A Systematic Survey on Federated Semi-supervised Learning

1 Introduction

Federated learning (FL) [Li et al., 2023b] is an advanced framework that enables multiple clients to collaboratively train a shared global model with help of a server while keeping their data local, thus prioritizing data privacy and security [Yin et al., 2022; Zhang et al., 2023d]. This distributed learning paradigm is increasingly recognized for its capability to mitigate challenges across various sectors, including edge computing [Nguyen et al., 2021] and healthcare [Nguyen et al., 2023], where data privacy is paramount. However, traditional FL approaches often assume the availability of fully labeled datasets, an assumption that rarely holds in practice. Given real-world constraints such as lack of time, expertise, or motivation, users often leave large portions of data unlabeled [Jin et al., 2023].

Addressing these practical challenges necessitates a shift towards federated semi-supervised learning (FSSL). Semisupervised learning (SSL), successful in centralized settings, employs both labeled and unlabeled data by exploiting the latent information within the latter to enhance model performance [Yang et al., 2023]. Transferring these SSL strategies to the federated paradigm yields FSSL, which aims to leverage both labeled and unlabeled data in a federated context. FSSL can thus enhance model efficacy in real-world applications where labeled data is scarce, maximizing the use of abundant yet underexploited unlabeled data in federated learning environments.

Integrating SSL into the FL framework introduces multifaceted challenges. First, FL's decentralized architecture, which safeguards data privacy by keeping data on multiple local clients, impedes the direct application of conventional SSL methods due to restricted access to global data. Second, the non-IID (independently and identically distributed) nature of FL data complicates the effective use of SSL, as biased data distributions can negatively affect label predictions. Third, the distribution of labeled and unlabeled data across the server and clients introduces varying scenarios, each necessitating tailored algorithmic approaches. Different configurations of labeled/unlabeled data locations demand distinct algorithmic solutions to address the specific challenges. Thus, the incorporation of SSL into FL motivates the development of novel strategies to overcome these obstacles.

Despite the accelerated progress recently observed in FSSL, there is still a noticeable absence of a comprehensive survey. Therefore, to elucidate the intersection of these two impactful paradigms, we conduct a systematic examination of FSSL methodologies, aiming to integrate the privacypreserving features of FL with the efficiency of SSL in utilizing unlabeled data. First, we outline several common and basic problem settings in FSSL with clear illustrations. Second, we delve into each scenario, analyzing its unique challenges, presenting a general solution framework, and reviewing some representative works published in prestigious journals and conferences. Third, we identify existing research gaps and propose potential trajectories for future exploration in the promising domain of FSSL. We recognize that a recent survey [Jin et al., 2023] investigates FL from a broader perspective of label efficient learning. However, our work stands apart by narrowly concentrating on FL specifically within the SSL framework, offering a more detailed analysis.

2 Preliminaries

2.1 Federated Learning

Federated learning is designed to train machine learning models using data distributed across various participants, with the primary goal of safeguarding data privacy. In a classic federated learning setting, a shared global model is trained across multiple devices, often referred to as clients, ensuring the privacy of their local data. Instead of sending data to a centralized server, the learning happens directly at the client level. Depending on how the data is split across participants, FL can be categorized into horizontal federated learning (HFL) and vertical federated learning (VFL). In HFL, all clients possess data with identical feature spaces, such as images from different users. In VFL, however, clients hold data pertaining to the same users but with different feature spaces, exemplified by a bank and a retail company holding transaction records and purchase history of the same users, respectively. In this paper, following the majority of existing research efforts, we primarily focus on HFL.

Formally, we assume a traditional FL scenario with N clients, and each client i has its own local fully-labeled dataset Di = {(xji , yj i )}ni j=1 with ni = |Di|. Then, the global training objective is defined as follows,

Here, local loss ℓi(Di; θ) represents how well the model fits the local data Di, and the global loss is a weighted average of all local losses. wi is the weight assigned to the i-th client, which can be set as wi = ni ∑Ni=1 ni in FedAvg [McMahan et al., 2017]. It ensures clients with more samples have a proportionately greater influence on the global model.

