# Personalized Federated Learning for Statistical Heterogeneity

1stMuhammad Firdaus  Department of AI Convergence
Pukyong National University
Busan, Republic of Korea
0000-0003-0104-848X  2nd Kyung-Hyune Rhee  Division of Computer Engineering
and AI
Pukyong National University
Busan, Republic of Korea
0000-0003-0466-8254

###### Abstract

The popularity of federated learning (FL) is on the rise, along with growing
concerns about data privacy in artificial intelligence applications. FL
facilitates collaborative multi-party model learning while simultaneously
ensuring the preservation of data confidentiality. Nevertheless, the problem
of statistical heterogeneity caused by the presence of diverse client data
distributions gives rise to certain challenges, such as inadequate
personalization and slow convergence. In order to address the above issues,
this paper offers a brief summary of the current research progress in the
field of personalized federated learning (PFL). It outlines the PFL concept,
examines related techniques, and highlights current endeavors. Furthermore,
this paper also discusses potential further research and obstacles associated
with PFL.

###### Index Terms:

federated learning, personalization, non-IID, statistical heterogeneity,
privacy-preserving

##  I Introduction

Recently, we have observed favorable advancements through the utilization of
machine learning (ML) support. ML facilitates model training by consolidating
and aggregating client data on a central server. However, these techniques
encounter significant privacy concerns, including the potential for sensitive
data exposure, the risk of single points of failure (SPoF), and the
substantial resource burdens associated with collecting and storing training
data. Moreover, due to the introduction of data privacy regulations like the
Health Insurance Portability and Accountability Act (HIPAA) [1] and the
General Data Protection Regulation (GDPR) [2], there is a growing demand for
safeguarding privacy in AI, as highlighted by Cheng et al. [3]. To tackle
these challenges, the concept of federated learning (FL) emerged as a
promising approach. FL allows distributed mobile devices to collectively train
models without centralizing the training data, thus maintaining local data on
the client’s devices. Furthermore, FL showcases its effectiveness and privacy
preservation by enabling collaborative local training and shared updates to
the machine learning model, all while safeguarding the confidentiality of
individual datasets [4].

However, despite their advantages, the existing methods of FL encounter
several difficulties. These challenges include statistical heterogeneity,
resulting in poor convergence and a lack of personalization due to the
influence of non-independent and identically distributed (non-IID) data
distribution across clients. As a result, these challenges have a detrimental
impact on the overall performance of the global FL model when applied to
individual clients with eminent performance outputs. Consequently, some
clients are reluctant or even unwilling to participate in and contribute to
the collaborative FL training. In order to address these issues, the concept
of personalized federated learning (PFL) has been introduced [5]. This paper
provides an overview of the current research landscape in PFL, highlighting
its high-level aspects. Additionally, the paper briefly outlines the core
concept of PFL and delves into the associated methodologies and ongoing
research. Lastly, we also discuss observations and challenges in the field of
PFL.

The paper’s structure is organized in the following manner: Section 2 provides
an explanation of the background knowledge pertaining to FL and the impact of
non-IID data. Section 3 provides a concise overview of the concept of PFL.
Subsequently, Section 4 provides an overview of the survey conducted on
pertinent methodologies and ongoing research efforts pertaining to PFL. In
Section 5, we examine several observations and concerns. Finally, this work is
concluded in Section 6.

##  II Preliminaries

###  II-A Federated Averaging (FedAvg)

In the context of the client-server architecture in traditional ML, the
process of training models is consistently executed on the server [6]. Clients
solely perform as data providers, whereas the server also accomplishes data
training and aggregation. However, several concerns are associated with the
classical ML strategy, especially regarding user privacy. Therefore, Google
introduced federated averaging (FedAvg) as a new communication-efficient
optimization algorithm for FL. FedAvg [7] is an effective approach for
training models in a distributed manner. This method enables mobile devices to
collaborate in training the models without the need to centralize the training
data, hence allowing the local data to be stored on the respective mobile
devices.

Figure 1: The illustration of FedAvg procedures

The illustration of the FedAvg processes is depicted in Figure 1. Initially,
the server, acting as a provider of models, transmits the global model to the
clients. Participating clients obtain the global model from the aggregator
server, train the current global model on their local data, and then upload
the resulting model to the aggregator server. In its role as an aggregator
server, the central server collects and consolidates all the model updates
from the clients in order to generate an updated global model for the
following iteration. Therefore, the FedAvg algorithm efficiently enhances the
privacy of clients by preventing some attacks that aim to get unauthorized
access to the local training data [8]. Additionally, it demonstrates improved
communication efficiency compared to traditional distributed stochastic
gradient descent (SGD) methods by reducing the number of communication rounds.
Moreover, the efficacy of FedAvg is evident in various domains of learning,
including predictive models in health [9], low latency vehicle-to-vehicle
communication [10], vocabulary estimation [11], and next word prediction [12].
In each of these instances, FedAvg consistently demonstrates enhanced
performance.

