Federated Semi-supervised Learning with Dual Regulator
Authors: Sikai Bai
Shuaicheng Li
Weiming Zhuang
Kunlin Yang
Jun Hou
Shuai Yi
Shuai Zhang
Junyu Gao
Song Guo
Venue: Submitted to ICLR 2023 (2023)
Keywords: federated learning
semi-supervised learning
dual regulator
class imbalance

Abstract: Federated learning emerges as a powerful method to learn from decentralized heterogeneous data while protecting data privacy. Federated semi-supervised learning (FSSL) is even more practical and challenging, where only a fraction of data can be labeled due to high annotation cost. Existing FSSL methods, however, assume independent and identically distributed (IID) labeled data across clients and consistent class distribution between labeled and unlabeled data within a client. In this work, we propose a novel FSSL framework with dual regulator, FedDure, to optimize and customize model training according to specific data distributions of clients. FedDure lifts the previous assumption with a coarse-grained regulator (C-reg) and a fine-grained regulator (F-reg): C-reg regularizes the updating of local model by tracking the learning effect on labeled data distribution; F-reg learns an adaptive weighting scheme tailored for unlabeled instances in each client. We further formulate the client model training as bi-level optimization that adaptively optimize the model in the client with two regulators. Theoretically, we show the convergence guarantee of dual regulator. Empirically, we demonstrate that FedDure is superior to the existing methods across wide range of settings, notably by more than 12% on CIFAR-10 and CINIC-10 datasets.

Under review as a conference paper at ICLR 2023
FEDERATED SEMI-SUPERVISED LEARNING WITH DUAL REGULATOR
Anonymous authors Paper under double-blind review
ABSTRACT
Federated learning emerges powerful method to learn from decentralized het- erogeneous data while protecting data privacy. Federated sumiisueereiee learn- ing (FSSL) .) is even more practical and challenging, where only fraction of data can be labeled due to high annotation costs. Existing FSSL methods, however, as- sume independent and identically distributed (IID) labeled data across clients and consistent class distribution between labeled and unlabeled data within a client. In this work, propose novel FSSL framework with dual regulator, FedDure, to optimize and customize model training according to specific data distributions of clients. FedDure lifts the previous assumption with coarse- -raained regula- tor (C-reg) and a fine-grained regulator (F-reg): C-reg regularizes the updating of the local model by tracking the learning effect on labeled data distribution; F- reg learns an adaptive weighting scheme tailored for unlabeled instances in each client. We further formulate the client model training as bi-level optimization that adaptively optimize the model in the client with two regulators. Theoretically, we show the convergence guarantee of the dual regulator. Empirically, we demon- strate that FedDure is superior to the existing methods across wide range of settings, notably by more than 12% on CIFAR- and CINIC-10 datasets.
INTRODUCTION
Federated learning (FL) is an emerging arvacc-preseeving machine-learning technique (McMahan et al. 2017), where multiple clients collaborativel learn model under the coordination of a central server without exchanging private data. Edge devices like mobile phones have generated and stored large amount of private data. Centralizing these data could lead to data privacy issues (Voigt & Von dem Bussche 2017). Federated learning is a decentralized learning paradigm to leverage these data and has empowered wide range of applications in many industries, including healthcare (Kaissis et al. 2020 Li et al.
2019), consumer products (Hard et al. 2018 Niu et al. 2020), and public security (Zhuang et al. 2022).
The majority of existing FL works (McMahan et al. 2017: Wang et al. 2020 Li ct al. 202 2021a) assume
that the private data in clients are fully labeled, but the assumption is unrealistic in real-world feder- ated applications as annotating data time-consuming. laborious, and expensive. To remedy these issues, federated suprviupe learning (FSSL) is proposed to improve model performance with a large amount of unlabeled data on each client. In particular, priors work (Jeong et al. 2022]) has achieved competitive performance by exploring the inter-client mutual knowledge, i.e., inter-client consistency loss Jeong et al. (202T). However, they usually focus mitigating inter-client hetero- geneous data distribution across clients (External Imbalance) and assume that the class distribution between the labeled and unlabeled data is consistent. These assumptions enforce strict requirements of data annotation and would not be practical in many real-world applications. general case is that labeled data and unlabeled data have different data distribution (Internal Imbalance). For example, photo gallery in mobile phones contains much more unlabeled images and irrelevant samples than the ones that can be labeled manually for image classification task Yang et al. (2011).
