Addressing Algorithmic Disparity and Performance Inconsistency in Federated Learning
Authors: Sen Cui
Weishen Pan
Jian Liang
Changshui Zhang
Fei Wang
Venue: NeurIPS 2021 Poster (2021)
Keywords: federated learning
fairness
performance inconsistency

Abstract: Federated learning (FL) has gain growing interests for its capability of learning from distributed data sources collectively without the need of accessing the raw data samples across different sources. So far FL research has mostly focused on improving the performance, how the algorithmic disparity will be impacted for the model learned from FL and the impact of algorithmic disparity on the utility inconsistency are largely unexplored. In this paper, we propose an FL framework to jointly consider performance consistency and algorithmic fairness across different local clients (data sources). We derive our framework from a constrained multi-objective optimization perspective, in which we learn a model satisfying fairness constraints on all clients with consistent performance. Specifically, we treat the algorithm prediction loss at each local client as an objective and maximize the worst-performing client with fairness constraints through optimizing a surrogate maximum function with all objectives involved. A gradient-based procedure is employed to achieve the Pareto optimality of this optimization problem. Theoretical analysis is provided to prove that our method can converge to a Pareto solution that achieves the min-max performance with fairness constraints on all clients. Comprehensive experiments on synthetic and real-world datasets demonstrate the superiority that our approach over baselines and its effectiveness in achieving both fairness and consistency across all local clients.

Addressing Algorithmic Disparity and Performance Inconsistency in Federated Learning
Sen Cui' Weishen Pan' Jian Liang² Changshui Zhang' Fei Wang'
IIntitute for Artificial Intelligence, Tsinghua University (THUAD) State Key Lab of Intelligent Technologies and Systems, Beijing National Research Center for Information Science and Technology (BNRist), Department of Automation, Doonmatioo,Tsiiguua University, Beijing, P.R.China Alibaba Group, China
Department of Population Health Sciences, Weill Cornell Medicine, USA {cuis19, pss15) @mails. tsinghua. edu.. cn xuelang. 1j Dealibbba-in com zcs0mail tsinghua. edu.cn few2001 @med. cornell.ede
Abstract
Federated learning (FL) has gain growing interests for its capability of learning from distributed data sources collectively without the need of accessing the raw data samples across different sources. So far FL research has mostly focused on improving the performance, how the algorithmic disparity will impacted for the model learned from FI. and the impact of algorithmic disparity on the utility inconsistency are largely unexplored. In this paper, we propose an FL framework to jointly consider performance consistency and algorithmic fairness across different local clients (data sources). We derive our framework from a constrained multi- objective optimization perspective, in which we learn model satisfying fairness constraints on all clients with consistent performance. Specifically, we treat the algorithm prediction loss each local client worst-performing client with fairness constraints through optimizing a surrogate maximum function with all objectives involved. A gradient-based procedure is employed to achieve the Pareto optimality of this optimization problem. Theoretical analysis is provided prove that method can converge Pareto solution that achieves the min-max performance with fairesss constraints on all clients. Comprehensive experiments on synthetic and real-world datasets demonstrate the superiority that our approach over baselines and its effectiveness in achieving both fairness and consistency across all local clients.
objective and maximize the
Introduction
Federated learning (FL.) [ refers to the paradigm of learning from fragmented data without sacrificing privacy. FI. has aroused broad interests from diverse disciplines including high-stakes scenarios such as loan approvals, criminal justice, healthcare, etc (2]. An increasing concern is whether these FI. systems induce disparity in local clients in these cases. For example, ProPublica reported that an algorithm used across the US for predicting a defendant's risk of future crime produced higher scores to
than Caucasians on average [ This has caused severe concerns from the public on the real deployment of data mining models and made algorithmic faimess an important research theme in recent years.
Existing works on algorithmic faimess in machine learning have mostly focused on individual learning scenarios. There has not been much research on how FL will impact the model fairness at
35th Conference on Neural Information Processing Systems (NcurIPS 2021).

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different local clients Recently. Du et al. [6] proposed fairness- aware method, which considered the global fairness of the model learned through kemel we-weigt mechanism. However, such a mechanism can not guarantee to achieve fairness at local clients in FL. scenario, since different clients will have different distributions across protected groups. For example, if we are building a mortality prediction model for COVID-19 patients within hospital system [7], where each individual hospital can be viewed as a local client. Different hospitals will have different patient populations with distinct demographic compositions including race or gender. In this case, the model fairness at each hospital is important because that's s where the model will be deployed, and it is unlikely that global model fairness can lead to local model fairness.
Due to the potential trade-off between algorithmic fairness and model utility, one aiming to mitigate the algorithmic disparity on local clients can exacerbate the inconsistency of the model performance (i.e., the model performance different at different local clients). There have been researches 4 ( trying to address the inconsistency without considering algorithmic fairness. In particular, Mohri et al. (5] proposed an agnostic federated learning (AFL) algorithm that maximizes the performance of the worst performing client. Li et al. 4 proposed a q-Fair Federated Learning (q-FFL) approach to weigh different local clients differently by taking the g-th power of the local empirical loss when constructing the optimization objective of the global model.