###  II-B Statistical Heterogeneity: The Effect of Non-IID Data

While FL offers numerous benefits for various real-world use cases, it also
presents several challenges due to the diverse data distribution among
clients. This diversity leads to a deficiency in personalization and poor
convergence. The data distribution among clients is notably dissimilar,
resulting in a situation where the data distribution is mostly non-IID.
Consequently, this statistical disparity complicates the training of a single
model capable of performing effectively for all clients. Furthermore, the
presence of non-IID data can substantially impact the accuracy of the FedAvg
algorithm. The local objectives of each client do not align with the global
optimum due to the significant differences in data distribution between
individual local datasets and the overarching global distribution. As a
consequence, a drift occurs in the updated local models[13]. In other words,
each model is updated during the local training phase towards its specific
local optima, which could be far away from the global optima. Primarily, when
numerous noteworthy local updates take place (indicating a considerable count
of local epochs), the resultant aggregated model may potentially drift from
the global optima [14],[15]. As a result, the convergence of the global model
is notably less precise compared to the scenario where data distribution is
independent and identical (IID).

##  III Personalized Federated Learning (PFL) Concept

The concept of PFL comes from shortcomings created by statistical
heterogeneity and the non-IID data distribution that force the need for
personalization methods in the current FL setting. The accuracy of FedAvg-
based techniques suffers a substantial decrease when training non-IID data,
mainly due to client drift. The study conducted by Tan et al. [16] presents
two distinct approaches for achieving PFL. The approaches encompass the global
model personalization strategy, which involves the training of a singular
global model, and the learning personalized models strategy, which entails the
individual training of PFL models. The majority of personalization techniques
for a global model FL [17] often involve two separate procedures: the initial
stage entails the collaborative development of a global model, followed by the
subsequent phase, which entails utilizing the client’s private data to
personalize the global model [18]. In summary, the PFL technique commonly
adopts FedAvg as the de facto method for training in broad FL environments.
The difference is that after the training process, the trained global model is
personalized through additional training and local adaptation steps tailored
to the local dataset of the client. The objective of PFL is stated as follows.

$\min_{w\in\mathbb{R}^{d}}F\left(w\right)=\frac{1}{M}\sum_{m=1}^{M}f_{m}({w_{m}}+\frac{\mu}{\alpha_{i}})$
(1)

where $F_{m}$ is a loss function associated with the $m-$th clients;
$w\in\mathbb{R}^{d}$ encodes the parameters of local model $w$, $\mu$ is the
regularization parameter, and $\alpha_{p}$ represents the local adaptation
steps in iteration $i$.

On the other hand, the learning personalized model strategy aims to apply
different learning algorithms and modify the process of FL aggregation to
achieve PFL by classifying it into architecture-based and similarity methods.
Moreover, the objective of PFL is to collaboratively train personalized models
for a particular group of clients by leveraging the non-IID nature of their
respective data distribution along with simultaneously protecting their
private information [19]. Further, the three following goals must all be
addressed simultaneously rather than separately in improving a more valuable
PFL for practical concerns [20]:

  * •

Attaining swift model convergence within a limited set of training iterations.

  * •

Enhancing personalized models that are advantageous to a significant portion
of clients.

  * •

Formulating more precise overarching models that aid clients possessing
restricted private data in achieving personalization.

##  IV Survey of Related Methods and Current Works for PFL

In this section, we survey the related methods and current works of PFL by
separating them into three classifications (i.e., based on data, model, and
similarity) for manageable knowledge. Moreover, we provide a classification
diagram of PFL that can be seen in Figure 2. Finally, Table 1 summarizes the
state-of-the-art methods for the PFL research area.

Figure 2: The classification diagram of PFL

###  IV-A Data-based Methods

Data-based methods desire to diminish the client data distributions’
statistical heterogeneity, which is encouraged by the client drift problem.
This method consists of capability-based client selection and data
augmentation that supports improving the global FL model’s generalization
performance.

#### Capability-based Client Selection

: In each FL communication round, these methods optimize the subset of
involved clients to enhance the model generalization performance and
facilitate sampling from a more uniform distribution of client’s data. The
authors in [21] proposed FAVOR, a client selection algorithm based on deep
Q-learning formulation that aims to minimize the number of communication
rounds while maximizing accuracy. To mitigate the impact of non-IID data,
FAVOR was designed to selectively choose a certain number of clients to
participate in each training round. Nevertheless, deep Q-learning demands
computationally higher algorithms that lead to increased computation overhead.

