# The Effect of Anthropomorphism on Trust in an Industrial Human-Robot
Interaction

Tim Schreiter1∗, Lucas Morillo-Mendez2∗, Ravi T. Chadalavada1, Andrey
Rudenko3,
Erik Alexander Billing4, and Achim J. Lilienthal1 1Mobile Robotics and
Olfaction Lab, Örebro University, Sweden {tim.schreiter, ravi.chadalavada,
<EMAIL_ADDRESS>Perception and Interaction Lab, Örebro
University, Sweden<EMAIL_ADDRESS>Bosch GmbH, Corporate Research,
Stuttgart, Germany<EMAIL_ADDRESS>Lab, University of
Skövde, Sweden<EMAIL_ADDRESS>authors contributed equally to the
work.This work was supported by the European Union’s Horizon 2020 research and
innovation program under grant agreement No. 101017274 (DARKO) and grant
agreement No. 754285

###### Abstract

Robots are increasingly deployed in spaces shared with humans, including home
settings and industrial environments. In these environments, the interaction
between humans and robots (HRI) is crucial for safety, legibility, and
efficiency. A key factor in HRI is trust, which modulates the acceptance of
the system. Anthropomorphism has been shown to modulate trust development in a
robot, but robots in industrial environments are usually not anthropomorphic.
We designed a simple interaction in an industrial environment in which an
anthropomorphic mock driver (ARMoD) robot simulates driving an autonomous
guided vehicle (AGV). The task consisted of a human crossing paths with the
AGV, with or without the ARMoD mounted on the top, in a narrow corridor. The
human and the system needed to negotiate trajectories when crossing paths,
meaning that the human had to attend to the trajectory of the robot to avoid a
collision with it. There was a significant increment in the reported trust
scores in the condition where the ARMoD was present, showing that the presence
of an anthropomorphic robot is enough to modulate the trust, even in limited
interactions as the one we present here.

##  I Introduction

Figure 1: Setup of the (a) Autonomous Guided Vehicle (AGV) with the (b)
Anthropomorphic Robotic Mock Driver (ARMoD), placed on top of the vehicle. The
AGV can potentially communicate intent through gestures, gazes and speech of
the Driver.

Non-humanoid robots are usually equipped with various non-verbal channels to
communicate their intent to humans, such as light signals, floor projections,
or auditory signals [1]. When navigating in a shared environment, such signals
help coordinating their motion with people, to avoid collision, increase
legibility and task efficiency. As for the tasks that require cooperation and
active coordination, like the handover task, more complex communication
channels might be required, such as verbal communication with additional
gestures and gazes. Humanoid robots with anthropomorphic features, e.g., arms,
legs, and facial features, are often used in this context to improve
interaction with human users [2], [3], and their anthropomorphism leads to an
increase of users’ trust in the interaction [4, 5].

As the usage and complexity of industrial robots increase, they take on
unfamiliar shapes and thus, complicate the interaction and establishment of
trust in shared environments with humans. Robot-related factors were shown to
be the most relevant for the development of trust in these interactions [6].
Among these factors, the design of the robot is particularly important to get
the human interaction partners to trust the robot appropriately [7].
Anthropomorphic features may aid the trust, but they are not often present in
industrial robots. As the complexity of the new systems increase, the
perception of these systems as collaborators rather than machines have been
deemed as positive [8]. For example, the addition of a pair of sunglasses to a
industrial robotic hand and gripper, along with a set of breathing-like
movements and gaze behavior, improved metrics from participants such as the
perceived sociability and likeability of the system [9]. However, in their
study, the authors did not find differences in trust. One possible reason for
this is that they included a scale that was not originally designed for
industrial collaborations [10]. Another study showed that trust does not seem
to be affected as a result of anthropomorphism in industrial settings [11]. In
this case the authors used a validated scale to trust in industrial
collaboration, developed by Charalambous et al.[12]. Nevertheless, the study
employed a limited form of anthropomorphism in which a face appeared on a
screen attached to a robotic arm and gripper. In contrast to previous
research, our study does not include a tactile interaction. Our research
explores a new perceived modality of navigation for a non-humanoid robot that
can potentially improve trust on the system by using a humanoid robot, NAO, in
industrial settings.

We propose a combined approach of a humanoid robot with an Autonomous Guided
Vehicle (AGV), used for instance in the intralogistic settings111http://iliad-
project.eu. We refer to this combination as a “robot-on-robot platform” (see
Figure 1). By combining an AGV with sophisticated social robots with
anthropomorphic features, successfully used in trust-related user studies
[13], we expect to achieve an increase in the trust of human users. To the
best of our knowledge, this is the first approach to study the interaction of
an navigating AGV equipped with an an Anthropomorphic Mock Driver (ARMoD) with
participants in a shared environment. To this extent, we chose an NAO robot
with a human-likeliness score of 46% [14], as it is the subject of recent user
based studies [15], it is small enough to be mounted on our AGV, and posses a
software development kits to develop custom modules. We designed an encounter
in a narrow corridor to measure the impact of the ARMoD on trust reported by
participants. In our scenario, as the participant approached the robot, it
looked at the participant’s head and traced it until the vehicle passed the
participant. We used the scale developed by Charalambous et al.[12] to measure
trust in industrial collaborations. With the data we obtained from 33
participants, we found that the users reported higher trust in the interaction
with the ARMoD than in the AGV alone.

##  II Experiment design

###  II-A Materials

The aim of this study was to explore the impact that an Anthropomorphic
Robotic Mock Driver (ARMoD) seated on top of an AGV has on users’ trust during
a basic human-robot interaction consisting of walking and avoiding the moving
platform. The AGV we used fits the definition of “mobile platform” after
ISO8373:2021. On top of the platform a seat was mounted to hold the NAO robot
in place, which enabled a fixed and repeatable placement (see Figure 1). We
used the same AGV as in our previous studies of intent communication [16], a
retrofitted Linde CitiTruck with a SICK S300 scanner at the back, to ensure
the safety of humans approaching from behind. The AGV is equipped with sensor
modules to localize itself within the laboratory and a onboard RGB-D camera
for short-range person detection ($\approx$2 meters).

###  II-B Task

We designed a scenario where participants encountered a moving robot platform
in a hallway with the aim to study trust as a result of the appearance of the
platform, either as it is (AGV), or with a anthropomorphic robot on the top
(ARMoD). In the experiment we chose a setup that reflects a potential
encounter between humans and robotic workers in an industrial environment. The
chosen width of the hallway was 2 meters, as it matches the regulations for
corridors proposed in the DIN-18040-1 and the EN-ISO-24341 (former EN 426)
standards for meeting areas. The participants and the platform started 14
meters apart, a feasible length for the definition as a corridor encounter.
During this sequence, the participants saw the platform as it approached them,
and they were simply instructed to walk by its side towards the opposite
direction. In the ARMoD condition, if the participants got close enough for
the short-range person detection ($\approx$2 meters), the robot simulated
awareness with the head motion to trace the participants’ movement until they
crossed paths. This encounter was repeated three times with the platform
randomly taking one of the different routes: (1) platform moved in a curve to
the right side of the hallway, (2) platform moved to the left side of the
hallway and (3) platform headed straight. The platform moved at a constant
speed of 0.6 m/s.

Figure 2: Participant encountering the robot-on-robot platform in a 2-meter
wide and 15-meter long corridor. The participant has to decide for a side to
pass the platform. The robot takes one of three different trajectories (1)
Curve to the right side, (2) Straight ahead, (3) Curve to the left side.

###  II-C Procedure, sample, and measurements

After the task, participants filled an adapted version of a scale to measure
trust in industrial human-robot collaboration developed by Charalambous et al.
[12]. In this version, the items referring to the grip of the robot (C, E, G,
J) were removed, as no gripper was used in our scenario. We also used a
7-point Likert scale ranging from 1 “strongly disagree” to 7 “strongly agree”.
Additionally, we obtained some demographic information (see Table I). The age
of participants ranged from 18 to 56 years (M=28.7, SD=7.88) and all of them
were fluent in English. Participants were recruited at Örebro University and
participation was voluntary. All participants were informed about the task,
consented to participate, and were aware of the possibility to leave at any
time. We analyzed the trust scores of 33 participants divided in two groups:
one that walked by the ARMoD on top of the AGV (n=19) and one that walked just
by the AGV (n=14).

TABLE I: Demographic information from the participants Group | N | Age (SD) | Women | Other gender | Left-handed
---|---|---|---|---|---
ARMoD | 19 | 29.7 (9.8) | 13 | 1 | 1
AGV | 14 | 27.3 (4) | 5 | 0 | 1

##  III Results

To ensure that the trust scale of Charalambous et al. [12] was still reliable
despite the removal of certain items, we calculated the Cronbach’s $\alpha$.
The scale yielded a score of 0.76, beyond the acceptable level of 0.7 [17].
The trust scale is composed of three major components, the robot’s motion and
pickup speed (1), safe co-operation (2), and robot and gripper reliability
(3). Because the first and last components involve the gripper and the pickup
action, which were not part of our experiment, we just used those items within
these that applied to the robot but not to the gripper: one item for the first
component (robot’s motion and pickup speed, two items in the original scale),
and one item for the third component (robot and gripper reliability, four
items in the original scale). To calculate the final trust score, we
multiplied each of these item’s score by the number of items belonging to that
component in the original scale, two and four respectively, and added these to
the sum of the scores of the second component (safe co-operation).

Once the trust score was obtained for each participant, we proceeded with the
analysis, performed in R [18]. Because the trust scores in both groups were
not normally distributed (see violin plots in Fig. 3), we opted for a Robust
variation of the Welch’s t-test [19] to compare the reported trust between the
two groups. The yuenbt function, based on bootstrapping, from the WRS2 [20,
21] package was used for the analysis. We kept the default bootstrapping value
of 599 samples of 20% trimmed means. The $\hat{\xi}$ measure was used as a
explanatory measurement of robust effect size, as suggested by Wilcox and Tian
[22]. This measure was calculated using the yuen.effect.ci function of the
WRS2 package. Values of $\hat{\xi}$= 0.1, 0.3, and 0.5 correspond to small,
medium and large effect sizes respectively.