Besides, these existing methods require sharing of additional information among clients, which could impose potential privacy risks. Specifically, they transmit models among clients to provide consistency regularization. However, inter-client interactions might open a loophole to unauthorized infringement for privacy risks Chen al. (2019): many reverse-engineering techniques Yin et al.

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Under review as a conference paper at ICLR 2023
2020) can even recover the client data from the mutual models, threatening the users' data privacy and security (Yonetani et al. 2017: Wu et al. 2018).
In this paper, propose flexible federated semi-supervised learning framework with dual regulator, termed FedDure, to handle the internal and external imbalance problems while account- ing for privacy. FedDure explores the adaptive regulators flexibly update the model parameters in clients; it dynamically adjusts dual regulators to optimize the model training in each client accord- ing to the learning process and outcome of the client's specific data distribution. Our framework includes two novel components: Coarse-grained regulator (C-reg) and Fine-grained regulator (F- reg). On the one hand. C-reg regularizes the updating of the local model by tracking the learning effect on labeled data distribution. It mitigates the distribution mismatching between labeled and unlabeled data to prevent corrupted pseudo labels and maintain generalization ability. On the other hand, F-reg learns an adaptive weighting scheme tailored for each client; it automatically equips a soft weight for each unlabeled instance to measure its contribution to the training. This scheme automatically adjusts the instance-level weights to strengthen (or weaken) its confidence according to the feedback of F-reg on the labeled data. FedDure utilizes the bi-level optimization strategy to alternately update the local model and dual regulators in clients. We theoretically show that C-reg and F F-reg converge with guarantee and empirically demonstrate that FedDure outperforms other methods on various benchmarks.
The main contributions of this work are three-fold. (1) We address a more practical scenario of FSSL, where data distribution is different not only across clients (external imbalance) but also be- tween labeled and unlabeled data within a client (internal imbalance). (2) We propose a flexible FSSL framework with dual regulator, (FedDure), which designs adaptive regulators flexibly up- date the local model according to the learning processes and outcomes on specific data distributions of each client. It does not require sharing of additional information among clients. (3) We theoret- ically analyze and present the convergence of the dual regulator and empirically demonstrate that FedDure superior to the state-of-the-art FSSL. approaches across multiple benehmarks.
2 RELATED WORK
Federated Learning (FL) is an emerging distributed training technique that trains models on de- centralized clients and aggregates model updates in a central server (Yang et al. (011)). It protects data privacy as raw data are always kept locally. FedAvg (McMahan al., 2017) is a pioneer- ing work that aggregates model updates by weighted averaging. Statistical heterogeneity is an im- portant challenge of FI. in real-world scenarios, where the data distribution is inconsistent among clients (Li et al.) 2020a). A plethora of works have been proposed to address this challenge with approaches like extra data sharing, regularization, new aggregation mechanisms, and personaliza- tion (Zhao al. 2018 Li et al. 2020b; Zhuang et al.) 2020 Li et al. 2021b Gao et al., 2022). However, these approaches commonly consider only supervised learning settings and may not be simply applied to scenarios where only small portion of data is labeled. Numerous studies fo- cus on purely unsupervised federated learning, but they are either application-specific or only learn generic visual representations (Zhuang al. 2021a b); they do not effectively leverage the small fraction of labeled data that could exist in real- real-world applications. Our work primarily focuses on federated semi-supervised learning, where small fraction of data has labels in each client.
Sume-iupere Learning aims to utilize unlabeled data for performance improvements and is usually divided into two popular branches pseudo labeling and consistency regularization. Pseudo- labeling methods (Lee et al. 2013 Zou et al.) 2022 Pham et al. 2021) usually generate artificial labels of unlabeled data from the model trained by labeled data and apply the filtered high-confidence labels as supervised signals for unlabeled data training. MPI. (Pamm et al. (2021) extends the knowl- edge distillation and meta-learning to SSL by optimizing the teacher model with feedback from the student model. Consistency regularization (Lee et al.) [2022] Tarvainen & Valpola (017) regularizes the outputs of different perturbed versions of the same input to be consistent. Many works (Sohn) perturbed strategy for pursuing outcome consistency. FixMatch Sohn et al. (2020) follows the UDA and brings the idea of labudo-label to model training with unlabeled samples filtered by fixed threshold.
et al. 2020. Zhang et al. 2021a Lee et al. 2022) apply data augmentation
Federated Semi-Supervised Learning (FSSL) considers learning models from decentralized clients where small amount of labeled data resides either clients the server JJi et al. (000))
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Server
Global model 0g
Aggregation
Model Downalod
Model Upload
Updale 6 with Eqn. 12
Labeled data gg
Untabeled data
SP
Local model 0
Supervised Loss
Eqn.