#### Data Augmentation

: These approaches are simple to implement in the conventional FL setting that
is offered to improve data statistical homogeneity and reduce data inequality.
In the study conducted by Zhao et al. [22], a data sharing approach was
introduced. This technique aims to disseminate a proportionate subset of
global data while addressing the issue of imbalanced allocation of client data
classes among individual clients. However, potential privacy leakage is the
main challenge since the client’s data distribution is frequently shared
during training.

###  IV-B Model-based Methods

Model-based methods obey the prevailing FL training setting that involves
training using a single global model. This method consists of meta-learning,
transfer learning, regularization with fine-tuning, knowledge distillation,
and parameter decoupling.

#### Meta-learning

: This method strives to solve new tasks with only a few training examples by
generating highly-adaptable models and applying training on multiple learning
tasks that can further learn. Moreover, the meta-learning method, also known
as initialization-based learning, provides fast adaptation to new tasks with
better generalization. Authors in [20] highlight the relationship between
FedAvg and model agnostic meta-learning (MAML). The MAML algorithm is executed
in two distinct phases, namely meta-testing and meta-training. They note that
solely optimizing for global model accuracy may not lead to strong
personalization results.

TABLE I: Summary of the state-of-the-art methods for the PFL research.

Paper Ref. Year PFL Protocols PFL Methods Key Contributions Remarks Wang, et
al. [21] 2020 FAVOR Capability-based client selection Enhancing the model
generalization performance. High communication and computation cost Zhao, et
al. [22] 2018 Based on FedAvg Data augmentation These methods are easy to
enforce in the standard FL setting. Potential privacy leakage is the main
challenge Jiang, et al. [20] 2019 MAML on FedAvg Meta-learning Highlight the
relationship between model agnostic meta-learning (MAML) and FedAvg. A single
global model setting with centralized approach Chen, et al. [23] 2020
FedHealth Transfer learning Reducing the domain dissimilarity between the
local models and global model to improve personalization. A single global
model setting and potential attacks considerations Li, et al. [14] 2020
FedProx Regularization with fine-tuning Evaluates the dissimilarity between
the global FL model and local models. A single global model setting with
centralized approach Li and wang, et al. [24] 2019 FedMD Knowledge
distillation Supports resource heterogeneity for each client with
communication-efficient. Requires the representative proxy datasets and
benchmark Arivazhagan, et al. [25] 2019 FedPer Parameter decoupling Simple
formulation and allows some model layers stored locally while the remaining
layers are trained using FL. Difficult to determine optimal system and
requires the representative proxy datasets and benchmark Sattler, et al. [26]
2020 FMTL Context-based client clustering Clustering approaches are beneficial
when client partitions are inherently present. Requires higher computational
overhead and potential attacks considerations Smith, et al. [27] 2017 MOCHA
Multi-task learning Utilize client relationships in pairs to discover models
that are comparable for similar clients. Requires the representative proxy
datasets and benchmark Peterson, et al. [28] 2019 Not defined Interpolation-
based Mixture Model leverages a mixture of local models and global model. A
single global model with centralized approach

#### Transfer Learning

: This method transfers the trained model parameters, called knowledge, from a
source to a destination to avoid the necessity to construct models from
scratch. Moreover, it lowers the domain dissimilarity between the local and
global models to improve personalization. In [23], the authors propose
FedHealth, a novel federated transfer learning framework tailored for wearable
healthcare, to address these challenges. They transfer the formerly trained
global model to each device after first training a global model using standard
FL. Additionally, FedHealth leverages FL for data aggregation and employs
transfer learning to build relatively personalized models.

#### Regularization with Fine-tuning

: Model regularization is a standard method to improve convergence and prevent
overfitting during model training. In order to tackle client drift,
regularization is implemented between the local models and global model. The
work in [14] proposed FedProx to alter the effect of updated models by
considering the disparity between the local models and the global FL model.
FedProx is a generalized and re-parametrized version of FedAvg, designed to
address heterogeneity in federated networks.

#### Knowledge Distillation

: The primary purpose of this method is to support resource heterogeneity for
each client with communication-efficient. The authors in[24] proposed FedMD
protocol to design a high degree of flexibility for clients through PFL that
facilitates creating various models utilizing their private data. This
framework accommodates scenarios where each participant designs their own
model due to intellectual property concerns and varying tasks and data.

#### Parameter Decoupling

: This method seeks to gain PFL from the global FL model parameters by
decoupling the local private model parameters. In [25], the authors suggested
that some model layers can be stored locally while the remaining layers are
trained using FL. In this sense, this approach includes a base model along
with a personalization layer to address the challenge of statistical
heterogeneity in FL.

###  IV-C Similarity-based Methods

Similarity-based methods seek to accomplish PFL by mapping client
associations. Every client learns a personalized model, while the associated
clients learn similar models. PFL has investigated many client relationship
types, including clustering takes into account group-level client
relationships, whereas model interpolation and multi-task learning take into
account pairwise client ties.