On average, participants reported higher levels of trust for the ARMoD
condition (M = 59.73, SE = 2.22), than for the AGV alone (M = 52.5, SE =
2.78). This difference was marginally significant
$t=-1.68,p=.051,95\%CI[-17,0.09];$ nevertheless, this difference did represent
a medium–large effect, $\hat{\xi}=0.41$.

Figure 3: Violin plots and box plots of the trust scores for both conditions.
Means and corresponding error bars in red. Error bars show 95% bootstrapped
confidence intervals.

##  IV Discussion

In this study we explored how trust from users varied as a result of the
anthropomorphic features of a robot in an industrial environment. Hancock et
al. [6] outlined the importance of robot-related factors for the development
of trust in a human-robot interaction. In [7], the authors state that
improving trust in a robot already starts with designing it appropriately.
Instead of designing a new robot from scratch to increase the trust of users
in industrial settings, we modified the design of an “Autonomous Guided
Vehicle” (AGV) by adding an “Anthropomorphic Robotic Mock Driver” (ARMoD).
AGVs such as the forklift in our experiment are frequently deployed in shared
industrial environments alongside human co-workers. We used the popular
anthropomorphic social robot “NAO” [15, 13] as the ARMoD.

The results of our study showed that the use of the ARMoD increased the
reported trust in the interaction of participants with the platform. The
simple addition of a robot on the top of the AGV, alongside basic gaze
behavior, was enough to increase users’ trust of the system within an
industrial setting. Our results are in line with recent research emphasizing
the role of anthropomorphism in trust [4, 5]. Contrary to other research set
in industrial environments [9, 11], our results showed that perceived trust
varies as a result of anthropomorphism in basic interactions such as the
avoidance of a moving robot. Although not complex, this kind of interaction is
probably one that will be common in busy industrial settings. The difference
in the results between this study and prior art is probably explained by the
different nature of the interactions, as previous studies involved tasks such
as handovers and precise object manipulations in which the success of the
interaction may have not been taken for granted by participants.

Our suggested solution increased trust through the use of anthropomorphic
features and gaze behavior. However, there are other features that can lead to
set an appropriate level of trust during the interactions with humans. For
example, we previously explored a different method of communicating intent for
the AGV using “Spatial Augmented Reality (SAR)” by projecting patterns on the
floor in front of the robot [16]. This form of communication is however
limited by the lighting conditions of the environment and can only be deployed
to communicate navigational intent. Using the ARMoD we can overcome the
disadvantages of the previous studied SAR to design future experiments, e.g.,
independence from the lighting conditions or two dimensional floor patterns.
The ARMoD can interact with participants in a proactive manner through the
usage of non-verbal communication, as well as gazes and gestures to
communicate any kind of intent. Future research should explore how these
social features beyond plain anthropomorphism might impact the trust that
users have on the robots in industrial environments.

This research comes with two limitations. First, although high levels of trust
are desirable, we just focused on the robot appearance component that
modulates it. Appropriate functioning and the minimization of failures by the
system can have a greater impact on the perceived trust. Moreover,
manipulating trust purely by appearance while ignoring other aspects could
lead to over-trust, which can be dangerous and is not desirable in potentially
threatening situations, such as the platform not breaking when headed towards
a person. Second, we designed a basic encounter that did not involve a tactile
interaction or manipulation, contrary to previous research with industrial
robots. Nevertheless, we believe that the scenario of a corridor encounter
with a robot will likely become an everyday common one. This is because this
situation may occur in a wide variety of industries, and other kind of shared
environments and with different types of workers, even with those not directly
involved in close collaborative works with the robot.

##  V Conclusion and Future Work

This work presented a study on a novel interaction method for an autonomous
guided vehicle (AGV) through an anthropomorphic robotic mock driver (ARMoD)
with 33 participants. We conducted an experiment, a hallway encounter, where
participants passed the AGV with the ARMoD mounted on top in a narrow corridor
in one condition and encountered only the AGV, but without the ARMoD in
another. We found that through adding the ARMoD to the AGV, participants
reported a higher trust on the interaction. Our results suggest that using
anthropomorphic robot in industrial settings can help to adjust the levels of
trust that users place on what otherwise would be a navigation vehicle. Under
the assumption of proper functioning, higher trust on industrial robots can
lead to higher levels of acceptability reported by the users.

##  VI Acknowledgement

We want to acknowledge Timm Linder and Chittaranjan Swaminathan for their help
in setting up the software, Per Sporrong for his help with setting up the
hardware and Per Lindström for manufacturing the seat of the mock driver used
in this study.

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# FAIR-FATE:
Fair Federated Learning with Momentum

Teresa Salazar, Miguel Fernandes, Helder Araujo, and Pedro Henriques Abreu T.
Salazar, M. Fernandes and P. H. Abreu are with the Centre for Informatics and
Systems, Department of Informatics Engineering, University of Coimbra,
3030-790 Coimbra, Portugal.
E-mail<EMAIL_ADDRESS>H. Araujo is with the Institute of Systems and
Robotics, Department of Electrical and Computer Engineering, University of
Coimbra, 3004-531 Coimbra, Portugal.September 2022

###### Abstract

While fairness-aware machine learning algorithms have been receiving
increasing attention, the focus has been on centralized machine learning,
leaving decentralized methods underexplored. Federated Learning is a
decentralized form of machine learning where clients train local models with a
server aggregating them to obtain a shared global model. Data heterogeneity
amongst clients is a common characteristic of Federated Learning, which may
induce or exacerbate discrimination of unprivileged groups defined by
sensitive attributes such as race or gender. In this work we propose FAIR-
FATE: a novel FAIR FederATEd Learning algorithm that aims to achieve group
fairness while maintaining high utility via a fairness-aware aggregation
method that computes the global model by taking into account the fairness of
the clients. To achieve that, the global model update is computed by
estimating a fair model update using a Momentum term that helps to overcome
the oscillations of noisy non-fair gradients. To the best of our knowledge,
this is the first approach in machine learning that aims to achieve fairness
using a fair Momentum estimate. Experimental results on four real-world
datasets demonstrate that FAIR-FATE significantly outperforms state-of-the-art
fair Federated Learning algorithms under different levels of data
heterogeneity.

###### Index Terms:

Fairness, Federated Learning, Momentum

##  1 Introduction

With the widespread use of machine learning algorithms to make decisions which
impact people’s lives, the area of fairness-aware machine learning has been
receiving increasing attention. Fairness-aware machine learning algorithms
ensure that predictions do not prejudice unprivileged groups of the population
with respect to sensitive attributes such as race or gender [1, 2]. However,
the focus has been on centralized machine learning, with decentralized methods
receiving little attention.

Federated Learning is an emerging decentralized technology that creates
machine learning models using data distributed across multiple clients [3]. In
Federated Learning, the training process is divided into multiple clients
which train individual local models on local datasets, without the need to
share private data. At each communication round, each client shares its local
model updates with the server that uses them to create a global shared model.

While centralized machine learning batches can typically be assumed to be IID
(independent and identically distributed), this assumption is unlikely to be
true in Federated Learning settings [4]. Since in Federated Learning each
client has its own private dataset, it may not be representative of all the
demographic groups and thus can lead to discrimination of unprivileged groups
defined by sensitive attributes. To solve the issue of heterogeneous client
distributions, Federated Learning solutions based on Momentum gradient descent
have been proposed [5, 6], but none of these has focused on fairness in
machine learning. Moreover, typical centralized fair machine learning
solutions require centralized access to the sensitive attributes information,
and, consequently, cannot be directly applied to Federated Learning without
violating privacy constraints. Because of these reasons, finding Federated
Learning algorithms which facilitate collaboration amongst clients to build
fair machine learning models while preserving their data privacy is a great
challenge.

Motivated by the importance and challenges of developing fair Federated
Learning algorithms, we propose FAIR-FATE: a novel fairness-aware Federated
Learning algorithm which aims to achieve group fairness while maintaining
classification performance. FAIR-FATE uses a new fair aggregation method that
computes the global model by taking into account the fairness of the clients.
In order to achieve this, the server has a validation set that is used at each
communication round to measure the fairness of the clients and the current
global model. Afterwards, the fair Momentum update is computed using a
fraction of the previous fair update, as well as the average of the clients’
updates that have higher fairness than the current global model, giving higher
importance to fairer models. Since Momentum-based solutions have been used to
help overcoming oscillations of noisy gradients, we hypothesize that the use
of a fairness-aware Momentum term can overcome the oscillations of non-fair
gradients. Therefore, this work aims to address the following research
question:

> _Can a fairness-aware Momentum term be used to overcome the oscillations of
> noisy non-fair gradients in Federated Learning?_

The proposed approach is evaluated on four real-world datasets which are
commonly used in the literature for fairness-related studies: the COMPAS [7],
the Adult [8], the Law School [9] and the Dutch Census [10] datasets. The
COMPAS dataset includes data about the risk assessment tool used in Broward
County, Florida [7], where the prediction task is to calculate the recidivism
outcome, indicating whether the people will be rearrested withing two years
after the first arrest. The Adult dataset [8] contains information indicating
whether a person’s income exceeds $50K/yr or not. The Law School [9] dataset
contains law school admission records across 163 law schools in the United
States where the prediction task is to predict whether a candidate would pass
the bar exam. The Dutch Census dataset [10] contains records which represent
aggregated groups of people in the Netherlands in 2001 where the prediction
task is to determine a person’s occupation which can be categorized as high
level (prestigious) or low level profession. These datasets contain sensitive
attributes such as race and gender.

Several experiments are conducted on a range of non-identical data
distributions at each client, considering the different sensitive attributes
and target classes in each dataset. Experimental results on the described
datasets demonstrate that FAIR-FATE significantly outperforms state-of-the-art
fair Federated Learning algorithms on fairness without neglecting model
performance under different data distributions.