The training procedure of FL typically involves multiple communication rounds, each comprising two key phases: local training and server aggregation. In the local training phase, a subset of participants is chosen to receive the current global model, which they then refine using their own data. In the following server aggregation phase, these participants transmit their updated model parameters back to the server. The server aggregates these parameters and obtains an updated global model for the next communication round.

2.2 Semi-supervised Learning

Semi-supervised learning (SSL) leverages both a small amount of labeled data and a large amount of unlabeled data during training. It is an effective way to improve learning accuracy without the need for fully labeled datasets. Given the training dataset D = L ∪ U with limited labeled samples L = {(xi, yi)}ni=1 and abundant unlabeled samples U = {xi}mi=1 (m≫ n). Then the overall training objective is defined as follows,

Here, ℓs denotes the per-example supervised loss, e.g., crossentropy for classification, ℓu denotes the per-example unsupervised loss, and λ is the trade-off parameter.

Several SSL methods are widely adopted in the literature. Pseudo-label [Lee and others, 2013] employs the class prediction with the highest probability that surpasses a predefined confidence threshold as the pseudo-label ˆ yi for unlabeled samples. These pseudo-labels are subsequently utilized for supervised training on the unlabeled data, formulated as ℓu(xi; θ) = ℓl(xi, ˆ yi; θ). Consistency regularization enforces the predictions from the augmented examples and original instances to output the same class label [Xie et al., 2020].

3 Problem Settings in FSSL

Incorporating SSL into FL renders the problem more intricate and multifaceted. Figure 1 sketches the various common scenarios that often arise in real-world applications. For simplicity's sake, we make the following assumptions for FSSL.

1. All clients hold data, either labeled, unlabeled, or both.
2. The server can possess data as well.
3. The system as a whole must contain a mix of labeled and unlabeled data, excluding solely one data type.

For the first assumption, clients without data do not actively contribute to the learning process. For the second, the server may hold labeled or unlabeled data, which can improve model performance. We simplify by not considering the server holding both data types, treating it as a simple combination of the two scenarios. The third assumption aligns with the semi-supervised framework. We concentrate on four basic FSSL scenarios based on the locations of labeled and unlabeled data (Figure 2), treating other situations as combinations of these. We consider a system with N clients.

• Label-at-all-client All the data are located on the client side D = {Di}Ni=1 and each client has both labeled and unlabeled data Di = Li ∪ Ui. Here, Li = {(xji , yj i )}ni j=1 with ni = |Li| and Ui = {xki }mi k=1 with mi = |Ui|.
• Label-at-partial-client All the data are located on the client side, but some clients only have labeled data while the remaining ones have unlabeled data D = {Dli }Nl i=1 ∪ {Du i }Nu i=1 with Nu+Nl = N. Here, Dli = {(xji , yj i )}ni j=1 with ni = |Dli | and Du i = {xki }mi k=1 with mi = |Du i |.
• Label-at-server All the data are located on both the client and the server sides D = Ds ∪ {Di}Ni=1 . The server has the labeled data only Ds = {(xjs , yjs )}ns j=1 with ns = |Ds| while each client has the unlabeled data only Di = {xki }mi k=1 with mi = |Di|.
• Unlabel-at-server All the data are located on both the client and the server sides D = Ds ∪ {Di}Ni=1 . The server has the unlabeled data only Ds = {xks }ms k=1 with ms = |Ds| while each client has the labeled data only Di = {(xji , yj i )}ni j=1 with ni = |Di|.

4 Approaches to FSSL

4.1 Label-at-all-client Case

Unique Challenges and Generic Solution Framework

This case is the most prevalent scenario, and it incorporates the semi-supervised learning setting into the traditional federated learning system in a most straightforward manner. Label-at-all-client case is widely applicable in real-world situations. For example, consider a company aiming to develop an object detection FL model using smartphone-captured images. The company has no access to the local data of users, and only users can annotate their images. However, it is common for users to refrain from labeling every image, resulting in a scenario where all clients possess partially labeled data, epitomizing the "label-at-all-client" setting.