In this paper, we consider the problem of enforcing both algorithmic fairness and performance consistency across all local clients in FL. Specifically, suppose we have N local clients, and u, represents the model utility for client i, and g; is the model disparity quantified by some computational faimnsss metric (e.g., demographic parity [8] or equal opportunity (9). Following the idea of AFL, we can maximize the utility of the worst-performed client to achieve performance consistency. We also propose to assign each client a "fairness budget" to ensure certain level of local fairness, i.e., gi S <vi = 1, 2, .... .... with E; being a pre-specified fairness budget for client i. Therefore, we can formulate our problem as constrained multi-objective optimization framework as shown in Figure [[a] where each local model utility can be viewed as an optimization objective.
Since models with fairness and min-max performance may be not unique, we also require the model to be Pareto optimal. A model is Pareto optimal if and only if the utility of any client cannot be further optimized without degrading some others. A Pareto optimal solution of this problem cannot be achieved by existing linear scalarization methods federated learning (e.g., federated average, or FedAve in [00), as the non-i.i.d data distributions across different clients can cause a non-convex Pareto Front of utilities (all Pareto solutions form Pareto Front). Therefore, we propose FCFL, new federated learning framework to obtain fair and consistent model for all local clients. Specifically, we first utilize a surrogate maximum function (SMF) that considers the N utilities involved simultaneously instead of the single worst, and then optimize the model to achieve Pareto optimality by controlling the gradient direction without hurting client utilities. Theoretical analysis proves that our method can converge a ftirness-constraince Pareto min-mat model and experiments on both synthetic and real-world data sets show that FCFL can achieve a Pareto min-max utility distribution with fairness guarantees in each client. The source codes of FCFL are made publicly available at https::/ //github....... cww/ comm/uis11//CFL
2 Related Work
Algorithm fairness is defined the disparities in algorithm decisions made across groups formed by protected variables (such as gender and race). Some approaches have been proposed to mathematically define if an algorithm fair. For example, demographic parity [8] requires the classification results to be independent of the group memberships and equalized opportunity [9] seeks for equal false negative rates across different groups. Besides, there are also recent works focusing on the interpretation of the source of model disparity [11]. Plenty of approaches have been proposed to reduce model disparity. One type of method is to train a classifier first and then post-adjust the prediction by setting different
thresholds for different groups [9] or learning transformation function 122 [3]. Other methods
have been developed for optimization of fairness metrics during the model training process through
adversarial learning [14] [5, 16 17 [8] or regularization 119 20 21). Du et al. [6] considered
algorithm fairness in the federated learning setting and proposed a regularization method that assigns
We would like to emphasize that the algorithmic fairness we studied in this paper is not the federated fairesss studied in 4 and (5). as their faimess is referring to the performance different clients, which is consistency.

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reweighing value on each training sample for loss objective and fairesss regularization to deal with the global disparity. This method cannot account for the discrepancies among the model disparities at different local clients. In this paper, we propose to treat fairness as constraint and optimize a multi-objective optimization with multiple fairness constraints for all clients while maximally maintain the model utility.
As we introduced in the introduction, the global consensus model learned from federated learning may have different performances on different clients. There are existing research trying to address such inconsistency issue by maximizing the utility of the porst-performing client. In particular, Li er al. 4 propose q- q-FFL to obtain a min-max performance of all clients by empirically adjusting the power of the objectives, which cannot always guarantee a more consistent model utility distribution without sufficient searching for appropriate power values. Mohri et al. [5] propose AFL, min-max max optimization scheme which focuses on the single worst client. However, focusing on the single worst objective can cause another client to perform worse, thus we propose to take all objectives into account and optimize a surrogate maximum function to achieve a min-max performance distribution in this paper.
Multi-objective optimization aims learn model that gives consideration to all objectives involved. The optimization methods for multi-objective typically involve linear scalarization or its variants, such as those with adaptive weights [22]. but it is challenging for these approaches handling the competing performance among different clients [23). Martinez et al. [24] proposed a multi- objective optimization framework called Min-Max Pareto Fairness (MMPF) to achieve consistency by inducing a min-max performance of all groups based on convex assumption, which is fairly strong as non-convex objectives are ubiquitous. In this paper, we formulate the problem of achieving both fairness and consistency in federated networks through constrained multi-objective optimization. Previous research on solving this problem has been mostly focusing on gradient- free algorithms such as evolutionary algorithms (25), physics-based and deterministic approaches (26). Gradient-based methods are still under-explored [27]. We propose a novel gradient-based method FCFL, which searches for the desired gradient direction iteratively by solving constrained Linear Programming (LP) problems to achieve fairness and consistency simultancously in federated networks.
3 Problem Setup
The problem to be solved in this paper is formally defined in this section. Specifically, we will introduce the algorithmic fairness problem, how extend existing fairness criteria to federated setting, and the consistency issues model utility in federated learning.