To the best of our knowledge, this is the first approach in machine learning
that aims to achieve fairness using a fair Momentum estimate. In addition,
FAIR-FATE is a flexible algorithm that does not rely on any fairness local
strategy at each client.

The remainder of this work is organized as follows: Section 2 provides
information relevant for understanding the work, Section 3 presents related
work on fair Federated Learning, Section 4 describes FAIR-FATE, Section 5
presents the experimental setup and results, and Section 6 presents the
conclusion and possible future research.

##  2 Preliminaries

In this section, information relevant for understanding FAIR-FATE is provided.
We start by describing Federated Learning algorithms, namely Federated
Averaging, Federated Averaging with Momentum and Federated Averaging with
Momentum Decay. Afterwards, we present fairness notions used in the
literature. Finally, some challenges of developing fairness-aware Federated
Learning algorithms are presented.

###  2.1 Federated Averaging

Federated Learning is an area that has been receiving increasing attention,
allowing multiple clients to learn a shared machine learning model under
privacy restrictions. The first work on Federated Learning was proposed in
[3], where the authors present an algorithm named Federated Averaging (FedAvg)
that consists of a way of generating the global model by periodically
averaging the clients’ locally trained models.

Figure 1: Federated Averaging diagram

Figure 1 presents a diagram demonstrating the FedAvg algorithm with clients
$K$ participating in the federation. Firstly, the server sends its current
model, $\theta_{t}$, to a random subset of clients, $K_{t}$ of size $|K_{t}|$,
$|K_{t}|<|K|$. Afterwards, the chosen clients then train their local models
using their private data. Lastly, the clients upload the resulting models
updates to the server where they are averaged element-wise to form the new
global model, $\theta_{t+1}$, with weights proportional to the sizes of the
clients’ datasets. This process is repeated for $T$ communication rounds. The
objective of the FedAvg framework [3] can be written as:

$\min_{\theta}f(\theta)=\sum_{k=1}^{K}\frac{n_{k}}{n}G_{k}(\theta),\qquad
G_{k}(\theta)=\frac{1}{n_{k}}\sum_{i=1}^{n_{k}}f_{i}(\theta),$ (1)

where $G_{k}(\theta)$ is the local objective for the client $k$,
$f_{i}(\theta)$ is the loss of the datapoint $i$ of client $k$, ${n_{k}}$ is
the number of datapoints of the client $k$, $n$ is the total number of
datapoints [3].

Algorithm 1 presents the FedAvg pseudo-code and Algorithm 2 presents a
client’s update. Algorithm 2 represents mini-batch stochastic gradient descent
but any type of optimizer can be used (e.g. Adam [11]).

Algorithm 1 FedAvg

1: Initialize global model: $\theta_{t}$, number of communication rounds: $T$.

2: for each round $t$ = 1,2,…, $T$ do

3: Select $K_{t}$ = random subset of clients ($|K_{t}|<|K|$)

4: for each client $k\in K_{t}$ do

5: $\theta_{t+1}^{k}$ = Algorithm 2 ($\theta_{t}$)

6: end for

7: $\theta_{t+1}=\sum_{k=1}^{|K_{t}|}\frac{n_{k}}{n}\theta_{t+1}^{k}$

8: end for

Algorithm 2 $client_{k}$ update

1: Receive $\theta$ from server

2: Initialize learning rate: $\eta_{l}$, batches: $B$, number of epochs: $E$.

3: for each local epoch $i$ from 1 to $E$ do

4: for batch $b\in B$ do

5: $\theta$ = $\theta-\eta_{l}\nabla l_{k}(\theta,b)$

6: end for

7: end for

8: return $\theta$

###  2.2 Federated Averaging with Momentum

Momentum gradient descent is a technique where an exponentially weighted
averaged of the gradients is used to help overcoming oscillations of noisy
gradients. By providing a better estimate of the gradients, it is faster than
stochastic gradient descent. Since vanilla FedAvg can be slow to converge [12,
13], Federated Learning solutions based on Momentum gradient descent have been
proposed [5, 6].

Algorithm 3 FedMom

1: Initialize global model: $\theta_{t}$, number of rounds: $T$, Momentum
parameter: $\beta$, Momentum update: $v_{t}$ ($v_{0}=0$).

2: for each round $t$ = 1,2,…, $T$ do

3: Select $K_{t}$ = random subset of clients $K$ ($|K_{t}|<|K|$)

4: for each client $k\in K_{t}$ do

5: $\theta_{t+1}^{k}$ = Algorithm 2 ($\theta_{t}$)

6: end for

7: $\alpha$ =
$\sum_{k=1}^{|K_{t}|}\frac{n_{k}}{n}(\theta_{t+1}^{k}-\theta_{t})$

8: $v_{t+1}=\beta v_{t}+(1-\beta)\alpha$

9: $\theta_{t+1}=\theta_{t}+v_{t+1}$

10: end for

Algorithm 3 represents the Federated Averaging with standard Momentum (FedMom)
algorithm. In the server, for every $\theta_{t+1}^{k}$ received, the local
update is calculated by subtracting $\theta_{t}$. Afterwards, the local
updates are averaged to form the global model update, $\alpha$. Then, the
Momentum update, $v_{t+1}$, is calculated by summing a fraction of the
previous update, $v_{t}$, and the global model update, $\alpha$. $\beta$ is
the Momentum parameter that controls the amount of the previous update.
Finally, the global model is updated by summing the previous model with the
Momentum update.

###  2.3 Federated Averaging with Momentum Decay

Motivated by decaying the total contribution of a gradient to all future
updates, decaying Momentum rules have been applied to neural networks,
significantly improving training and being less sensitive to parameter tuning.

Algorithm 4 FedDemon

1: Initialize global model: $\theta_{t}$, number of rounds: $T$, Initial
Momentum parameter: $\beta_{0}$, Momentum update: $v_{t}$ ($v_{0}=0$).

2: for each round $t$ = 1,2,…, $T$ do

3: Select $K_{t}$ = random subset of clients $K$ ($|K_{t}|<|K|$)

4: for each client $k\in K_{t}$ do

5: $\theta_{t+1}^{k}$ = Algorithm 2 ($\theta_{t}$)

6: end for

7: $\alpha$ =
$\sum_{k=1}^{|K_{t}|}\frac{n_{k}}{n}(\theta_{t+1}^{k}-\theta_{t})$

8:
$\beta_{t}=\beta_{0}*\frac{(1-\frac{t}{T})}{(1-\beta_{0})+(\beta_{0}(1-\frac{t}{T})}$

9: $v_{t+1}=\beta v_{t}+(1-\beta_{t})\alpha$

10: $\theta_{t+1}=\theta_{t}+v_{t+1}$

11: end for

Decaying Momentum rules have been previously applied to Federated Learning in
[5]. Algorithm 3 represents the Federated Averaging with with Momentum Decay
(FedDemon) algorithm presented in [5]. The procedure is similar to the FedMom
algorithm, with the difference being the beta update statement presented in
line 8. The fraction $(1-t/T)$ refers to the proportion of iterations
remaining.

###  2.4 Fairness-Aware Machine Learning

Broadly, fairness-aware algorithms have been categorized into three different
groups, according to the stage in which they are performed: preprocessing, in-
processing and post-processing [2, 1, 14]. Preprocessing techniques modify the
training data by resampling [15, 16, 17, 18], relabelling [19, 17] or
transforming/perturbing the data [20, 21]. In-processing methods directly
train fair machine learning models by modifying the optimization problem. This
is usually achieved by either adding a fair regularizer to the objective
function or by adding fairness constraints to the optimization problem [22,
23, 24]. Finally, post-processing approaches apply transformations to the
output of the model to achieve fair predictions [25, 26]. The algorithm
proposed in this work falls into the in-processing category.

Many notions of fairness have been proposed for supervised learning and
specifically for classification tasks [27, 28]. Broadly, fairness metrics can
be divided into two main groups: group fairness and individual fairness [29,
30, 31, 32]. The algorithms that focus on group fairness in machine learning
are based on the notion of sensitive attributes, such as gender or race, which
should not have influence on the algorithms’ predictions. A sensitive
attribute contains privileged and unprivileged groups (man/women, White/Black)
that have more/less probability of receiving a certain outcome by the
algorithm [2, 1]. Group fairness states that privileged and unprivileged
groups should be equally treated by the algorithm. On the other hand,
individual fairness notions aim to give similar predictions to similar
individuals. In this work, we focus on optimizing group fairness to attenuate
classification bias.

For the metrics considered, we assume that each training dataset, $D$,
contains:

  * •

$S$ \- the sensitive attribute (e.g. race) that contains privileged groups
(e.g. White) represented as $1$ and unprivileged groups (e.g. Black)
represented as $0$;

  * •

$Y$ \- a target class where $1$ is the positive class and $0$ is the negative
class (e.g. ”won’t recidividate”, ”will recidivate”);

  * •

$\hat{Y}$ \- the predicted class where $1$ is the positive class and $0$ is
the negative class.

Different fairness metrics can be defined with respect to a sensitive
attribute, $S$. Statistical Parity (SP) requires the prediction to be
statistically independent of the sensitive attribute. A predictor has SP [21,
23] if the proportion of individuals that were predicted to receive a positive
output is equal for two groups: an unprivileged group and a privileged group.

$SP=\frac{P[\hat{Y}=1\mid S=0]}{P[\hat{Y}=1\mid S=1]}$ (2)

As SP may never be aligned with a perfect predictor $\hat{Y}=Y$ [33], there
are other group fairness metrics based on confusion based metrics conditioned
on the true outcome $Y$. In other words, these metrics require the prediction
to be conditionally independent from the sensitive attribute, given the actual
outcome. In particular, a predictor has Equal Opportunity (EO) [34] if
privileged and unprivileged groups have equal True Positive Rates.