A naive solution to this case involves applying existing offthe-shelf semi-supervised learning techniques at each client, coupled with the use of federated learning algorithms to aggregate the locally trained weights back to the server. The detailed training procedure is shown in Algorithm 1 and the training objective can be formulated as

However, this approach does not fully exploit the knowledge of the multiple models trained on heterogeneous data

Algorithm 1 Generic label-at-all-client FSSL framework

Input: Initialized model parameters θ = θ1

• 1: for communication round t = 1 to R do
• 2: Randomly select a subset of clients C t ⊆ {1, . . . ,N}.
• 3: for each selected client i ∈ C t in parallel do
• 4: Train a local model θt i with Di and θt using SSL.
• 5: end for
• 6: Server aggregates weights {θt i}i∈Ct and updates θt+1 .
• 7: end for

distributions. The client heterogeneity makes the simple combination of SSL and FL algorithms suffer severely from slow convergence and performance degradation. This heterogeneity manifests in two primary forms: statistical and system. The former refers to the prevalence of non-IID data, which undermines algorithmic convergence as many FL algorithms (e.g. FedAvg) are inefficient in dealing with this issue. As for the latter, the clients may have varied system capabilities and computational resources, which can lead to inconsistent client participation and exacerbate the straggler problem, where slower clients delay overall progress, thereby significantly reducing the speed of the learning algorithm.

Representative Methods

FedMatch [Jeong et al., 2021] is the first to improve upon naive combinations of FL and SSL. It incorporates an interclient consistency loss to encourage the same predictions across clients. Additionally, FedMatch divides the model parameters into two sets: one dedicated to supervised learning and the other to unsupervised learning. This disjoint learning reduces the communication overhead. FedMatch is even designed with flexibility, allowing easy adaptation to the following label-at-server case.

FedAvg-DS [Nandury et al., 2021] builds upon the foundational FedAvg algorithm by introducing a sophisticated aggregation mechanism that accounts for the diversity in updates from clients.This enhancement is particularly effective when it is combined with existing SSL methods, addressing the issue of client heterogeneity.

FedTriNet [Che et al., 2021] first pretrains the model on the labeled data using FedAvg and then utilizes a dynamic quality control mechanism to generate high-quality pseudo labels of the unlabeled data for retraining [Lin et al., 2021].

FedFAPL [Wei and Huang, 2022] derives a fairer federated model across all clients. It strategically balances the involvement of active unlabeled samples (AUS) in the local model training. By setting global numerical restrictions on AUS participation and then allocating these restrictions into personalized local constraints for each client, FedFAPL facilitates more effective local pseudo-labeling.

FedGAN [Zhao et al., 2022] adapts the Triple GAN architecture [Li et al., 2017], originally designed for conventional SSL, to the FL context. It consists of three generators and one discriminator to learn the relationship between labeled and unlabeled data effectively. Importantly, FedGAN dynamically adjusts aggregation weights of local models based on optimization difficulty posed by non-IID data distributions.

F2CMT [Wen et al., 2022] improves over the mean teacher model [Tarvainen and Valpola, 2017], a popular consistency

Algorithm 2 Generic label-at-partial-client FSSL framework

Input: Initialized model parameters θ = θ1

• 1: for communication round t = 1 to R do
• 2: Randomly select a subset of clients C t ⊆ {1, . . . ,N}.

3:

4:

for each selected client i ∈ C t in parallel do

if client i is a labeled client then

• 5: Train a local model θt i with Dli and the initialized θt .

6:

end if

• 7: if client i is an unlabeled client then

8:

9:

Train a local model θt

end if

10: end for

11: Server aggregates {θt

i}i∈Ct based on client type, gets θt+1 .

12: end for

within one single client for local training. However, it remains feasible to engage in supervised learning with labeled clients and unsupervised learning with unlabeled clients. The local models' weights can then be aggregated into the global model, taking into account the specific data type each client contributes. The detailed training procedure is shown in Algorithm 2 and the training objective can be formulated as

Representative Methods

FedIRM [Liu et al., 2021a] enhances the consistency regularization framework by introducing an inter-client relation matching strategy. The proposed learning scheme fosters coherence in learning between labeled and unlabeled clients. It ensures that the unlabeled clients mirror the class relationships observed in labeled clients and preserves the discriminative task knowledge.