3.1 Preliminaries
Federated Learning. Suppose there are N local clients c1, .N.. and each client associated with a specific dataset DD* = {X*, "K*K J. k E {1, (1,2,... ..., N), where the input space X and output space y shared across all N clients. There are n² samples in the k-th client and each sample is denoted as (a vt1 The goal the federated learning is to collaboratively learn a global model h with the pa- rameters 9 to predict the label ý>h the empirical risk over the samples from all clients i.c., mina where lg the loss objective of the k-th client.
each client. The classical federated learning aims minimize Σ = (x(he (att)a))) ),v())
EE
Fairness. Fairness refers to the disparities in the algorithm decisions made across different groups formed by the sensitive attribute, such as gender and race. we denote the dataset on the k-th client as D = {x* A y* where A E A is the binary sensitive attribute, then we can define the multi-client fairness as follows:
Definition 1 (Multi-client fairness (MCF)). A learned model h achieves multi-client fairness if meets the following condition:
Dish (h) ex 50 Vk [1,,,N}
where Dish (h) denotes the disparity induced by the model h and ex is the given faimesss budget of the k-th client. The disparity on the k-th client ADis can be measured by demographic parity
3

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(DP) g and Equal Opportumity (EO) 9 as follows:
ADP; P( 1| 0) P(P* 1|A 1)1
(2)
A = p( = 1|4 0, -P = 1| = 1, = =1]
As data heterogeneity may cause different disparities across all clients, the fairness budgets Cg in Definition 3.1 specifies the tolerance of model disparity at the k-th client.
Consistency. Due to the discrepancies among data distributions across different clients, the model performance different clients could be different. Morever, the inconsistency will be magnified when we adjust the model to be fair on local clients. There are existing research trying to improve the model consistency by maximizing the utility of the worst performing client [1:
min max kE(D..,N) n E." 4e(ho(0)).u5
where the max over the losses across all clients.
3.2 Fair and Consistent Federated Learning (FCFL)
Our goal is to learn a model which 1) satisfies MCF as we defined Definition 2) maintains consistent performances across all clients. We will use ADPs defined in Eq. measurement of disparity in our main text while the same derivations can be developed when adapting other metrics, so have gie (f((x))) A5) ADPk, and gl is the function of calculating model disparity on the k-th client. Similarly, the model utility loss l ),, Y*) cross-entropy, hinge loss and squared loss, etc). the rest of this paper we will use 4, (h) (gi (h)) for (h(*),, y² (x**, )²) without causing further confusions. We formulate FCFLas the problem of optimizing the N utility-relate objectives (4),,, (h)) to achieve Pareto Min-Max performance with N fairness constraints:
can be evaluated by different metrics (such as
min REW
(.).),)) s.t. (h) c S Vk E [1..,N..
The definitions of Pareto Solution and Pareto Front, which are fundamental concepts in multi-objective optimization, are as follows:
Definition 2 (Pareto Solution and Pareto Front), Suppose 1(h) [41 (2),, (. represents the utility loss vector on N learning tasks with hypothesis h E H. we say h is a Pareto Solution if there is no hypothesis h' that dominates h: h h, i.e.,
Ah' E H, Vi (,,'k)) - (h)) and 3j 1,(h) < <,)())
All Pareto solutions form Pareto Front P.
From Definition 2 for a given hypothesis set and the objective vector I(h), the Pareto solution avoids unnecessary harm to client utilities and may not be unique. We prefer Pareto solution that achieves a higher consistency. Following the work in 4 (. we want obtain a Pareto solution h* with min-max performance. Figure ( shows the relationships among different model hypothesis sets, and we explain the meanings of different notations therein as follows:
(1) H is the set of model hypotheses satisfying MCF, i.e.,
gh(h) c Ak E (), vh E H.
(2) H.F is the set of model hypotheses achieving min-mat performance (consistency) with MCF:
FF C H.P and Anax(h)) < (max(h), Yh H., wh' e FFF.
(4)
(3) HPP is the set of model hypotheses achieving Pareto optimality with MCF:
HF C HH"
(5a)
N h wh' W H.. vh FF
(5b)
where (5) satisfies Yh E HP meets MCF, and Eq. (bb) ensures that Yh. E HPP a Pareto model with MCF
(4) H is our desired set model hypotheses achieving Pareto optimality and min-max performance with MCF: H" FP n FFU.

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H
h
h
Clann
Clant
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Glann
71
H
T. P
92
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mis min (N,, Ric.on Aay a.s mas (or siom for (N)
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Figure 1: (a) The architecture of our proposed (b) relationship of the hypothesis involved and H." HPP HF is the desired hypothesis set. (c) Two optimization paths to achieve fair Pareto min-max model: 1) ho 7FF - H": the gray dotted line represents that the initial model h first achieves Pareto optimality with MCF then achieves min-max performance; 2) Ao + FFU - H² the black solid line denotes that the initial model A first achieves min-max performance with MCF then achieves Pareto optimality.
(a)
(c)
min- max problem. (b) The
Theorem 1. (proof Appendix) The hypothesis set H² is non-empty, i.e.
3h E
(6)
In summary, from Theorem [ our goal is to obtain fair and consistent model h" E: H." achieve Pareto optimality and min-max performance with MCF.