$EO=\frac{P[\hat{Y}=1\mid S=0,Y=1]}{P[\hat{Y}=1\mid S=1,Y=1]}$ (3)

A predictor has Equality of Odds (EQO) [34] if the probability of a person in
the positive class being correctly assigned a positive outcome and the
probability of a person in a negative class being incorrectly assigned a
positive outcome is equal for both groups. The EQO is a metric that measures
the mean of the True Positive Rate and the False Positive Rate ratios between
the two groups as follows:

$EQO=\frac{P[\hat{Y}=1\mid S=0,Y=y]}{P[\hat{Y}=1\mid S=1,Y=y]},\quad
y\in\\{0,1\\}$ (4)

All of the metrics presented have an ideal value of 1. When a value is bigger
than 1, it means that the unprivileged class became the privileged class. In
these cases, for a metric $F$, $\frac{1}{F}$ is calculated instead.

###  2.5 Fair Federated Learning Challenges

There are several challenges of developing fairness-aware algorithms in
Federated Learning due to its intrinsic characteristics.

####  2.5.1 Data Heterogeneity

While centralized machine learning batches can typically be assumed to be IID
(independent and identically distributed), this assumption may not hold for
Federated Learning settings. Since each client has its own private dataset, it
may not be representative of the global distribution and thus can lead to the
introduction or exacerbation of bias in the global model [35].

####  2.5.2 Restricted Information

Federated Learning requires the training data to be stored locally and only
accessible to the clients in order to protect their privacy. Without accessing
the necessary information about the raw training data of the clients and their
sensitive attributes, the Federated Learning server cannot apply current fair
centralized machine learning solutions which require this information on a
global level to achieve fair classification [36].

####  2.5.3 Aggregation Algorithms

The aggregation algorithms used in the server may introduce bias based on
whether the aggregator performs an equal or weighted average [35]. For
example, the algorithm may give higher importance to models of clients which
contain more data, amplifying effects of under-representing unprivileged
groups in a dataset.

FAIR-FATE mitigates the data heterogeneity and aggregation algorithms
challenges by estimating a fair model update and validating the fairness of
each client participating in the federation setting. In addition, FAIR-FATE
does not need clients’ restricted information, respecting the data privacy
constraints associated with Federated Learning.

##  3 Related Work

Few efforts have been made in the area of fairness-aware Federated Learning.
Mugunthan and Gokul et al. [37] proposed a method which generates bias-free
synthetic datasets at the server using local generators received from the
clients and retrains the model to achieve fairer results. Zhang et al. [36]
use a deep multi-agent reinforcement learning framework and an aggregation
procedure which optimizes both the accuracy and the fairness of the global
model. Du et al. [38] assign reweighing values for each data sample and
incorporate an agnostic fairness constraint to achieve group fairness. Zeng
et. al [39] propose a bi-level optimization algorithm that minimizes a
reweighted loss function based on the difference between each group’s loss.
However, [38] and [39] require prior knowledge to determine the reweighing
function, hence, relying on a secure protocol mechanism.

Abay et al. [35] propose to apply three existing fair machine learning
techniques to the Federated Learning setting. The first is to use the local
reweighthing algorithm which was proposed in [17] where, for each client, the
weights of each sample are computed using the ratio of the expected
probability to the observed probability of the sample’s sensitive attribute.
The second is to use a global reweighing technique where, at each
communication round, each party agrees to share their sensitive attributes and
sample counts with the aggregator to compute the global weights. The third one
is the use of an in-processing fairness-aware regularization term in the
training objective which was first proposed in [22] for centralized machine
learning. However, studies have shown that local debiasing strategies are
ineffective in the presence of data heterogeneity [40].

Similar to our work, other works have focused on proposing strategies for
aggregating the local models in order to improve fairness [40, 41]. Kanaparthy
et al. [40] propose simple strategies for aggregating the local models based
on different heuristics such as using the model which provides the least
fairness loss for a given fairness notion or using the model with the highest
ratio of accuracy with fairness loss. Ezzeldin et al. [41] propose a method to
achieve global group fairness via adjusting the weights of different clients
based on their local fairness metric. However, this work assumes that there is
a local debiasing method at each client. Mehrabi et al. [42] propose FedVal
that is a simple aggregation strategy which performs a weighted averaged of
the clients models based on scores according to fairness or performance
measures on a validation set. This work is similar to the ”FairAvg” strategy
proposed in [40].

To the best of our knowledge, we have yet to see a fairness-aware machine
learning approach that uses Momentum to estimate a fair update of the global
model. Since Momentum-based solutions have been used to help overcoming
oscillations of noisy gradients, we use a fairness-aware Momentum term to
overcome the oscillations of non-fair gradients. In addition, many works,
including [35, 41] violate privacy restrictions in Federated Learning since
the clients have to share different types of information with the server such
as their local fairness metric values and other datasets’ statistics. Instead,
FAIR-FATE uses a validation dataset in the server to evaluate the clients’
models, thus respecting privacy Federated Learning constraints. Moreover, many
works, including [41] use all clients at each federation round, which does not
mimic real-world scenarios and might bias results. Furthermore, FAIR-FATE is
flexible since it does not rely on any fairness local strategy at each client,
contrary to the works in [41, 35]. Finally, very few works consider multiple
data heterogeneity scenarios (non-IID), which is a characteristic of Federated
Learning settings.

##  4 FAIR-FATE: Fair Federated Learning with Momentum

FAIR-FATE is a novel fair Federated Learning algorithm developed in this work
which consists of a new approach of aggregating the clients’ local models in a
fair manner using a fairness-aware Momentum term that has the objective of
overcoming the oscillations of non-fair gradients. In this approach, the
server has access to a small validation set. Given an update from a client,
the server can use the validation set to verify whether the client’s update
would improve the global model’s fairness [43]. As such, at each communication
round, the validation set is used to compare the fairness of the current
global model against the fairness of the client’s local models. The metric
used to evaluate each model on the validation set is denoted as $F$.

Two model updates are calculated on the server: $\alpha_{N}$ and $\alpha_{F}$.
$\alpha_{N}$ represents the global model update and is the same as $\alpha$ in
Algorithm 3. On the other hand, $\alpha_{F}$ is a weighted average of the
client’s updates which have higher fairness than the server on the validation
set, given by:

$\alpha_{F}=\sum_{k=1}^{|K_{tFair}|}\frac{{F}_{\theta_{t+1}^{k}}}{{F}_{total}}(\theta_{t+1}^{k}-\theta_{t}),\
\textnormal{where}\quad{F}_{total}=\sum_{k=1}^{|K_{tFair}|}{F}_{\theta_{t+1}^{k}},$
(5)

where $K_{tFair}$ represents the clients which have higher fairness than the
server on the validation set. As such, the weighted average gives higher
importance to models with higher fairness values on the validation set.

Similar to the FedDemon algorithm, in order to decay the total contribution of
a gradient to all future updates, $\beta_{t}$ is updated as follows:

$\beta_{t}=\beta_{0}*\frac{(1-\frac{t}{T})}{(1-\beta_{0})+(\beta_{0}(1-\frac{t}{T})}$
(6)

where $\beta_{0}$ is the initial Momentum parameter.

Afterwards, the Momentum update, $v_{t+1}$, is calculated by summing a
fraction of the previous update, $v_{t}$, and the global model fair update,
$\alpha_{F}$, as follows:

$v_{t+1}=\beta_{t}v_{t}+(1-\beta_{t})\alpha_{F},$ (7)

where $\beta_{t}$ controls the amount of the global fair update against the
previous update.

Finally, the global model, $\theta_{t+1}$, is updated by summing the previous
model, $\theta_{t}$, with the fair Momentum update, $v_{t+1}$, and the normal
update, $\alpha_{N}$, as follows:

$\theta_{t+1}=\theta_{t}+\lambda_{t}v_{t+1}+(1-\lambda_{t})\alpha_{N},$ (8)

where $\lambda_{t}$ has the objective of controlling the amount of estimated
fairness against the actual model update. It follows an exponential growth
calculated as follows:

$\lambda_{t}=\lambda_{0}(1+\rho)^{t},\qquad\lambda_{t}\leq MAX,$ (9)

where $\rho$, $\lambda_{0}$ and $MAX$ are hyperparameters that can be tuned
which represent the growth rate, the initial amount, and the upper bound of
$\lambda_{t}$, respectively. By exponentially increasing $\lambda$, FAIR-FATE
allows that in the early stages of training, the model will prioritize the
optimization of the main objective function using $\alpha_{N}$. In the latter
stages, when it is expected that the model has a good performance and there is
a better Momentum estimate, FAIR-FATE will have a higher value of $\lambda$
and, as a consequence, it will prioritize the global model’s fair update,
$\alpha_{F}$. Regarding the $MAX$ hyperparameter, a higher value will
prioritize fair model updates, while a lower value will take more the model
performance into consideration. The Appendices sections present more
information regarding hyperparameter tuning and their influence on fairness vs
model-performance trade-off.

Figure 2 and Algorithm 5 present the FAIR-FATE algorithm.

Figure 2: FAIR-FATE’s outline Algorithm 5 FAIR-FATE

1: Initialize global model: $\theta_{t}$, number of rounds: $T$, Initial
Momentum parameter: $\beta_{0}$, growth rate: $\rho$, initial amount:
$\lambda_{0}$, Momentum update: $v_{t}$ ($v_{0}=0$).

2: for each round $t$ = 1,2,…, $T$ do

3: Select $K_{t}$ = random subset of clients $K$ ($|K_{t}|<|K|$)

4: for each client $k\in K_{t}$ do

5: $\theta_{t+1}^{k}$ = Algorithm 2 ($\theta_{t}$)

6: end for

7: $K_{tFair}\in K_{t},$ where ${F}_{\theta_{t+1}^{k}}>={F}_{\theta_{t}}$

8: ${F}_{total}=\sum_{k=1}^{|K_{tFair}|}{F}_{\theta_{t+1}^{k}}$

9:
$\alpha_{F}=\sum_{k=1}^{|K_{tFair}|}\frac{{F}_{\theta_{t+1}^{k}}}{{F}_{total}}(\theta_{t+1}^{k}-\theta_{t})$

10:
$\alpha_{N}=\sum_{k=1}^{|K_{t}|}\frac{n_{k}}{n}(\theta_{t+1}^{k}-\theta_{t})$

11:
$\beta_{t}=\beta_{0}*\frac{(1-\frac{t}{T})}{(1-\beta_{0})+(\beta_{0}(1-\frac{t}{T})}$

12: $v_{t+1}=\beta_{t}v_{t}+(1-\beta_{t})\alpha_{F}$

13: $\lambda_{t}=\lambda_{0}(1+\rho)^{t},\qquad\lambda_{t}\leq MAX$

14: $\theta_{t+1}=\theta_{t}+\lambda_{t}v_{t+1}+(1-\lambda_{t})\alpha_{N}$

15: end for

##  5 Experiments

In this section, a comprehensive set of experiments to evaluate FAIR-FATE is
conducted in a Federated Learning scenario. We start by describing the
datasets used to evaluate FAIR-FATE. Afterwards, the solution for studying the
algorithms under different data heterogeneities is presented. Moreover, the
implementation and setup details are explained in order to reproduce the
experimental results. Finally, the results and discussion are presented.