Fed-Consist [Yang et al., 2021] also introduces a consistency-based method, in which different augmentations were applied to unlabeled images with their predictions similarity maximized. However, its performance significantly decreases when the proportion of unlabeled clients increases.

i with Du

i and the initialized θt .

regularization method, with a cross-clients ensemble module and a model-wise self-ensembling module. F2CMT can yield reliable teacher targets to guide the learning process of student models on local clients.

FedCPSL [Wang et al., 2023b; Wang et al., 2023c] focuses on model personalization within the FSSL framework. It introduces novel strategies such as adaptive client variance reduction, local momentum, and normalized global aggregation to combat the challenge of device heterogeneity. These strategies are designed to enhance algorithm convergence, theoretically achieving a sublinear convergence rate.

DS-FL [Itahara et al., 2023] exchanges model outputs instead of model parameters, significantly enhancing communication efficiency, especially as model sizes increase. It also presents a new model-output aggregation method designed to be robust against the heterogeneity in model outputs caused by non-IID data distributions.

FedLoKe [Zhang et al., 2023a] generates more accurate pseudo-labels with local knowledge to boost the performance of the global model in the non-IID scenarios. The local model is also trained on the pseudo-label dataset generated by the global model, transferring general knowledge to the local model and preventing it from overfitting.

4.2 Label-at-partial-client Case

Unique Challenges and Generic Solution Framework

This case can be viewed as an extreme case of the previous label-at-all-client case. In the conventional label-at-all-client setting, each client is homogeneous, containing a mix of both labeled and unlabeled data. In contrast, the label-at-partialclient case now features heterogeneous clients: some possess exclusively labeled data, while others have only unlabeled data. Here, the "semi-supervised" aspect applies at the intraclient level, with each client holding data that is either entirely labeled or completely unlabeled.

The strategies effective in the label-at-all-client situation often falter in the label-at-partial-client case due to the extreme non-IID nature of client data. The division of labeled and unlabeled data across multiple clients prevents the application of standard semi-supervised learning techniques

Algorithm 3 Generic label-at-server FSSL framework

data. The label-at-server case is quite common in real-world applications. For instance, a healthcare system may involve a central hub ("server") with domain experts and a limited number of labeled data, such as medical records, together with many rural branches ("clients") with large volumes of unlabeled data without expert annotation.

The main challenge of this case lies in the lack of direct supervision on the client side due to the disjoint distribution of labeled and unlabeled data, and thus, no classic SSL methods can be directly applied to either the client or the server. The clients now must rely on indirect supervision, such as the pseudo-labels generated based on the server's model, to learn from their unlabeled data, making the learning process less efficient and potentially less accurate. Therefore, the model is trained in a supervised manner on the server before it is distributed to the clients, as shown in Algorithm 3. The corresponding training objective is given as

Representative Methods

FedMix [Zhang et al., 2021a] designs parameter decomposition strategies for disjointed learning of labeled and unlabeled data. To alleviate the non-IID issue, FedMix proposes a novel aggregation rule, which dynamically adjusts the weight of each local model based on the client's participation frequency, thus balancing the influence of varying data distributions across clients.

This is due to the potential for the global model to become overly influenced by the unlabeled data, which can skew learning outcomes and degrade overall model performance.

RSCFed [Liang et al., 2022] addresses the uneven reliability of non-IID local clients by moving beyond straightforward aggregation of local models. It introduces a novel concept of updating the global model through the aggregation of multiple sub-consensus models. This is achieved by randomly sub-sampling clients to form sub-consensus models and employing a distance-reweighted aggregation module to integrate these models during each synchronization round.

FedSSL-DP [Fan et al., 2022] designs a mixed-data generation strategy to utilize both labeled and unlabeled clients by establishing a unified data space without direct data exchange. Furthermore, the differential privacy (DP) scheme can be integrated smoothly into the model, prohibiting excessive access to the labeled data with theoretical guarantees.