Fairness-Constraanee Min-Max Pareto Optimization
4.1 Preliminary: Gradient-based Multi-Objective Optimization
Pareto solutions of the multi-objective optimization problem be reached by gradient descent procedures. Specifically, given the initial hypothesis h with parameter 0 E R" we optimize hag by moving to a specific gradient direction d with step size vy: 0 0² + nd. d is descent direction if it decreases the objectives (4, (haur)) < 4 (har), ), Vi). Suppose Vol, is the gradient of the i-th objective 4 with respect the parameter 0, if select d" which satisfies d S for all i, d' is a descent direction and (hgr)) decreases after the + 1 iteration.
If directly search for the descent direction d achieve d'l, S 0, Vi, the computation cost be tremendous when d a high-dimensional vector. Désidéri et al. (28) proposed to find a descent direction d in the convex hull of the gradients of all objectives denoted G (Voh, Vol2.... Volxx by searching for a N N-dimension vector a* (typically < n in deep model), which is formulated as follows:
E Voli aj 2 Vj and Σn a -
d = G where G
(7)
4.2 Overview of the Optimization Framework
To obtain fair Pareto min-max max model, there are optimization paths shown in Figure I(c) The gray dotted line denotes the optimization path where we first achieve Pareto optimality with MCF, then we try achieve min-max performance while keeping Pareto optimality. However, it's hard to adjust Pareto model to another (23). Therefore, we propose to first achieve min-max performance with MCF then achieve Pareto optimality as the black solid line in Figure I(c) In particular, we propose a two-stage optimization method for this constrained multi-objective problem: 1) constrained min-max optimization to achieve a fair min-max model; 2) constrained Pareto optimization to continue to optimize the model to achieve Pareto optimality while keeping min-man max performance with MCE
5

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min-max optimization problem on Constrained Min-Max Optimization We define a constrained min max the hypothesis H:
min bEH H
Iman (h)
Imax (l) max (4(h)) iE [1,,,N
(8)
s.t.
Iman (h) - O
Imax (h) max (h)) = max (0:(h) G.) i (1,.,.N)
where 6; is the given fairness budget the i-th client. By optimizing the constrained objective in Eq.(8). we obtain a model h² E HPU that 1) h! satisfies MCF; 2) ht achieves the optimal utility on the worst performing client.
Constrained Pareto Optimization Caring only about the utility of the worst-performing client can lead to unnecessary harm to other clients since the rest objectives can be further optimized. Therefore, we then continue to optimize h' E HF to achieve Pareto optimality:
min bEH N i= 4(h)
(9a)
S.t. ((h) S 4(h)) Vi N3,
(9b)
(h) 0
(9c)
Inan (h) max (h)( max (g:(h) G.) iE N)
(9d)
where we optimize h without hurting the model utility on any client so that the converged Pareto model h- of (9) satisfies (ma I mmaz(h+). Morever, ht satisfies MCF as the constraint in Eq. so h E F a Pareto min-max model with N fairness constraints on all clients.
4.3 Achieving Min-Max Performance with MCF
Minimizing the current maximum value of all objectives directly in Eq. () can cause another worse objective and can be computationally hard when faced with tremendous amount of clients. We will use (h) (I'm (h)) to denote Iea (h) (maz (h)) without causing further confusions for expression simplicity. We propose to smooth surrogate maximum function (SMF) 29 approximate an upper bound of lm (h) and 9m (h) as follows:
(h, 61) = 5, In Σ
N
exp
(1((k)) 81
I' ml, 8g) = og Σ N
exp
g((h)) 8g
(5g. > 0).
t=1
(10)
It is obvious that 4m (h) S 1m (h, d1) S 4m (h) 8m In(N) and limns -0- im (1(x), 5,) I. (h). For
g' m (h, 6g), we can get similar conclusion. The objective Eq. (8) approximated follows:
min kEH
in 81)
(11a)
s.t.
(m 5g) S O.
(11b)
Property 1. There always exists an initial trivial model which satisfies the MCF criterion by treating all samples equally (e.g.. h(x)) = 1,
From Property we can always initialize h to satisfy (h, 5,) & O in Eq. 11b). Then we optimize the upper bound of (h) when ensuring MCF. As the hypothesis h owns the parameter 0, we use vpl and Vog' to represent the gradient Voln (hg. dr) and Vog' (he, 5,), respectively. We propose to search for descent direction d for E1. in the convex hull of G = [Vll, Veg'l in two cases where d defined in 7q. For the t-th iteration:
(1) if hgs satisfies the fairness constraint defined in Eq. 11b), we focus on the descent of im (hor, 8t):
min deG
Vorl if (hgr, 5%) z O,
(12)

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(2) if hgs violates the faireess constraint, we aim to the descent of g' (har, 6')) without causing the ascent of fm (hge, 8f):
min dEG
Vo s.t. d' val 0.
(13a)
If the obtained gradient d satisfies
|[d]] I cd. we decrease the parameter 6f, 63 as:
ott1 B 6/ 6t1
3 -6)
if ||d| Ed
(14)
5t+1 5/ 6g 69
otherwise,
where B is the decay ratio that 0 < < 1. From Eq. 14. we narrow gap between im (h, 5t) and Imaz (h) by decreasing the parameter ói every time the algorithm approaches convergence. From
Eq. and Eq. 13), optimize either i. or g' and keep im without ascent in each iteration.