###  5.1 Datasets

FAIR-FATE is evaluated on four real-world datasets which have been widely used
in the literature [2] to access the performances of fairness-aware algorithms:
the COMPAS [7], the Adult [8], the Law School [9] and the Dutch Census [10]
datasets.

##### COMPAS

The COMPAS dataset includes data about the risk assessment tool used in
Broward County, Florida [7]. It includes information such as the number of
juvenile felonies and the charge degree of the current arrest for 6167
individuals. The prediction task is to calculate the recidivism outcome,
indicating whether the people will be rearrested within two years after the
first arrest. It contains sensitive attributes such as race, where Caucasian
is considered to be the privileged class.

##### Adult

The Adult dataset contains information about individuals from the 1994 U.S
Census [8]. It includes 48842 instances of personal information where the
prediction task is to determine whether a person’s income exceeds $50K/yr or
not. It contains 14 attributes and sensitive attributes such as gender, where
male is considered to be the privileged class.

##### Law School

The Law School dataset contains information from a Law School Admission
Council survey across 163 law schools in the United States in 1991, including
the law school admission records. The prediction task is to predict whether a
candidate would pass the bar exam. It contains 20 798 students and 12
features, with race being the sensitive attributes, where White is considered
to be the privileged class.

##### Dutch Census

The Dutch Census dataset contains 189 725 samples records which represent
aggregated groups of people in the Netherlands in 2001. The prediction task is
to determine a person’s occupation which can be categorized as high level
(prestigious) or low level profession. The dataset is often preprocessed by
dropping instances of under-aged people and individuals with unknown or middle
level profession. The resulting preprocessed dataset contains 60 420
instances. It has 12 features and contains sensitive attributes such as
gender, where male is considered to be the privileged class.

The appendices sections present the pie charts of the four full datasets that
are divided into slices to illustrate the numerical proportion of the outcomes
of the different groups of sensitive attributes.

###  5.2 Non-identical Client Data

Because of its decentralized nature, Federated Learning exacerbates the
problem of bias since clients’ data distributions can be very heterogeneous.
This means that there may exist a client that contains a very high
representation of datapoints belonging to an unprivileged class with a
positive outcome (e.g. women’s income exceeding $50K/yr) and another client
that has a very low representation of the same group.

Following the works in [4, 41], we study the algorithms under different
sensitive attribute distributions across clients. We use a non-IID synthesis
method based on the Dirichlet distribution proposed in [4] and apply it in
configurable sensitive attribute distribution such as the work in [41] but
including the target distributions as well. More specifically, for each
sensitive attribute value $s$ and target value $y$, we sample $p_{s,y}\sim
Dir(\alpha)$ and allocate a portion $p_{s,y,k}$ of the datapoints with $S=s$
and $Y=y$ to client $k$. The parameter $\alpha$ controls the heterogeneity of
the distributions in each client, where $\alpha\longrightarrow\infty$ results
in IID distributions [41].

(a)

(b)

Figure 3: Examples of heterogeneous data distributions on the COMPAS dataset
using race as the sensitive feature for 10 clients with $\alpha=0.5$ and
$\alpha\rightarrow{}\infty$

Figure 3 presents different examples of heterogeneous data distributions on
the COMPAS dataset using race as the sensitive feature for 10 clients with
$\alpha=0.5$ and $\alpha\rightarrow{}\infty$. On one hand it can be observed
that for $\alpha=0.5$, different clients have very different representations
of privileged and unprivileged groups and positive and negative outcomes. For
example, while client 10 has about 40% of the Caucasians that won’t
recidivate, client 2 has only about 10%. Moreover, it can be observed that
different clients have different number of datapoints. On the other hand, for
$\alpha\rightarrow{}\infty$, the representations of the different groups for
different clients are the same.

###  5.3 Implementation and Setup Details

We train a fully connected feed-forward neural network for binary
classification on the described datasets with one hidden layer with 10 $tanh$
units. On the local clients models, mini-batch stochastic gradient descent and
the standard binary cross-entropy loss are used.

The data instances are split into 60-20-20 for training, validation and test.
The training data is divided into private training datasets, one for each
client. The private training datasets owned by the clients are used to train
the local models. The validation set is used to calculate the fairness of the
models for the fair Momentum update as explained in Section 4. The testing
dataset is used to evaluate the model performance and fairness of the proposed
approach and the baselines. The results presented correspond to the average
values of the last communication round over 10 runs. All configuration setups
are summarized in Table I. 111Source code can be found at
https://github.com/teresalazar13/FAIR-FATE.

Variables | Datasets
---|---
COMPAS | Adult |  Law School |  Dutch Census
Number of clients | 10 | 15 | 12 | 20
Number of clients per round | 3 | 5 | 4 | 6
Number of runs | 10
$\alpha$ | 0.5, 1.0
Communication rounds | 100
Local epochs | 10
Local batch size | 10
Local learning rate | 0.01
$\lambda_{0}$ | 0.1, 0.5
$\rho$ | 0.04, 0.05
$MAX$ | 0.8, 0.9, 1.0
$\beta_{0}$ | 0.8, 0.9, 0.99
$F$ | SP, EO, EQO
TABLE I: Experimental setup for the COMPAS, Adult, Law School and Dutch Census
datasets.

The following algorithms are used as the baselines 222We also implemented the
algorithm proposed in [42] but did not present the results since it assumed
all clients were participating in every round. Since in our experimental setup
only a small number of clients participates in each round and the data is very
heterogeneous, the results were very similar to using a local debiasing
strategy such as the baseline FedAvg+LR baseline from [35].:

  * •

FedAvg \- the classical Federated Averaging algorithm presented in Algorithm
1;

  * •

FedMom \- the Federated Averaging with Momentum presented in Algorithm 3;

  * •

FedDemon \- the Federated Averaging with Momentum Decay presented in Algorithm
4;

  * •

FedAvg+LR \- the fair Federating Learning approach proposed in [35] that was
described in Section 2 where each client uses the local reweighing technique;

  * •

FedAvg+GR \- the fair Federating Learning approach proposed in [35] that was
described in Section 2 where each client uses the global reweighing technique;

  * •

FedVal \- the fair Federating Learning approach proposed in [42] that was
described in Section 2 where the server performs a weighted average based on
the validation scores. 333Similar to FAIR-FATE, we optimize the work in [42]
for different metrics to allow for a better comparison. In addition, the
scores are calculated based using the specific metric that is being optimized
plus a small epsilon term that is added to ensure that at the initial rounds
(when fairness levels might be too small) some models are considered on the
averaging. This work is similar to the ”FairAvg” strategy proposed in [40].

###  5.4 Experimental Results

Figure 4 presents the results over communication rounds under different
sensitive attribute distributions and random splits on the COMPAS and the
Adult datasets, considering either race or gender as the sensitive attributes.
The appendices sections present the results for the Law School and the Dutch
Census datasets. The algorithms are analysed from two aspects: the model
performance and the fairness. The accuracy and the F1Score are used to measure
model performance and to evaluate fairness the SP, EO and EQO are used.

It can be observed that FAIR-FATE is able to surpass the baselines in terms of
fairness in almost every configuration, especially in heterogeneous
configurations ($\alpha=0.5$ and $\alpha=1.0$), without neglecting the
classification performance. Moreover, the stability of the algorithms
decreases in the presence of heterogeneous data. However, FAIR-FATE is able to
overcome the oscillations of non-fair gradients using a fairness-aware
Momentum term and, as a consequence, the fairness performance does not drop
after some communication rounds.

(a)

(b)

