Improving Fairness via Federated Learning

1 INTRODUCTION . As machine learning is now used to make critical decisions that affect human life , culture , and rights , fair learning has recently received increasing attention . Various fairness notions have been introduced in the past few years ( Dwork et al. , 2012 ; Hardt et al. , 2016 ; Zafar et al. , 2017b ; a ; Kearns et al. , 2018 ; Friedler et al. , 2016 ) . Among various fairness notions , group fairness is the most studied one ( Hardt et al. , 2016 ; Zafar et al. , 2017a ) . Group fairness requires the classifier to treat different groups similarly , where groups are defined with respect to sensitive attributes such as gender and race . One of the most commonly used group fairness notions is demographic parity , which requires that different groups are equally likely to receive desirable outcomes . There has been a large amount of work in training fair classifiers ( Zafar et al. , 2017c ; Hardt et al. , 2016 ; Roh et al. , 2021 ) , and almost all of these studies assume that the learner has access to the entire training data . Unfortunately , this is not the case in many critical applications . To see this , consider a scenario where multiple data owners ( e.g . courts or financial institutions ) have their own private data . Even if they are willing to coordinate with the other institutions to obtain a single model that works well on the combined data , they can not directly share their data with the others due to the privacy act . This precisely sets the core question we aim to answer in this paper – how can we privately train a fair classifier on decentralized data ? To answer this , we first study three existing approaches : Unfederated Fair Learning ( UFL ) , Federated Fair Learning via FEDAVG ( FFL via FEDAVG ) , and Centralized Fair Learning ( CFL ) . See Fig . 1 for illustration . Unfederated Fair Learning ( UFL ) and Centralized Fair Learning ( CFL ) UFL is the most naı̈ve yet most private approach . As the name indicates , this strategy refers to a scenario where multiple data owners simply decide to not coordinate . Instead , each of them learns a fair model on its local data to serve its own users . This approach is completely private as the participating data owners share nothing with the others . However , the overall performance of UFL is expected to be poor , because each data owner may have a highly biased view of the entire data distribution , making their locally trained classifiers fair only on a biased subset of the data , but not on the entire data . To evaluate the performance of this approach , we consider the randomized classifier that makes a prediction using a randomly chosen local classifier . Note that this can be viewed as a random customer model , i.e. , a user drawn from the overall data distribution picks and visits one of the institutions , uniformly at random . Another extreme approach is CFL , where a fair model is trained on the pooled data . We expect CFL to achieve the best performance tradeoff , at the cost of no privacy . Federated Fair Learning via FEDAVG ( FFL via FEDAVG ) FFL via FEDAVG applies federated learning ( Konečnỳ et al. , 2017 ) together with existing fair learning algorithms . Federated learning is a distributed learning framework , using which many data owners can collaboratively train a model under the orchestration of a central server while keeping their data decentralized . For instance , under FEDAVG , the standard aggregation protocol for federated learning , the central server periodically computes a weighted average of the locally trained model parameters . If each data owner runs a fair learning algorithm on its own data and these locally trained models are aggregated via FEDAVG , then one might hope to obtain a model that is accurate and fair on the overall data distribution . We call this approach Federated Fair Learning via FEDAVG ( FFL via FEDAVG ) . Goal and Main Contributions The performances of these approaches have not been rigorously analyzed in the literature . In the first place , it has been unknown whether there is any strict performance gap between UFL and FFL via FEDAVG . This makes it unclear whether or not federated learning is necessary at all for decentralized fair learning . The performance comparison between FFL via FEDAVG and CFL also remains unclear . Can FFL via FEDAVG always match the performance of CFL ? If not , can we develop a better federated learning approach for decentralized fair learning ? Inspired by these open questions , this work rigorously analyzes the performance of the existing approaches and proposes a new solution to decentralized fair learning . Our major contributions can be summarized as follows : • We develop a theoretical framework for analyzing various approaches for decentralized fair learning . Using this , we prove the strict ordering between the existing approaches , i.e. , under some mild conditions , UFL < FFL via FEDAVG < CFL , w.r.t . their fairness-accuracy tradeoffs . • Improving upon the state-of-the-art algorithm for ( centralized ) fair learning ( Roh et al. , 2021 ) , we design FEDFB , a novel approach to learning fair classifiers via federated learning . • Via extensive experiments , we show that ( 1 ) our theoretical findings hold under more general settings , and ( 2 ) FEDFB significantly outperforms the existing approaches on various datasets and achieves similar performance as CFL . To the best of our knowledge , our work is the first theoretical performance comparison of various approaches to fair learning on decentralized data . Moreover , it characterizes the necessity of federated learning for improved fairness-accuracy tradeoff , and we expect this to expedite the adoption of federated learning-based approaches . Our proposed solution FEDFB achieves state-of-the-art performance on many datasets , sometimes achieving a similar tradeoff as the one trained on centralized data . 