4.4 Achieving Pareto Optimality and Min-Max Performance with MCF
As the model hg E HU obtained from constrained min- max optimization cannot guarantee Pareto optimality, we continue to optimize hg to be Pareto model without causing the utility descent on any client. We propose a constrained linear scalarization objective to reach Pareto model and the t-th iteration formulated as follows:
1 N N
min deG
Σ 1=1
d' Vork
(15a)
d' Vorl S
Vi [},
(15b)
d V Vogg $ 0,
(15c)
where G Voll, Vol2.... Voln, Vogi, Vog2..... VøgNl and G is the convex hull of G. The non- positive angle of with each gradient Varl, ensures that all objective values decrease. Similarly, aim to reach the Pareto solution without causing utility descent only on the worst performing client, the constraint in Eq. is replaced by Vo < O.
Different from constrained min-max optimization in Section 4.3 where the objective to be optimized in each iteration depends whether 9m (hge, , 6%) < O, in constrained Pareto optimization procedure, as we have achieved MCF, we optimize the objective in (1) for a dominate model in each iteration. Specifically, we restrict g', S O to keep fairness on each client given the reached hypothesis ht HFF Meanwhile, objective cannot be further minimized. Algorithm in Appendix shows all steps of our method. The convergence analysis and the time complexity analysis of our framework in Appendix. Moreover, we also present our discussion about the fairness budget in Appendix.
constrain (hh) descend remain unchanged until any
Experiments
We intuitively demonstrate the behavior of our method by conducting experiments on synthetic data. For the experiments on two real-world federated datasets with fairness issues, we select two different settings to verify the effectiveness of our method: (I) assign equal fairness budgets for local clients: (2) assign client-specific fairness budgets. More experimental results and detailed implementation are Appendix.
5.1 Experimental Setup
the synthetic data is from two given non-convex objectives; (2) UCI Adult dataset [5]: Adult contains more than 40000 adult records and the task is to predict whether an individual earns more than 50K/year given other features. Following the federated setting in [4] [5), we split the dataset into two clients. One PhD client in which all individuals are PhDs and the other is non-PhD client. In our experiments, we select ruce and gender as sensitive attributes, respectively. (3)eICU dataset: We select (31, clinical datasct collecting patients about their admissions to ICUs with hospital information. Each instance
Federated Datasets (1) Synthetic dataset: following the setting in 30 23
7

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is specific ICU stay. We follow the data preprocessing procedure in [32] and naturally treat 11 hospitals as 11 local clients in federated networks. We conduct the task of predicting the prolonged length of stay (whether the ICU stay is longer than I week,) ) and select race as the sensitive attribute.
Evaluation Metries (1) Utility metric:
accuracy measure the model utility in our exper- iments; (2) Disparity metrics: our method is compatible with various of fairness metries. In our experiments, we select two metrics (marginal-based metric Demographic Parity [ and conditional- based metric Equal Opportunity [ (The results of Equal Opportunity are in the Appendix) to measure the disparities defined Eq.(2) (3) Consistency: following the work utility on the worst- performinn client to measure consistency.
we use the
Baselines As do not find prior works proposed for achieving fairness in each client, we select FA 66. MMPF (24) and build FedAve+ Fairkeg as baselines in our experiments. For all baselines, we try to train the models to achieve the optimal utility with fairness constraints. If the model cannot satisfy the fairness constraints, we keep the minimum of disparities with reasonable utilities. (1) MMPF [24], Martinez et al. develop MMPF which optimizes all objectives on convex assumption to induce a min-max utility of all groups; (2) FA [6), Du et al. propose FA, a kernel-based model-agnostic method with regularizations for addressing fairness problem on a new unknown client instead of all involved clients; (3) Feiire,,,,,,eg, we build FedAve+FairReg FairReg, which optimizes the linear scalarized objective with the fairness regularizations of all clients.
5.2
Experiments on Synthetic Dataset
Following the setting in 330 23 the syn- thetic data is from the two non-convex objectives be minimized in Eq. and the Pareto Front of the two objec- tives is also non-convex.
(0
1.5
0.8
0.6
0.4
Pasitt
0.4
Pando
0.2
0.2
(0) 1
0.0
(0
(16)
1.0%
(0( 1
(a) 6 violates the constraints(b) 8 satisfies the constraints
Figure 2: Optimization trajectories of FCFL in = 20 dimensional solution space (# E R220). The initializa- tion violates fairness constrains (left) and satisfies faimeess constraints (right).
Non-convex Pareto Front means that lin- ear scalarization methods (e.g.. FedAve) miss any solution in the concave part of the Pareto Front. In this experiment, we optimize I under the constraint l2 S e (0.2, 0.4, 0.6, 0.8). Considering the effect of the initialization in experiment, conduct experiments when the initialization d satisfies the constraints and violates the constraints.