Figure 4: Performance over communication rounds on the COMPAS and the Adult datasets for the different algorithms under different $\alpha$ heterogeneity levels and random (RND) splits. Metric | Algorithm | COMPAS (race) | Adult (gender)
---|---|---|---
$\alpha$ | RND | $\alpha$ | RND
0.5 | 1.0 | 0.5 | 1.0
ACC | FedAvg | 0.60+-0.04 | 0.64+-0.03 | 0.68+-0.01 | 0.79+-0.05 | 0.83+-0.01 | 0.84+-0.01
FedMom | 0.62+-0.05 | 0.63+-0.04 | 0.69+-0.01 | 0.83+-0.02 | 0.82+-0.01 | 0.82+-0.01
FedDemon | 0.68+-0.01 | 0.68+-0.01 | 0.68+-0.01 | 0.84+-0.01 | 0.84+-0.01 | 0.84+-0.01
FedAvg+LR | 0.62+-0.04 | 0.65+-0.02 | 0.68+-0.01 | 0.81+-0.03 | 0.82+-0.01 | 0.84+-0.01
FedAvg+GR | 0.62+-0.04 | 0.65+-0.03 | 0.68+-0.01 | 0.80+-0.03 | 0.82+-0.01 | 0.84+-0.01
FedVal ($F=SP$) | 0.61+-0.04 | 0.64+-0.03 | 0.68+-0.01 | 0.75+-0.10 | 0.83+-0.01 | 0.84+-0.01
FedVal ($F=EO$) | 0.62+-0.05 | 0.66+-0.03 | 0.68+-0.01 | 0.78+-0.06 | 0.82+-0.03 | 0.84+-0.01
| FedVal ($F=EQO$) | 0.62+-0.04 | 0.66+-0.03 | 0.68+-0.01 | 0.76+-0.07 | 0.82+-0.03 | 0.84+-0.01
|  FAIR-FATE ($F=SP$) | 0.57+-0.02 | 0.61+-0.04 | 0.66+-0.01 | 0.70+-0.17 | 0.80+-0.06 | 0.80+-0.02
|  FAIR-FATE ($F=EO$) | 0.63+-0.04 | 0.65+-0.02 | 0.67+-0.01 | 0.69+-0.11 | 0.78+-0.06 | 0.83+-0.02
|  FAIR-FATE ($F=EQO$) | 0.63+-0.04 | 0.65+-0.03 | 0.67+-0.01 | 0.75+-0.09 | 0.79+-0.05 | 0.77+-0.01
F1Score | FedAvg | 0.64+-0.08 | 0.68+-0.09 | 0.73+-0.01 | 0.47+-0.19 | 0.57+-0.10 | 0.64+-0.02
FedMom | 0.68+-0.11 | 0.71+-0.03 | 0.73+-0.01 | 0.57+-0.12 | 0.44+-0.11 | 0.49+-0.09
FedDemon | 0.73+-0.01 | 0.73+-0.01 | 0.73+-0.01 | 0.64+-0.02 | 0.64+-0.02 | 0.64+-0.02
FedAvg+LR | 0.65+-0.11 | 0.70+-0.06 | 0.72+-0.01 | 0.47+-0.21 | 0.51+-0.12 | 0.61+-0.01
FedAvg+GR | 0.66+-0.09 | 0.68+-0.08 | 0.72+-0.01 | 0.46+-0.18 | 0.52+-0.11 | 0.60+-0.01
FedVal ($F=SP$) | 0.71+-0.04 | 0.71+-0.07 | 0.73+-0.01 | 0.44+-0.17 | 0.59+-0.10 | 0.64+-0.02
FedVal ($F=EO$) | 0.64+-0.13 | 0.70+-0.06 | 0.73+-0.01 | 0.51+-0.18 | 0.61+-0.09 | 0.64+-0.02
| FedVal ($F=EQO$) | 0.70+-0.04 | 0.72+-0.05 | 0.73+-0.01 | 0.49+-0.18 | 0.61+-0.09 | 0.64+-0.02
|  FAIR-FATE ($F=SP$) | 0.72+-0.01 | 0.73+-0.02 | 0.71+-0.02 | 0.39+-0.18 | 0.53+-0.06 | 0.59+-0.04
|  FAIR-FATE ($F=EO$) | 0.73+-0.01 | 0.73+-0.02 | 0.71+-0.02 | 0.54+-0.06 | 0.54+-0.14 | 0.62+-0.02
|  FAIR-FATE ($F=EQO$) | 0.74+-0.02 | 0.72+-0.03 | 0.71+-0.02 | 0.53+-0.11 | 0.53+-0.13 | 0.55+-0.01
SP | FedAvg | 0.59+-0.34 | 0.86+-0.17 | 0.83+-0.04 | 0.41+-0.30 | 0.27+-0.10 | 0.31+-0.02
FedMom | 0.75+-0.23 | 0.83+-0.20 | 0.82+-0.03 | 0.39+-0.16 | 0.63+-0.24 | 0.46+-0.20
FedDemon | 0.83+-0.04 | 0.83+-0.04 | 0.83+-0.04 | 0.31+-0.03 | 0.31+-0.03 | 0.31+-0.03
FedAvg+LR | 0.93+-0.10 | 0.91+-0.08 | 0.94+-0.02 | 0.69+-0.19 | 0.70+-0.10 | 0.67+-0.05
FedAvg+GR | 0.76+-0.28 | 0.87+-0.16 | 0.94+-0.02 | 0.66+-0.27 | 0.64+-0.20 | 0.67+-0.05
| FedVal ($F=SP$) | 0.87+-0.17 | 0.88+-0.13 | 0.83+-0.04 | 0.71+-0.20 | 0.52+-0.18 | 0.32+-0.02
|  FAIR-FATE ($F=SP$) | 1.00+-0.01 | 0.98+-0.01 | 0.95+-0.03 | 0.82+-0.16 | 0.81+-0.11 | 0.79+-0.13
|  | +7% | +7% | +1% | +11% | +11% | +8%
EO | FedAvg | 0.46+-0.34 | 0.81+-0.19 | 0.85+-0.05 | 0.51+-0.27 | 0.68+-0.21 | 0.78+-0.04
FedMom | 0.74+-0.24 | 0.73+-0.34 | 0.83+-0.05 | 0.66+-0.26 | 0.65+-0.17 | 0.77+-0.17
FedDemon | 0.84+-0.05 | 0.84+-0.05 | 0.84+-0.05 | 0.78+-0.04 | 0.78+-0.04 | 0.78+-0.04
FedAvg+LR | 0.77+-0.31 | 0.91+-0.08 | 0.98+-0.03 | 0.66+-0.21 | 0.69+-0.15 | 0.76+-0.03
FedAvg+GR | 0.54+-0.38 | 0.84+-0.21 | 0.97+-0.03 | 0.55+-0.28 | 0.71+-0.14 | 0.75+-0.04
| FedVal ($F=EO$) | 0.58+-0.34 | 0.83+-0.22 | 0.85+-0.05 | 0.72+-0.15 | 0.80+-0.12 | 0.79+-0.04
|  FAIR-FATE ($F=EO$) | 0.95+-0.06 | 0.96+-0.02 | 0.95+-0.03 | 0.86+-0.09 | 0.95+-0.02 | 0.90+-0.07
|  | +11% | +5% | -3% | +8% | +15% | +11%
EQO | FedAvg | 0.39+-0.32 | 0.77+-0.19 | 0.76+-0.06 | 0.36+-0.21 | 0.42+-0.15 | 0.48+-0.03
FedMom | 0.65+-0.26 | 0.71+-0.26 | 0.73+-0.05 | 0.47+-0.24 | 0.53+-0.21 | 0.60+-0.19
FedDemon | 0.75+-0.06 | 0.75+-0.06 | 0.75+-0.06 | 0.48+-0.04 | 0.48+-0.04 | 0.48+-0.04
FedAvg+LR | 0.78+-0.29 | 0.87+-0.11 | 0.93+-0.03 | 0.58+-0.23 | 0.75+-0.09 | 0.80+-0.05
FedAvg+GR | 0.59+-0.26 | 0.82+-0.21 | 0.93+-0.04 | 0.46+-0.30 | 0.69+-0.19 | 0.80+-0.05
| FedVal ($F=EQO$) | 0.62+-0.29 | 0.83+-0.17 | 0.76+-0.06 | 0.59+-0.21 | 0.56+-0.12 | 0.49+-0.03
|  FAIR-FATE ($F=EQO$) | 0.94+-0.05 | 0.93+-0.03 | 0.92+-0.04 | 0.78+-0.10 | 0.79+-0.11 | 0.82+-0.10
|  | +16% | +6% | -1% | +19% | +4% | +2%
TABLE II: Results for the COMPAS and Adult datasets under different $\alpha$
heterogeneity levels and random (RND) splits. The blue cells and the red cells
represent the improvements of FAIR-FATE over the baselines and the
improvements of the baselines over FAIR-FATE, respectively, with the darker
cells representing statistically significant improvements.

Table II presents the corresponding results of the last communication round
for the COMPAS and the Adult datasets. Similarly, the appendices sections
present the results for the Law School and the Dutch Census datasets.
Moreover, the fairness improvements of the best algorithm over the second best
are presented. In addition, the Wilcoxon Signed-Rank one-sided test is
performed with significance level of 0.05 to verify the statistical
significance of the best improvements. The blue cells and the red cells
represent the improvements of FAIR-FATE over the best baseline and the
improvements of the baselines over FAIR-FATE, respectively, with the darker
cells representing statistically significant improvements.

For all four datasets and the fairness metrics considered, FAIR-FATE surpasses
the baselines in terms of fairness in 86% of the times, with 58% of those
being statistically significant. In addition, the baselines slightly
outperformed FAIR-FATE in terms of fairness only 11% of the times. Moreover,
it can be observed that the baselines only surpassed FAIR-FATE for random
train-test splits, which do not represent typical Federated Learning settings.
On the other hand, for heterogeneous configurations, FAIR-FATE was always able
to improve the fairness performance.

Regarding the COMPAS dataset, FAIR-FATE was able to surpass the baselines 78%
of the times, with 57% of those being statistically significant. In addition,
the average improvements for all of the configurations for this dataset was
5%. In particular, for $\alpha=0.5$, FAIR-FATE presented substantial
improvements: 7% for SP, 11% for EO, and 16% for EQO. In addition, FAIR-FATE
was able to maintain the classification performance compared to the baselines.

With regard to the Adult dataset, FAIR-FATE was always able to surpass the
baselines with an average improvement of fairness of 10%. In particular, for
$\alpha=0.5$, FAIR-FATE presented substantial improvements: 11% for SP, 8% for
EO, and 19% for EQO. However, the accuracy results dropped, which is not
ideal. We believe that with more tuning of the hyperparameters better values
of model performance can be obtained.

In addition, considering all datasets, regarding the different $F$ metrics
that are being optimized, it can be concluded that FAIR-FATE presented higher
improvements for $F=SP$ and $F=EO$ than for $F=EQO$ with average improvements
of 8%, 9% and 4%, respectively. This might be justified by the fact that EQO
considers both True Positive Rates and False Positive Rates ratios.

Finally, the Appendices sections present more information regarding the
fairness vs model-performance trade-offs considering the different
hyperparameters.

To sum up, it can be concluded that FAIR-FATE improves the fairness of the
Federated Learning models under different heterogeneity configurations when
compared to other solutions.

##  6 Conclusion and Future Work

We proposed FAIR-FATE: a fairness-aware Federated Learning algorithm that uses
a novel aggregation technique that estimates a fair Momentum update and
validates the fairness of each client participating in the federation. In
addition, FAIR-FATE does not need clients’ restricted information, respecting
the data privacy constraints associated with Federated Learning. Furthermore,
FAIR-FATE is a flexible algorithm that does not rely on any local fairness
strategy at each client.