#### Context-based Client Clustering

: When client partitions are inherently present, clustering approaches are
beneficial. It is more appropriate to use a multi-model method where an FL
model is trained for every similar group of clients. Hierarchical clustering
has been added to FL in [26] as a postprocessing step. The clients in FL are
grouped together using an optimal partitioning technique that relies on the
cosine similarity of the gradient updates generated by the clients.

#### Multi-task Learning

: Smith et al. [27] introduced MOCHA, an algorithm designed to address the
challenge of federated multitask learning. This method aims to learn both user
task settings and a similarity matrix concurrently. The distributed multitask
MOCHA algorithm tackles several learning challenges, such as communication
restrictions, stragglers, and fault tolerance. They concentrate on the convex
case, and it is opaque how they involve deep learning models that are not
convex when powerful duality is no longer assured.

#### Interpolation-based Mixture Model

: This method is a simple formulation that leverages a mixture of global model
and local models. In [28], the authors suggested using methods from various
expert literature. Their method of model interpolation learns an interpolation
weight depending on features to improve model accuracy for all users. They
validate their approach using both real and synthetic data, highlighting its
effectiveness in enhancing FL performance.

##  V Discussion and Remarks

Recently, PFL research has been garnering attention due to its potential to
tackle the fundamental challenges of current FL, including statistical
heterogeneity that leads to poor convergence and a lack of personalization
because of the influence of non-IID data distribution across clients. However,
based on the explanation in Table I about the survey on PFL methods, we can
see that several remarks need to be considered for future directions, as
follows:

#### Reliable computation with multiple models

: The existing PFL methods still rely on a centralized strategy where the
server orchestrates all processes, demanding high communication and incurring
computational costs. Furthermore, most methods employ a single global model,
which is not suitable and poses challenges for achieving PFL due to notable
dissimilarities in data distribution among clients (i.e., non-IID). To address
the challenges mentioned, a solution that combines edge computing with a
multi-model approach should be considered. This approach aims to reduce
communication overhead, adapt models to client-specific data distributions,
and enhance the overall efficiency and effectiveness of PFL.

#### Privacy-preserving

: While the PFL framework shows potential as a more favorable approach in
contrast to the traditional centralized model training framework, it
encounters notable difficulties, particularly concerning the selection of
users for the model training procedure and the technique of augmenting data.
Moreover, the problem shifts even worse when malicious clients exist and
conduct various adversarial activities, such as providing incorrect
information messages known as false data injection attacks [14] during
collaborative training. Therefore, several privacy techniques, such as secure
multiparty computation, homomorphic encryption, differential privacy, and
trusted execution environment (TEE), might be leveraged for PFL in further
research.

#### Trustworthy PFL

: Recent studies have shown FL flaws that may possibly endanger client
security and privacy [29]. Hence, it is of utmost importance to study attack
methods on FL and formulate protective strategies to counteract them, thereby
guaranteeing the security of the FL system. In order to develop resilient PFL
approaches, additional research is necessary to delve into various forms of
attacks and corresponding safeguards, especially as more intricate PFL
protocols and structures are being introduced. Additionally, designing
incentive mechanisms is a viable study area for achieving these goals to
maintain fairness and motivate clients’ contributions. Blockchain, as a
distributed ledger technology, may be used to construct decentralized
incentive systems [30], [31] . These systems can play a crucial role in
promoting the development of future collaborative PFL scenarios

#### Representative Datasets and Benchmark

: The growth of the PFL field depends on representative datasets. Additional
datasets encompassing a wider range of modalities like sensor data, video, and
audio, and encompassing a more diverse set of machine learning tasks pertinent
to real-world use cases, are necessary to underpin PFL investigations.
Moreover, conducting performance benchmarking holds equal importance as a
pivotal factor in fostering the continuous advancement of the PFL research
domain in the long run.

##  VI Conclusion

The notion of personalized federated learning is introduced to tackle
statistical heterogeneity that leads to poor convergence and a lack of
personalization due to the influence of non-IID data distribution among
clients. This paper comprehensively summarizes the present research landscape
in personalized federated learning (PFL). It also offers a concise explanation
of the PFL concept and investigates associated techniques and ongoing efforts,
encompassing data-based, model-based, and similarity-based methods. Lastly,
this paper also discusses the need for further research and development in the
field of privacy-preserving and trustworthy PFL. Additionally, it highlights
the need to use representative datasets and benchmarks to ensure the
effectiveness and reliability of PFL methods.

## Acknowledgments

This research was supported by the Republic of Korea’s MSIT (Ministry of
Science and ICT), under the ICT Convergence Industry Innovation Technology
Development Project (2022-0-00614) supervised by the IITP and partially
supported by the Basic Science Research Program through the National Research
Foundation of Korea (NRF) funded by the Ministry of Education (No.
2021R1I1A3046590).

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