From the results in Figure 2 when the initialization d, violates the constraints in Figure ((a) the objective l2 decreases in each step until it satisfies the constraint and finally FCFL reaches the constrained optimal 1 (hh).. As the initialization On satisfies the constraints in Figure 2(b) our method
focuses on optimizing 4 until achieves the optimal I (h") with the constraint l
5.3 Experiments on Real-world Datasets with Equal Fairness Budgets
CXI
0/0
New
Now 180
(b) Figure 3: The disparities and accuracies on both clients as é = 0.05 (top) and as = 0.01 of on Adult dataset when race is the sensitive attribute.
(d)
8

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5.3.1 Income Prediction on Adult Dataset
We show the results with the sensitive attribute being race in our main text and the results when gender the sensitive attribute are in Appendix. We set the fairesss budgets defined in Eq in Two different cases, (1) looser constraint: ADP; S = 0.05 vi E [ (2) stricter constraint: ADP; S 6 = 0.01 Vi E [),
From Figure 3 FCFL achieves min-max performance on PhD client in the two cases with MCF MMPF fails achieve MCF as e 0.05. FA and Foirve+FairReg achieve MCF with e, 0.05 but violate fairness constraint as e, = 0.01. From Figure 3 our method achieves a comparable performance on non-PhD client compared baselines.
5.3.2 Prolonged Length of Stay Prediction on eICU Dataset
The length of the patient's hospitalization is critical for the arrangement of the medical institutions as it is related to the allocation of limited ICU resources. We conduct experiments on the prediction of prolonged length of stay(whether the ICU stay is longer than I week) on eICU dataset. We use race as sensitive attribute and set the fairness budgets defined in Eq. in two cases: (1) looser constraint:
ADP; S 6; 0.1 vi E (I,,, N); (2) stricter constraint: ADP;
0.05 vi E N}
tale
0.
0.3
0.5
0.3
0.00
6,2
0.10
6.6
0.55
0.05
Dapurtt
Dispanty
Dipurity
Seeprrky
Dieparty
(a) MMPF
(b) FA
(c) FedAve+FairReg (d) ours with é = 0.1 (c) ours with 0.05
Figure 4: Experiments on LoS Prediction task with the sensitive attribute being race. The points in each figure denote the clients and X and Y coordinates of the points denote the disparities and the accuracies, respectively.
From Figure 4 our method achieves min-max performance with fairness budget = 0.1 compared to the baselines. When we constrain ADP; < 0.05 vi, all baselines fail to satisfy the constraints and the disparities are about 0. while our method significantly decreases the disparities and the maximum of the disparities is 0.68. Besides, maintain comparable utilities all clients compared to baselines.
5.4 Experiments with Client-Specific Fairness Budgets
Data heterogeneity encourages the different levels of the disparities on different clients. Consistent fairness budgets can cause unexpected hurt on some specific clients with severe disparities. We explore the performance of our method given client-specific faireess budgets. Specifically, we firstly conduct unconstrained min-max experiments and measure the original disparities ADP [ADP, PN] on all clients, then we constrain the model disparities based on the original disparities of all clients, i.e., 62,, EN] = w ADP, w E {1.0, 0.9,0.8,........ 0.8,.,
Disaattics
Acunda
Disparty 11 Climb
Accuracy
0.20
0013
0.5
(a) Adult Disparity (b) Adult Accuracy (c) eICU Disparity w (d) eCCU Accuracy
Figure 5: Client-specific constraint experiment on Adult and eICU.
From Figure 5()) and Figure 5(b) we show the effect of the client-specific fairness budgets on
model disparities and utilities. The decreasing means the stricter constraints on both clients and
FCFL reduces the disparities significantly as shown in Figure ((a) With the stricter client-specific constraints on both clients, the utilities both clients decrease slightly shown in Figure 5(b)

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which implies that FCFL achieves great balance between the faimess and the utility of all clients. FCFL is compatible with sheet-sppcifii fairness budgets which enhances its flexibility and avoids severe hurt to the specific clients.
The results of LoS prediction task with client-specific faimess budgets shown in Figure ((c) and Figure [ As w decreases from 1.0 to 0.2, the maximum of all client disparities in Figure ((c) decrease from 0.2 to 0.05 which means the model becomes fairer on all clients. Figure ( shows the minimum of the utilities which slightly decreases from 0.62 to 0.6 and our method achieves an acceptable trade-off between model faimess and utility as the amount of clients increases this task.
Conclusion
In this paper, we investigate the consistency and fairness issues in federated networks as the learned model deployed on local clients can cause inconsistent performances and disparities without elabo- rate design. We propose novel method called FCFL to overcome the disparity and inconsistency concerns in the favored direction of gradient- based constrained multi-objective optimization. Compre- hensive empirical evaluation results measured by quantitative metrics demonstrate the effectiveness, superiority, and reliability of our proposed method.
Acknowledgments
Sen Cui, Weishen Pan and Changshui Zhang would like to acknowledge the funding by the National Key Research and Development Program of China (No. 201 00AAA0000070)), Fei Wang acknowledges the support from AWS Machine Learning for Research Award and Google Faculty Research Award.