To the best of our knowledge, this is the first approach in machine learning
that aims to achieve fairness using a fair Momentum estimate. Revisiting the
question presented at the start of this work:

> _Can a fairness-aware Momentum term be used to overcome the oscillations of
> noisy non-fair gradients in Federated Learning?_

Experimental results on four real-world datasets demonstrate that FAIR-FATE
can effectively increase the fairness results under different data
distributions compared to state-of-the-art fair Federated Learning approaches
by using a fairness-aware Momentum term.

Interesting directions for future work are: testing FAIR-FATE using multiple
fairness metrics and multiple sensitive attributes simultaneously; extending
the work to various application scenarios such as regression or clustering;
focusing on individual fairness notions.

We hope that this work inspires the community to develop more fairness-aware
algorithms, in particular, in Federated Learning, and consider Momentum
techniques for addressing bias in machine learning.

## Acknowledgments

This work is funded by the FCT - Foundation for Science and Technology,
I.P./MCTES through national funds (PIDDAC), within the scope of CISUC R&D Unit
- UIDB/00326/2020 or project code UIDP/00326/2020 and by European Social Fund,
through the Regional Operational Program Centro 2020. This work was supported
in part by the Portuguese Foundation for Science and Technology (FCT) Research
Grants 2021.05763.BD.

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|  Teresa Salazar received a B.S. degree in Informatics Engineering from the
University of Coimbra in 2018 and a M.S. degree in Informatics from the
University of Edinburgh in 2019 with specialization in Machine Learning and
Natural Language Processing. Since 2020, she is attending the Doctoral Program
in Information Science and Technology at the University of Coimbra, being a
member of the Centre for Informatics and Systems of the University of Coimbra.
Her primary research interests are mainly focused on topics in fairness and
imbalanced data, natural language processing, and information retrieval.
---|---
|  Miguel Fernandes received a B.S. degree in Informatics Engineering from the
University of Coimbra and a M.S. degree in Intelligent Systems from the same
university in 2020. Since 2021, he is attending the Doctoral Program in
Information Science and Technology at the University of Coimbra, being a
member of the Centre for Informatics and Systems of the University of Coimbra.
His research interests include Federated Learning, Condition-Based Maintenance
and Neural Networks.
---|---
|  Helder Araujo is a Professor at the Department of Electrical and Computer
Engineering of the University of Coimbra. His research interests include
computer vision applied to robotics, robot navigation and visual servoing. He
has also worked on non central camera models, including aspects related to
pose estimation, and their applications. Recently he has started work on the
development of vision systems applied to medical endoscopy with focus on
capsule endoscopy.
---|---
|  Pedro Henriques Abreu received the Informatics Engineering degree and the
Ph.D. degree in Informatics Engineering from the University of Porto, in 2006
and 2011, respectively. He is currently an Assistant Professor with the
Department of Informatics Engineering, University of Coimbra and full member
of cognitive and media system group of the Centre for Informatics and Systems
of the University of Coimbra. He has authored more than 80 publications in
highly rated JCR journals and international conferences. His research
interests include medical informatics and personal healthcare systems applied
to oncology.
---|---

##  Appendix A Datasets

Figures 5, 6, 7 and 8 present the pie charts of the four full datasets that
are divided into slices to illustrate the numerical proportion of the outcomes
of the different groups of sensitive attributes. In addition, the SP* of the
training dataset using $P[Y=1\mid S=s]$ instead of $P[\hat{Y}=1\mid S=s]$. For
all the datasets the proportion of individuals that receive a positive output
is bigger for the privileged groups than the unprivileged groups in both
datasets since the value of SP is not close to 1, with the discrepancy being
higher in the Adult and in the Dutch Census datasets. In addition, the
percentage of positive outcomes is significantly different, with the Adult
dataset containing only about 23.9% of people receiving a positive outcome,
the COMPAS dataset containing 54.4%, the Law School dataset containing 89%
(”pass”), and the Dutch Census containing 47.6% (”1”).

Figure 5: Pie Chart of the COMPAS dataset representing the outcomes of the
different groups of sensitive attributes. Figure 6: Pie Chart of the Adult
dataset representing the outcomes of the different groups of sensitive
attributes. Figure 7: Pie Chart of the Law School dataset representing the
outcomes of the different groups of sensitive attributes. Figure 8: Pie Chart
of the Dutch Census dataset representing the outcomes of the different groups
of sensitive attributes.

##  Appendix B Results for the Law School and Dutch Census Datasets

Figure 9 and Table III present the results for the different algorithms on the
Law School and the Dutch Census datasets.

(a)

(b)

Figure 9: Performance over communication rounds on the Law School and the Dutch Census datasets for the different algorithms. Metric | Algorithm | Law School (race) | Dutch Census (gender)
---|---|---|---
$\alpha$ | RND | $\alpha$ | RND
0.5 | 1.0 | 0.5 | 1.0
ACC | FedAvg | 0.89+-0.01 | 0.89+-0.02 | 0.90+-0.01 | 0.81+-0.02 | 0.82+-0.01 | 0.83+-0.00
FedMom | 0.89+-0.01 | 0.90+-0.01 | 0.90+-0.01 | 0.81+-0.01 | 0.82+-0.01 | 0.83+-0.00
FedDemon | 0.90+-0.01 | 0.90+-0.01 | 0.90+-0.01 | 0.82+-0.01 | 0.82+-0.01 | 0.82+-0.01
FedAvg+LR | 0.89+-0.00 | 0.88+-0.03 | 0.89+-0.01 | 0.81+-0.03 | 0.82+-0.01 | 0.82+-0.03
FedAvg+GR | 0.90+-0.01 | 0.88+-0.01 | 0.89+-0.01 | 0.81+-0.02 | 0.82+-0.01 | 0.82+-0.00
FedVal ($F=SP$) | 0.88+-0.03 | 0.89+-0.01 | 0.90+-0.01 | 0.78+-0.04 | 0.82+-0.01 | 0.83+-0.00
FedVal ($F=EO$) | 0.80+-0.12 | 0.88+-0.02 | 0.90+-0.00 | 0.81+-0.02 | 0.82+-0.01 | 0.83+-0.00
| FedVal ($F=EQO$) | 0.85+-0.07 | 0.89+-0.02 | 0.99+-0.00 | 0.80+-0.03 | 0.82+-0.01 | 0.83+-0.00
|  FAIR-FATE ($F=SP$) | 0.89+-0.00 | 0.89+-0.01 | 0.89+-0.01 | 0.74+-0.08 | 0.78+-0.04 | 0.81+-0.01
|  FAIR-FATE ($F=EO$) | 0.90+-0.01 | 0.89+-0.03 | 0.90+-0.00 | 0.77+-0.07 | 0.77+-0.08 | 0.82+-0.00
|  FAIR-FATE ($F=EQO$) | 0.90+-0.01 | 0.90+-0.01 | 0.90+-0.01 | 0.75+-0.08 | 0.76+-0.06 | 0.81+-0.01
F1Score | FedAvg | 0.94+-0.01 | 0.94+-0.01 | 0.95+-0.01 | 0.80+-0.02 | 0.81+-0.02 | 0.82+-0.01
FedMom | 0.94+-0.01 | 0.94+-0.01 | 0.94+-0.01 | 0.80+-0.03 | 0.80+-0.02 | 0.82+-0.00
FedDemon | 0.95+-0.01 | 0.95+-0.01 | 0.95+-0.01 | 0.82+-0.01 | 0.82+-0.01 | 0.82+-0.01
FedAvg+LR | 0.94+-0.00 | 0.93+-0.02 | 0.94+-0.00 | 0.79+-0.02 | 0.80+-0.02 | 0.79+-0.01
FedAvg+GR | 0.94+-0.01 | 0.94+-0.01 | 0.94+-0.00 | 0.79+-0.02 | 0.80+-0.02 | 0.79+-0.01
FedVal ($F=SP$) | 0.93+-0.02 | 0.94+-0.01 | 0.95+-0.01 | 0.79+-0.02 | 0.80+-0.02 | 0.82+-0.01
FedVal ($F=EO$) | 0.87+-0.10 | 0.93+-0.01 | 0.95+-0.01 | 0.80+-0.02 | 0.80+-0.02 | 0.82+-0.01
| FedVal ($F=EQO$) | 0.91+-0.05 | 0.94+-0.01 | 0.94+-0.01 | 0.80+-0.02 | 0.80+-0.02 | 0.82+-0.01
|  FAIR-FATE ($F=SP$) | 0.94+-0.00 | 0.94+-0.00 | 0.94+-0.00 | 0.77+-0.04 | 0.77+-0.02 | 0.78+-0.02
|  FAIR-FATE ($F=EO$) | 0.94+-0.01 | 0.94+-0.02 | 0.94+-0.01 | 0.78+-0.04 | 0.78+-0.04 | 0.80+-0.01
|  FAIR-FATE ($F=EQO$) | 0.94+-0.01 | 0.94+-0.01 | 0.94+-0.01 | 0.76+-0.04 | 0.76+-0.03 | 0.78+-0.01
SP | FedAvg | 0.87+-0.13 | 0.88+-0.09 | 0.89+-0.02 | 0.60+-0.12 | 0.61+-0.09 | 0.60+-0.02
FedMom | 0.91+-0.12 | 0.91+-0.07 | 0.91+-0.04 | 0.62+-0.09 | 0.59+-0.10 | 0.60+-0.01
FedDemon | 0.91+-0.03 | 0.91+-0.03 | 0.91+-0.03 | 0.60+-0.01 | 0.60+-0.01 | 0.60+-0.01
FedAvg+LR | 0.96+-0.04 | 0.95+-0.06 | 0.98+-0.01 | 0.72+-0.04 | 0.72+-0.04 | 0.74+-0.02
FedAvg+GR | 0.95+-0.05 | 0.97+-0.03 | 0.98+-0.01 | 0.72+-0.10 | 0.73+-0.08 | 0.74+-0.02
| FedVal ($F=SP$) | 0.89+-0.11 | 0.92+-0.05 | 0.89+-0.02 | 0.67+-0.13 | 0.70+-0.09 | 0.60+-0.01
|  FAIR-FATE ($F=SP$) | 1.00+-0.00 | 0.99+-0.01 | 0.99+-0.01 | 0.78+-0.11 | 0.84+-0.10 | 0.74+-0.03
|  | +4% | +2% | +1% | +6% | +12% | 0%
EO | FedAvg | 0.57+-0.41 | 0.79+-0.30 | 0.91+-0.02 | 0.83+-0.08 | 0.89+-0.07 | 0.90+-0.02
FedMom | 0.52+-0.47 | 0.73+-0.39 | 0.92+-0.03 | 0.86+-0.05 | 0.88+-0.13 | 0.90+-0.02
FedDemon | 0.92+-0.03 | 0.92+-0.03 | 0.92+-0.03 | 0.91+-0.02 | 0.91+-0.02 | 0.91+-0.02
FedAvg+LR | 0.67+-0.46 | 0.76+-0.41 | 0.99+-0.01 | 0.93+-0.05 | 0.91+-0.04 | 0.91+-0.02
FedAvg+GR | 0.86+-0.30 | 0.77+-0.41 | 0.99+-0.01 | 0.90+-0.07 | 0.90+-0.05 | 0.91+-0.02
| FedVal ($F=EO$) | 0.62+-0.29 | 0.88+-0.12 | 0.91+-0.03 | 0.86+-0.05 | 0.90+-0.05 | 0.90+-0.02
|  FAIR-FATE ($F=EO$) | 0.96+-0.04 | 0.98+-0.01 | 0.96+-0.01 | 0.94+-0.04 | 0.99+-0.01 | 0.97+-0.03
|  | +4% | +6% | -3% | +1% | +8% | +6%
EQO | FedAvg | 0.50+-0.32 | 0.67+-0.29 | 0.75+-0.05 | 0.59+-0.17 | 0.62+-0.15 | 0.58+-0.02
FedMom | 0.49+-0.39 | 0.62+-0.34 | 0.79+-0.08 | 0.63+-0.16 | 0.60+-0.14 | 0.58+-0.02
FedDemon | 0.78+-0.05 | 0.78+-0.05 | 0.78+-0.05 | 0.59+-0.02 | 0.59+-0.02 | 0.59+-0.02
FedAvg+LR | 0.64+-0.44 | 0.74+-0.40 | 0.97+-0.02 | 0.78+-0.05 | 0.80+-0.06 | 0.82+-0.03
FedAvg+GR | 0.83+-0.16 | 0.82+-0.19 | 0.97+-0.02 | 0.76+-0.14 | 0.78+-0.12 | 0.82+-0.03
| FedVal ($F=EQO$) | 0.64+-0.25 | 0.78+-0.12 | 0.74+-0.04 | 0.62+-0.13 | 0.73+-0.14 | 0.82+-0.03
|  FAIR-FATE ($F=EQO$) | 0.92+-0.06 | 0.95+-0.04 | 0.90+-0.04 | 0.81+-0.06 | 0.89+-0.08 | 0.83+-0.04
|  | +9% | +13% | -7% | +3% | +9% | +1%
TABLE III: Results for the Law School and the Dutch Census datasets under
different $\alpha$ heterogeneity levels and random (RND) splits. The blue
cells and the red cells represent the improvements of FAIR-FATE over the
baselines and the improvements of the baselines over FAIR-FATE, respectively,
with the darker cells representing statistically significant improvements.