2 RELATED WORK . Model Fairness Among various algorithms for fair training ( Zemel et al. , 2013 ; Jiang & Nachum , 2020 ; Zafar et al. , 2017c ; a ; Hardt et al. , 2016 ; Roh et al. , 2021 ; 2020 ) , the current state-of-the-art is FairBatch ( Roh et al. , 2021 ) , which reweights the samples by solving a bi-level optimization problem , whose inner optimizer is the standard training algorithm and outer optimizer aims to find the best weights attached to groups of samples for the sake of model fairness . Federated Learning Unlike traditional , centralized machine learning approaches , federated learning keeps the data decentralized throughout training , reducing the privacy risks involved in traditional approaches ( Konečnỳ et al. , 2017 ; McMahan et al. , 2017 ) . FEDAVG ( McMahan et al. , 2017 ) is the first and most widely used federated learning algorithm . The idea is to iteratively compute a weighted average of the local model parameters , with the weights proportional to the local datasets ’ sizes . Prior work ( Li et al. , 2020b ) has shown that FEDAVG provably converges under some mild conditions . The design of our proposed algorithm FEDFB is also based on that of FEDAVG . Federated Fair Learning for Client Parity There have been only a few attempts in achieving fairness under the federated setting . Moreover , the definition of “ fairness ” used in the existing federated learning work is slightly different from the standard notion used in the centralized setting . One popular definition of fairness in the federated setting is that all clients ( i.e . data owners ) achieve similar accuracies ( or loss values ) , which we call client parity , and several algorithms have been proposed to achieve this goal ( Li et al. , 2021 ; 2020a ; Mohri et al. , 2019 ; Yue et al. , 2021 ; Zhang et al. , 2020a ) . To compare our methods with existing federated fair learning algorithms designed for client parity , we also extend our FEDFB such that it can also achieve client parity instead of the standard notion of group fairness . In Sec . 5 , we will show that FEDFB can achieve as good client parity as the existing algorithms , though FEDFB is not specifically designed for client parity . Federated Fair Learning for Group Fairness A few very recent studies ( Ezzeldin et al. , 2021 ; Rodrı́guez-Gálvez et al. , 2021 ; Chu et al. , 2021 ; Du et al. , 2021 ; Cui et al. , 2021 ) , conducted concurrently with our work , also aim at achieving group fairness under federated learning . In particular , Du et al . ( 2021 ) , Rodrı́guez-Gálvez et al . ( 2021 ) and Chu et al . ( 2021 ) mimic the centralized fair learning setting by exchanging information for each local update . In contrast , our FEDFB requires much fewer communication rounds , ensuring higher privacy and lower communication costs . Simlar to FEDFB , Ezzeldin et al . ( 2021 ) employs FEDAVG and a reweighting mechanism to achieve group fairness . However , FAIRFED only applies to the case with one single binary sensitive attribute , while Rodrı́guez-Gálvez et al . ( 2021 ) and Chu et al . ( 2021 ) are not applicable to demographic parity . Therefore , we summarize the comparison of UFL , FFL via FEDAVG , CFL , FEDFB and AGNOSTICFAIR ( Du et al. , 2021 ) in terms of performance and privacy in Fig . 2 . There is also work that aims at achieving local fairness for each data owner ( Cui et al. , 2021 ) . This is in contrast to our work , which instead focuses on achieving global fairness in the overall data distribution . Our setting is more appropriate in domains such as criminal justice and social welfare . 3 PERFORMANCE ANALYSIS OF UFL , FFL VIA FEDAVG AND CFL . In Sec . 3.1 , we first show the necessity of federation by proving that FFL via FEDAVG can achieve strictly higher fairness than UFL . We then prove the limitation of FFL via FEDAVG by comparing its performance with an oracle bound of CFL in Sec . 3.2 . These two results together imply that federated learning is necessary , but there exists a limit on what can be achieved by FEDAVG-based approaches . We will present informal theoretical statements , deferring the formal versions and proofs to Sec . A . Problem Setting Denote [ N ] : = { 0 , 1 , . . . , N − 1 } for any N ∈ Z+ . We assume I clients , which have the same amount of data . We further assume a simple binary classification setting with a binary sensitive attribute , i.e. , x ∈ X = R is the input feature , y ∈ Y = [ 1 ] is the outcome and a ∈ A = [ A ] = [ 1 ] is the binary sensitive attribute . Assume x is a continuous variable . The algorithm we will develop later in Sec . 4 will be applicable to general settings . We now introduce parameters for describing the data distribution . Let y | x ∼ Bern ( η ( x ) ) for all client i , where η ( · ) : X → [ 0 , 1 ] is a strictly monotone increasing function . Assume x | a = a , i = i ∼ P ( i ) a , a | i = i ∼ Bern ( qi ) , where i is the index of the client , P ( i ) a is a distribution , and qi ∈ [ 0 , 1 ] for a = 0 , 1 , i ∈ [ I ] . Let F = { f : X × A → [ 0 , 1 ] } . Given f ∈ F and data sample ( x , a ) , we consider the following randomized classifier : ŷ | x , a ∼ Bern ( f ( x , a ) ) . Using these definitions , we now define demographic parity , specialized for a binary sensitive attribute : Definition 1 ( Demographic Parity ( binary cases ) ) . P ( ŷ = 1 | a = 0 ) = P ( ŷ = 1 | a = 1 ) . To measure how unfair a classifier is with respect to demographic parity ( DP ) , we measure DP disparity , i.e . the absolute difference between the two positive prediction rates : DP Disp ( f ) = |P ( ŷ = 1 | a = 0 ) − P ( ŷ = 1 | a = 1 ) | .

Summary: This paper investigates how one can achieve group fairness under a decentralized setting. The authors develop a theoretical framework for decentralized fair learning algorithms and analyzed the performance of existing approaches including UFL, FFL via FedAvg, and CFL. They provide novel insights showing that UFL<FFL via FedAvg<CFL. They also propose a new federated fair learning algorithm FEDFB by letting each client share extra information about the unfairness of its local classifier with the server, which then computes the optimal samples weights for the following round of local training. The experimental results demonstrate that FEDFB achieves state-of-the-art performance, while still ensuring data privacy.