References
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[11] Weishen Pan, Sen Cui, Jiang Bian, Changshui Zhang, and Fei Wang. Explaining algorithmic faimesss through fairness-aware causal path decomposition. In Proceedings of the 27th ACM SIGKDD Conference Knowledge Discovery & Data Mining, pages 1287 1297,1297,00
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Checklist
The checklist follows the references. Please read the checklist guidelines carefully for information on how to answer these questions. For each question, change the default [TODO] [Yes], [No] [N/A] You
strongly encouraged include justification your answer, either by referencing the appropriate section of your paper or providing a brief inline description. For example:
Did you include the license to the code and datasets? [Yes]
Did you include the license the code and datasets? [No] The code and data are proprietary.
Did you include the license to the code and datasets? [N/A]
Please do not modify the questions and only use the provided macros for your answers. Note that the Checklist section does not count towards the page limit. In your paper, please delete this instructions block and only keep the Checklist section heading above along with the questions/answers below.
1. For all authors...
(a) Do the main claims made in the abstract and introduction accurately reflect the paper's contribu- tions and scope? [Yes]
(b) Did you describe the limitations of your work? [Yes] We describe the limitations in Appendix
(c) Did you discuss any potential negative societal impacts of your work? [N/A] We discuss in
Appendix
(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
2. If you including theoretical results...
(a) Did you state the full set of assumptions of all theoretical results? [Yes] We state all assumptions in Appendix
(b) Did you include complete proofs of all theoretical results? [Yes] We include the complete proofs in Appendix
If you ran experiments..
(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material URL)? [Yes] We made our source code
publicly on github
(h) Did you specify all the training details (e.g., data splits, hyperparamcters, how they were chosen)? [Yes] We discuss the training details Appendix
(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] We report the error bars of all experimental results
(d) Did you include the total amount of compute and the type resources used (e.g., type GPUs, internal cluster, or cloud provider)? [Yes] We report the resources in Appendix
4. If you using existing assets (e.g.. code, data, models) curating/releasing new assets...
(a) If your work uses existing assets, did you cite the creators? [Yes] We cite the creators and discuss it in Appendix
(b) Did you mention the license of the assets? [Yes] We mention it in Appendix
(c) Did you include any new assets either in the supplemental material or as a URL? [Yes] We made our code publicly on github
(d) Did you discuss whether and how consent was obtained from people whose data you't 're us- ing/curating? [Yes] We discuss it in Appendix
(c) Did you discuss whether the data you are using/curating contains personally identifiable informa- tion or offensive content? [N/A]
If you used crowdsourcing or conducted research with human subjects...
(a) Did you include the full text of instructions given to participants and screenshots, if applicable?
[N/A]
(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]
(c) Did you include the estimated hourly wage paid to participants and the total amount spent participant compensation? [N/A]
12


Reviews:
[{"review_id": "rVAM56Mstve", "reviewer": "Reviewer_QSf7", "summary": "This paper presents a framework for finding solutions that achieve both demographic parity and performance consistency across local clients in FL. They propose first achieving min-max performance with multi-client fairness and then finding a solution that is Pareto optimal and demonstrate their method on experiments with both synthetic and real-world data. ", "questions": "", "limitations": "", "rating": 7, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Proposing individual fairness criteria for each client is novel (as far as I am aware) and can be very important in many domains. \n\nThe proposed multi-client fairness definition can be better explained and justified. How are the $\\epsilon$ related to one another? When should they be the same? What kind of disparity is introduced when $\\epsilon_k$ 's are different across different k’s? Can small $\\epsilon_k$ across a large k lead to large global disparity? \n\n\nDoes there always exist a Pareto-optimal Min-Max Performance model that satisfies MCF? It seems like the set of $\\mathcal{H}^{FP}$ is defined independently from the $\\mathcal{H}^{FU}$? How do we know $H^*$ the intersection is non-empty? \n\nNot sure what line 193-194: “minimizing the current maximum value of all objectives directly in Eq(7) can cause another worse objective and can be computational hard when faced with a tremendous amount of clients” means. Is this saying runtime is exponential in k? \n\nThis submission could benefit from grammar fixes but the grammar issues did not prevent me from understanding the paper. \n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "The authors have not addressed limitations and potential negative impacts. The authors should consider what types of additional disparities or unintentional concequences their local definition of fairness may introduce. ", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "2"}, "extra_text": {}}, {"review_id": "inhl4jb3aqi", "reviewer": "Reviewer_qPfz", "summary": "This paper first introduces a new task about federated learning in which fairness and consistency are jointly considered, then proposes a solution named FCFL to solve the problem. After introducing fairness, the problem is transferred to a min-max optimization problem, and the two-stage optimization algorithm works well on it. The main contributions are as follows:\n\n1) Introduce a new task which jointly considers model fairness and consistency in federated learning,\n2) Propose an optimization method called FCFL to address the problem,\n3) Conduct experiments on a synthetic dataset and two public datasets and compare the proposed algorithm with three baseline methods, and show that the proposed method outperforms the rest.", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Both method and task in this paper are new, and the proposed method is a good utilize of several existing approaches. Related works are cited in a proper way. The idea of the task is interesting, as few work has ever considered fairness in a federated learning setting and introducing it makes the whole problem a min-max optimization. Most of the paper is well-written, a few details can be further improved (e.g. introduce full name of FCFL when it first appears).The paper is technically sound, both theoretical analysis and experimental results are sufficient. However, I believe more models in the area of federated learning should be taken into consideration. Some recent works are focusing on the inconsistency caused by non-iid in federated learning and proposed good solutions (e.g.  