Regarding the Law School dataset, FAIR-FATE was able to surpass the baselines
78% of the times, with 89% of those being statistically significant. In
addition, the average improvements of fairness were 3%. Moreover, FAIR-FATE
was able to maintain the classification performance for all configurations. In
this dataset, the baselines also presented good fairness results, leaving a
small margin for improvements.

With respect to the Dutch Census dataset, FAIR-FATE was able to surpass the
baselines 78% of the times. The average improvements for all of the
configurations for this dataset were only 5%. Similar to the Law School
dataset, in this dataset the baselines also presented good fairness results,
leaving a small margin for improvements. Reasons for this might have to do
with the fact that this dataset has a higher number of instances (189 725) and
is balanced with regard to the target class.

##  Appendix C Hyperparameter Tuning and Fairness vs Model Performance Trade-
offs

In multi-objective optimization, it is usual to consider different trade-offs
satisfying the different objectives. The following Figures present FAIR-FATE’s
different fairness-accuracy trade-offs, considering different the different
hyperparameter values from the experimental setup.

On a broad level, it can be observed that the results produce a shape similar
to a pareto front, especially for random splits and for $F=SP$. However, for
$F=EO$ and $F=EQO$ this phenomenon rarely occurs in all the datasets. This
might be justified by the fact that these metrics consider the actual
predictions ($\hat{Y}$), and, consequently, are more aligned with the
performance of the algorithm.

In addition, it can be observed that for the Law School dataset the results
for the different hyperparameters are very similar to each other. This might
have to do with the fact that this dataset is very imbalanced towards the
positive class and the fact that this dataset presents a high value of SP* on
the training dataset.

###  C.1 $MAX$ Hyperparameter

Figures 10, 11, 12 and 13 present FAIR-FATE’s fairness-accuracy trade-offs
considering the $MAX$ hyperparameter on the COMPAS, Adult, Law School and
Dutch Census datasets, respectively.

It can be observed that generally this hyperparameter can be used to select
different trade-offs, with higher values of $MAX$ resulting in higher values
of fairness and lower values of accuracy, and lower values of $MAX$ resulting
in lower values of fairness and higher values of accuracy. However, in some
situations, when $MAX=1.0$ the results lead to lower values of both accuracy
and fairness.

Figure 10: FAIR-FATE’s fairness-accuracy trade-offs on the COMPAS dataset
considering the $MAX$ hyperparameter. Figure 11: FAIR-FATE’s fairness-accuracy
trade-offs on the Adult dataset considering the $MAX$ hyperparameter. Figure
12: FAIR-FATE’s fairness-accuracy trade-offs on the Law School dataset
considering the $MAX$ hyperparameter. Figure 13: FAIR-FATE’s fairness-accuracy
trade-offs on the Dutch Census dataset considering the $MAX$ hyperparameter.

###  C.2 $\lambda_{0}$ Hyperparameter

Figures 14, 15, 16 and 17 present FAIR-FATE’s fairness-accuracy trade-offs
considering the $\lambda_{0}$ hyperparameter on the COMPAS, Adult, Law School
and Dutch Census datasets, respectively.

For the Adult and COMPAS datasets, it can be observed that generally a low
value of $\lambda_{0}$ may lead to a better fairness-accuracy trade-off. In
these datasets, a high value of $\lambda_{0}$ may create instability in the
initial rounds and lead to sub-optimal performance. Reasons for this might
have to do with the fact that the COMPAS dataset has a smaller number of
instances and that the Adult dataset has a very low value of SP* on the
training dataset.

On the other hand, for the Dutch Census dataset a higher value of
$\lambda_{0}$ generally leads to higher values of fairness without degrading
the accuracy. Reasons for this might have to do with the fact that this
dataset contains a very high number of instances.

Figure 14: FAIR-FATE’s fairness-accuracy trade-offs on the COMPAS dataset
considering the $\lambda_{0}$ hyperparameter. Figure 15: FAIR-FATE’s fairness-
accuracy trade-offs on the Adult dataset considering the $\lambda_{0}$
hyperparameter. Figure 16: FAIR-FATE’s fairness-accuracy trade-offs on the Law
School dataset considering the $\lambda_{0}$ hyperparameter. Figure 17: FAIR-
FATE’s fairness-accuracy trade-offs on the Dutch Census dataset considering
the $\lambda_{0}$ hyperparameter.

###  C.3 $\rho$ Hyperparameter

Figures 18, 19, 20 and 21 present FAIR-FATE’s fairness-accuracy trade-offs
considering the $\rho$ hyperparameter on the COMPAS, Adult, Law School and
Dutch Census datasets, respectively.

It can be observed that for random splits, a higher value of $\rho$ can be
used to obtain higher fairness values without decreasing the accuracy too
much. However, for heterogeneous configurations, a smaller value of $\rho$
should be used instead. Hence, the value of $\rho$ should be chosen according
to the heterogeneity of the data with respect to the sensitive attributes.

Figure 18: FAIR-FATE’s fairness-accuracy trade-offs on the COMPAS dataset
considering the $\rho$ hyperparameter. Figure 19: FAIR-FATE’s fairness-
accuracy trade-offs on the Adult dataset considering the $\rho$
hyperparameter. Figure 20: FAIR-FATE’s fairness-accuracy trade-offs on the Law
School dataset considering the $\rho$ hyperparameter. Figure 21: FAIR-FATE’s
fairness-accuracy trade-offs on the Dutch Census dataset considering the
$\rho$ hyperparameter.

###  C.4 $\beta_{0}$ Hyperparameter

Figures 22, 23, 24 and 25 present FAIR-FATE’s fairness-accuracy trade-offs
considering the $\rho$ hyperparameter on the COMPAS, Adult, Law School and
Dutch Census datasets, respectively.

For this hyperparameter it is more difficult to analyse its impact on the
fairness vs model performance trade-off and more experimentation is needed to
access it.

Figure 22: FAIR-FATE’s fairness-accuracy trade-offs on the COMPAS dataset
considering the $\beta_{0}$ hyperparameter. Figure 23: FAIR-FATE’s fairness-
accuracy trade-offs on the Adult dataset considering the $\beta_{0}$
hyperparameter. Figure 24: FAIR-FATE’s fairness-accuracy trade-offs on the Law
School dataset considering the $\beta_{0}$ hyperparameter. Figure 25: FAIR-
FATE’s fairness-accuracy trade-offs on the Dutch Census dataset considering
the $\beta_{0}$ hyperparameter.