; Reingold, O.; and Zemel, R. 2012. Fairness through awareness. In Proceedings of the 3rd innovations in theoretical computer science conference, 214 226.

Ezzeldin, Y. H.; Yan, S.; He, C.; Ferrara, E.; and Avestimehr, S. 2021. Fairfed: Enabling group fairness in federated learning. ar Xiv preprint ar Xiv:2110.00857.

Feldman, M.; Friedler, S. A.; Moeller, J.; Scheidegger, C.; and Venkatasubramanian, S. 2015. Certifying and removing disparate impact. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 259 268. ACM.

G alvez, B. R.; Granqvist, F.; van Dalen, R.; and Seigel, M. 2021. Enforcing fairness in private federated learning via the modified method of differential multipliers. In Neur IPS 2021 Workshop Privacy in Machine Learning.

Grgi c-Hlaˇca, N.; Zafar, M. B.; Gummadi, K. P.; and Weller, A. 2018. Beyond distributive fairness in algorithmic decision making: Feature selection for procedurally fair learning. In Thirty-Second AAAI Conference on Artificial Intelligence.

Hardt, M.; Price, E.; Srebro, N.; et al. 2016. Equality of opportunity in supervised learning. In Advances in neural information processing systems, 3315 3323.

He, C.; Li, S.; So, J.; Zeng, X.; Zhang, M.; Wang, H.; Wang, X.; Vepakomma, P.; Singh, A.; Qiu, H.; et al. 2020. Fedml: A research library and benchmark for federated machine learning. ar Xiv preprint ar Xiv:2007.13518.

He, Y.; Burghardt, K.; and Lerman, K. 2020. A geometric solution to fair representations. In Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society, 279 285. Hsu, H.; Qi, H.; and Brown, M. 2019. Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification. ar Xiv preprint ar Xiv:1909.06335. Kairouz, P.; Mc Mahan, H. B.; Avent, B.; Bellet, A.; Bennis, M.; Bhagoji, A. N.; Bonawitz, K.; Charles, Z. B.; Cormode, G.; Cummings, R.; D Oliveira, R. G. L.; Rouayheb, S. Y. E.; Evans, D.; Gardner, J.; Garrett, Z.; Gasc on, A.; Ghazi, B.; Gibbons, P. B.; Gruteser, M.; Harchaoui, Z.; He, C.; He, L.; Huo, Z.; Hutchinson, B.; Hsu, J.; Jaggi, M.; Javidi, T.; Joshi, G.; Khodak, M.; Konecn y, J.; Korolova, A.; Koushanfar, F.; Koyejo, O.; Lepoint, T.; Liu, Y.; Mittal, P.; Mohri, M.; Nock, R.; Ozg ur, A.; Pagh, R.; Raykova, M.; Qi, H.; Ramage, D.; Raskar, R.; Song, D. X.; Song, W.; Stich, S. U.; Sun, Z.; Suresh, A. T.; Tram er, F.; Vepakomma, P.; Wang, J.; Xiong, L.; Xu, Z.; Yang, Q.; Yu, F. X.; Yu, H.; and Zhao, S. 2021. Advances and Open Problems in Federated Learning. Found. Trends Mach. Learn., 14: 1 210. Kamiran, F.; and Calders, T. 2012. Data preprocessing techniques for classification without discrimination. Knowledge and Information Systems, 33(1): 1 33. Kamishima, T.; Akaho, S.; Asoh, H.; and Sakuma, J. 2012. Fairness-aware classifier with prejudice remover regularizer. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases, 35 50. Springer. Kim, M. P.; Ghorbani, A.; and Zou, J. 2019. Multiaccuracy: Black-box post-processing for fairness in classification. In Proceedings of the 2019 AAAI/ACM Conference on AI, Ethics, and Society, 247 254. ACM. Larson, J.; Mattu, S.; Kirchner, L.; and Angwin, J. 2016. How we analyzed the COMPAS recidivism algorithm. Pro Publica (5 2016), 9. Li, T.; Sanjabi, M.; Beirami, A.; and Smith, V. 2019. Fair resource allocation in federated learning. ar Xiv preprint ar Xiv:1905.10497. Lohia, P. K.; Ramamurthy, K. N.; Bhide, M.; Saha, D.; Varshney, K. R.; and Puri, R. 2019. Bias mitigation postprocessing for individual and group fairness. In ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2847 2851. IEEE. Lyu, L.; Xu, X.; Wang, Q.; and Yu, H. 2020. Collaborative fairness in federated learning. In Federated Learning, 189 204. Springer. Mc Mahan, B.; Moore, E.; Ramage, D.; Hampson, S.; and y Arcas, B. A. 2017. Communication-efficient learning of deep networks from decentralized data. In Artificial intelligence and statistics, 1273 1282. PMLR. Mohri, M.; Sivek, G.; and Suresh, A. T. 2019. Agnostic federated learning. In International Conference on Machine Learning, 4615 4625. PMLR. Mundnich, K.; Booth, B. M.; l Hommedieu, M.; Feng, T.; Girault, B.; L hommedieu, J.; Wildman, M.; Skaaden, S.; Nadarajan, A.; Villatte, J. L.; et al. 2020. TILES-2018, a longitudinal physiologic and behavioral data set of hospital workers. Scientific Data, 7(1): 1 26.

Papadaki, A.; Martinez, N.; Bertran, M.; Sapiro, G.; and Rodrigues, M. 2021. Federating for Learning Group Fair Models. ar Xiv preprint ar Xiv:2110.01999. Reddi, S.; Charles, Z.; Zaheer, M.; Garrett, Z.; Rush, K.; Koneˇcn y, J.; Kumar, S.; and Mc Mahan, H. B. 2020. Adaptive federated optimization. ar Xiv preprint ar Xiv:2003.00295. Roh, Y.; Lee, K.; Whang, S. E.; and Suh, C. 2021. Fair Batch: Batch Selection for Model Fairness. In International Conference on Learning Representations. Wang, J.; Charles, Z.; Xu, Z.; Joshi, G.; Mc Mahan, H. B.; Al-Shedivat, M.; Andrew, G.; Avestimehr, S.; Daly, K.; Data, D.; et al. 2021a. A field guide to federated optimization. ar Xiv preprint ar Xiv:2107.06917. Wang, J.; Liu, Q.; Liang, H.; Joshi, G.; and Poor, H. V. 2020. Tackling the objective inconsistency problem in heterogeneous federated optimization. ar Xiv preprint ar Xiv:2007.07481. Wang, Z.; Fan, X.; Qi, J.; Wen, C.; Wang, C.; and Yu, R. 2021b. Federated Learning with Fair Averaging. In IJCAI. Zeng, Y.; Chen, H.; and Lee, K. 2021. Improving fairness via federated learning. ar Xiv preprint ar Xiv:2110.15545. Zhang, B. H.; Lemoine, B.; and Mitchell, M. 2018. Mitigating unwanted biases with adversarial learning. In Proceedings of the 2018 AAAI/ACM Conference on AI, Ethics, and Society, 335 340. ACM. Zhang, D. Y.; Kou, Z.; and Wang, D. 2020. Fairfl: A fair federated learning approach to reducing demographic bias in privacy-sensitive classification models. In 2020 IEEE International Conference on Big Data (Big Data), 1051 1060. IEEE.