CBAFed [Li et al., 2023a] rethinks the standard pseudolabeling methods used in FSSL. Recognizing the potential imbalance in the training distribution of unlabeled data due to the non-IID issue, CBAFed proposes class-balanced adaptive thresholds. These thresholds are dynamically adjusted based on the empirical distribution of all training data across local clients, as observed in the previous communication round, to accommodate the non-IID data distributions more effectively.

UM-pFSSL [Shi et al., 2023] investigates the personalized FL model under the label-at-partial-client case. Unlabeled clients struggle to obtain competent personalized models due to insufficient knowledge of their local data distributions, while labeled clients may dominate the collaborative training and obtain superior performance. UM-pFSSL enables unlabeled clients to assimilate knowledge from selected "helper" clients, thereby acquiring reliable pseudo-labels guided by an uncertainty metric. To reduce the communication cost, a ranking update protocol is designed to select the suitable helper clients as well.

4.3 Label-at-server Case

Unique Challenges and Generic Solution Framework

Unlike two previous cases where the server acts as the parameter server only, the server now has direct access to its own

Algorithm 4 Generic unlabel-at-server FSSL framework

Input: Initialized model parameters θ = θ1

• 1: for communication round t = 1 to R do
• 2: Server trains model θt on Ds with pseudo-labels.
• 3: Randomly select a subset of clients C t ⊆ {1, . . . ,N}.
• 4: for each selected client i ∈ C t in parallel do
• 5: Train a local model θt i with Di and the initialized θt .
• 6: end for
• 7: Server aggregates {θt i}i∈Ct , pseudo-labels and updates θt+1 .
• 8: end for

possess labeled data. This setup is relevant in scenarios where data privacy is a critical concern. For instance, a research institution ("server") working with local hospitals ("clients") on a new drug development project illustrates this well. The hospitals have access to labeled patient data for individuals diagnosed with rare conditions but are restricted from sharing this sensitive information due to privacy regulations. Conversely, the research institution has a wealth of unlabeled patient data derived from public datasets and published research.

The main challenge is that the server cannot directly evaluate the quality of the local models during the server aggregation since it lacks labeled data. It must employ indirect measures to assess and incorporate client contributions effectively. Hence, we train the model with the help of pseudolabels from the selected local models. The training procedure is shown in Algorithm 4 with the training objective given as

Representative Methods

PATE-G [Papernot et al., 2017] collects local models from clients to serve as teacher models, which then generate pseudo-labels for the server's unlabeled data based on their collective predictions. These pseudo-labeled datasets are leveraged to refine the global model. To ensure the privacy of this knowledge transfer process, PATE-G utilizes the moments accountant technique, which facilitates the training of student models under stringent privacy constraints, providing meaningful privacy guarantees for the data involved.

GDST [Liu et al., 2021b] integrates global distillation and self-training into local training within the FL framework, jointly with server-side fine-tuning, to further stabilize and enhance the learning process of the global model.

CRL-Grouping [Zhang et al., 2021b] combines consistency regularization with group normalization (GN), reducing gradient diversity and improving test accuracy. It employs a grouping-based averaging technique to expedite convergence, offering a substantial improvement in speed over FedAvg.

FedIL [Yang et al., 2022] enforces the consistency between the predictions made by clients and the server during the training process, achieving a provable convergence guarantee. FedIL also introduces a group-based asynchronous training algorithm in combination with a time-slot-based task scheduling to allow more clients to participate in training simultaneously.

SSFL [Diao et al., 2022] resorts to an alternate training scheme, which fine-tunes the aggregated global model with labeled data and generates pseudo-labels only once upon receiving the global model from the server. Compared to the existing solutions, which all train and aggregate server and client models in parallel and generate pseudo-labels with the training models for every batch of unlabeled samples, SSFL is much more communication efficient.

FedFAME [Malaviya et al., 2023] offers a versatile framework that eliminates the need for data augmentation in local model training by utilizing contrastive learning. This feature makes FedFAME particularly suitable for domains lacking standard augmentation techniques, like text or graphs, providing a robust solution across diverse data types.

pFedKnow [Wang et al., 2023a] generates lightweight personalized client models via neural network pruning techniques to reduce communication costs. Moreover, it leverages pretrained large models as a form of prior knowledge to guide the aggregation of personalized client models and further enhance the learning efficiency.