FedNova). Weakness of the work should also be discussed, especially the possible usage of this framework. The results are reproducible, with some help of the authors. The experimental results are nice, researchers should be interested to further build on them. The datasets are existed. Since this is a brand new task, no previous methods can be used to compare with, but the results still show that performance of the framework is generally good.", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "The authors has discussed the limitations in the appendix. However, potential negative social impact is not discussed. Moreover, more limitations should be considered, for example, from the aspect of how important fairness is in federated learning, as it has never be mentioned before.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "4"}, "extra_text": {}}, {"review_id": "_YyHf64IoLF", "reviewer": "Reviewer_Nsjv", "summary": "The paper studies how to solve the model fairness and performance consistency among clients in federated learning. There exist work on model fairness and performance inconsistency separately as mentioned in the paper and the contribution of this work is to provide a FL framework which considers both effects. The problem is formulated as a constrained min-max pareto optimization problem. The authors use a two-stage optimization method to approximate the optimal solution. ", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "The paper brings local model fairness into federated learning that allows clients to set its own “fairness budget”. The model fairness is an important problem in recent machine learning communities to avoid the model being biased by the sensitive attributes. The problem is quite interesting and practical. It is not evident to see how to combine fairness with performance consistency in federated learning. The authors gave a solution easy to follow and performs well in logistic regression problems.  The paper is well organized and the ideas are easy to follow although it makes use of the existing techniques.    \n\nI have the following comments:\n1. The main algorithm 1 in Appendix for FCFL is presented in a centralized way. It would be better to present it from both the client and the server perspectives.  It is not clear from the main paper how to parallelize the calculations of FCFL.\n2. The experiments part is a little bit weak as only logistic regression problems are considered. It would be better to show the neural network performance. \n3. It seems the definition of $\\triangle DP_k$ in Eq. 2 is for binary classification. Just for curiosity, what does the  $\\triangle DP_k$ look like for multiple classification problems? \n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Yes, the authors have adequately addressed the limitations and potential negative societal impact of their work?", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "5"}, "extra_text": {}}, {"review_id": "UJdqrAszmyP", "reviewer": "Reviewer_qMLa", "summary": "This paper proposes a federated learning algorithm which is fair and gives consistent performance across different clients in the following sense.  To achieve fairness, some measure of disparity is considered and enforced as a constraint for each client (i.e. each client has an upper bound on how high the disparity measure can go).  To achieve consistency, the objective is to find model parameters that minimize the maximum loss incurred across the clients.  This contrasts with prior work which does not directly address the fairness locally at each client.  Compared to [21], this paper adds constraints on a disparity measure for each client, in addition to the min-max objective.  Compared to [6], this paper considers a fairness constraint at each client as opposed to a single, global fairness constraint.\n\nThe proposed gradient descent-based algorithm first aims to satisfy the fairness constraints, and then it aims to find a Pareto optimal solution (w.r.t the clients’ utilities) while continuing to satisfy the fairness constraints.  The proposed algorithm replaces the (non-smooth) max’s in the problem formulation with a smooth surrogate, which is basically the log-sum-exp trick.\n\nThe proposed method is evaluated on three datasets with respect to prediction accuracy as the loss/utility metric and two different fairness metrics: demographic parity and equal opportunity.  The results show that the proposed method typically performs significantly better with respect to the fairness measure, with a small loss in accuracy compared to other methods which do not achieve the same level of fairness.\n", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "This paper considers two currently relevant topics - fairness in ML and federated learning.  The main contribution here is the problem formulation and the experimental results, which are interesting.  I would not consider the algorithm design (including the tricks such as replacing max with log-sum-exp) very novel.  Below I outline some issues I have with the current presentation.  Overall, I would be okay with accepting this paper.\n\n - The authors claim that their method converges in theory, but no claim is made as to the convergence rate.\n - The experiments seem to focus on reporting the accuracy and fairness performance.  The proposed method involves solving an LP at each iteration (for both stages of the algorithm).  What is the impact on the runtime of solving these?  How does the overall runtime of the proposed method compare to the baselines considered?  Are the improvements to fairness/accuracy coming at a significant computational cost compared to other methods?\n - The number of clients considered in the experiments seems rather small.  How does the proposed method perform in situations where there are significantly more clients?\n\nMinor comments:\n - Line 33 - “in FL scenario” -> “in a FL scenario”\n - Line 42 - “There have been researches” -> “There has been prior work”\n - Line 170 - “in deep model” -> “in a deep model”\n\n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Some discussion about the choice of fairness metric may be useful (this paper looks at demographic parity and equal opportunity).  I do not see a major potential for negative societal impact directly stemming from this work.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "4"}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper studies the notion of fairness concerns in Federated Learning settings where a vanilla global model may be particularly bad on some clients versus others. Their solve this issue by maximizin the performance of the model on the worst client, leading to minimax style of fairness gurantees. The authors complement this analysis with an empirical evaluation of their method. 
Decision: Accept (Poster)