4.4 Unlabel-at-server Case

Unique Challenges and Generic Solution Framework

In the unlabel-at-server case, the locations of labeled and unlabeled data are swapped compared to the label-at-server case, with the server now holding unlabeled data while clients Ada-FedSemi [Wang et al., 2022] selects partial local models to produce pseudo-labels for the unlabeled data. A multi-armed bandit (MAB) based online learning algorithm is introduced to adaptively determine the participating fraction and confidence threshold during training. HeteroAdaFedSemi [Xu et al., 2023] extends Ada-FedSemi for the heterogeneous clients with diverse computation and communication resources. It customizes local models derived from the same global model to match the capabilities of individual clients by adjusting the model depths.

5 Future Directions

FSSL is an emerging research topic. Although significant progresses have been made for FSSL, there still remain plenty of research directions worthy of future explorations.

• FSSL for Vertically Partitioned Data: Investigating FSSL for vertically partitioned data presents an intriguing frontier with unique challenges. This new VFL setting, where different clients hold different features or the labels for the overlapping samples, requires the clients to communicate with the server for each iteration of local training (rather than after several epochs under the horizontal FSSL setting), introducing extremely high communication costs [Sun et al., 2023]. Therefore, the key research question revolves around effectively and efficiently leveraging the limited supervision information across diverse feature spaces while solving extra issues related to data alignment, feature heterogeneity, and privacy preservation across vertical partitions [Kang et al., 2022]. An in-depth exploration of vertical FSSL enables collaborative learning of featurepartitioned partially-labeled data distributed across multiple institutions in industrial applications.
• FSSL across Diverse Data Modalities: The current exploration of FSSL has predominantly focused on image data, yet the potential of FSSL extends far beyond to include a variety of data modalities encountered in realworld scenarios, such as text, graphs, and time series. Specifically, the complex non-Euclidean structure of graph data [Ma et al., 2023; Song et al., 2023c; Song et al., 2023a; Song et al., 2023b; Zhang et al., 2023c; Song et al., 2024], necessitates customized designs for effective SSL within an FL framework at both the node level [Yao et al., 2023] and graph level [Tao et al., 2022]. The adaptation of FSSL to these diverse data types or even environments with multimodal clients is a critical area for future research. The main challenge lies in handling the heterogeneity inherent to different data types.
• FSSL with Enhanced Model Robustness: There has been an emerging concern about the robustness of FSSL, especially in some safety-critical healthcare applications like medical diagnosis. The paramount goals of enhancing robustness against noisy labels and adversarial attacks hold significant implications. Noisy labels can severely degrade FSSL model performance by introducing inaccuracies in training data [Kim et al., 2022], and adversarial attacks pose a substantial risk, potentially manipulating FSSL model predictions [Fu et al., 2022; Liu et al., 2022]. Therefore, addressing these open problems is not merely a technical endeavor but a means to safeguard the trustworthiness of FSSL applications in sensitive sectors where the stakes involve human lives.
• FSSL under Additional Learning Settings: Recent studies have shifted from basic FSSL investigation to exploring advanced FSSL with additional learning settings' constraints. FedPU [Lin et al., 2022] focuses on positive and unlabeled learning under the FSSL framework, where the labeled data is only of the positive class. FedoSSL [Zhang et al., 2023b] extends open-world SSL to an FL context with unseen classes in test data. These developments push the boundaries of FSSL and highlight the need for practical FSSL models that can operate effectively under extra learning conditions encountered in real-world environments.

6 Conclusion

In conclusion, this survey underscores the burgeoning field of FSSL, highlighting its potential to synergize the privacypreserving aspects of FL with the data efficiency of SSL. Despite existing progress, considerable obstacles remain, uncovering a wealth of opportunities for crafting diverse FSSL models for practical applications.

Acknowledgments

The work described in this paper was partially supported by the Research Grants Council of the Hong Kong Special Administrative Region, China (RGC GRF 2151185).