C-reg (1
Coarse-grained regulstor updale Eqn.
C-reg (+++1)
Entropy difference d
Coarse-grained Lass
F-reg (t
Eqn. 6
C-reg d
Eqn.
F-reg w
Eqn.
Instance weight
Eqn.
Fine-grained
Loss
Fine-grained reguiator update
Figure 1: Illustration Federated Semi-Supervised Learning Framework with Dual Regulator (FedDure). FedDure updates the coarse grriined regulator (C-reg) and the fine- aneegrained regulator (F- reg) to adaptively regularize the model training in each client: C-reg dynamically regulates the importance of local training the unlabeled data by reflecting the overall learning effect labeled data; F-reg regulates the performance contribution of each unlabeled sample.
FSSL scenarios can be classified into three categories: (1) Labels-at- attevvr assumes that clients have purely unlabeled data and the server contains some labeled data (Lin et al. [021 He et al. 2021 Zhang et al. 2021b; Diao al. 2021) I): (2) Labels-at-Clients considers each client has mostly unlabeled data and a small amount of labeled data (Jeong et al. 2021); (3) Labels-at-Partia--CHI Partial-Clients assumes that the majority of clients contain fully unlabeled data while numerous clients have fully labeled data (Zhang al. 20211; Lin et al.) 2021 Liang et al.) 2022). Labels-at-Clients has been largely overlooked; the prior work (Jeong al. 202 1) proposes inter-client consistency loss, shares extra information among clients and bypasses the internal class imbalance issue. This work introduces the dual regulator to address the issue, with no extra information shared among clients.
Class Imbalance Methods concerned with dataset resampling (Chawla et al. 2002 Buda al.
for gradient cal- culation. In the centralized learning setting, many methods (Chawla et al. 2002 Liu et al., 2008) focus on resampling from the minority class for balanced class-wise distribution. Important exam- ples receive more attention and align larger weights than others for accelerating the optimization of networks. The important examples are quantified by their loss [Zhao & Zhang (2015) or the uncer- tainty Chang al. (2017). Besides, the loss reweighting methods usually formulate the sampling scheme on certain prior knowledge. Typical methods include the AdaBoost [Freund & Schapire (1997) and focal loss Lin al. (2017), which focus on those hard examples and align larger weights for them.
2018 or loss reweighting (Ling & Sheng, 2008 [Snn et al. 2007| Cui et al. 2019)
3 METHOD
This section first defines the problem and introduces a novel framework with dual regulators (Fed- Dure). Using the dual regulator, we then build a bi-level optimization strategy for federated semi- supervised learning.
3.1 PROBLEM DEFINITION
We focus Federated Semi-Suuii Sumerisuee Learning (FSSL) with external and internal class imbalance problems, where each client data is partially labeled. We assume that there are K clients, denoted as CC,,...CCk) Federated learning aims train a generalized global model fg with parameter 0y- It coordinates decentralized clients to train their local models Fi (f.,,.... ft,k with parameters (Ot, 1. ). where each client is only allowed to access its own local private dataset. In the stan- dard supersupe setting, the dataset contains a labeled set D = yx,,y, y. and an unlabeled set D = [u, where 2 < N Under FSSL, the private dataset DD of each client Cte contains Ng labeled instances D (Xi,kr Ns
Nf. and No unlabeled instances DE {u.A) (u.A)e

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In this work, primarily focus on image datasets. For unlabeled image in in client Ck. compute the corresponding pseudo label y with the following equation:
n ar (M.
where (ug) is the weakly-augmented version of Up and the pseudo labeling dataset in the client Ck denoted as D {u Fr.edi NN For simplicity of notation, omit the symbol k in the parameters later.
3.2 DUAL REGULATOR
In this section, we present federated cemi-supervised learning with dual regulator, termed FedDure. FedDure adaptively adjusts gradient updates in each client according to the class distribution charac- teristics with two regulators, coarse- sranseegr regulator (C-reg) and a fine- grained regulator (F-reg)- Figure the optimization process with these two regulators. We first introduce the regulators in this section and present the optimization process in Section 3.3
Coarse-grained Regulator (C-reg). C-reg dynamically regulates the importance of local training on the unlabeled data by quantifying the learning effect using labeled data. We define C-reg as fa with parameters $ Intuitively, C-reg and local models are collaboratively optimized during the local training process in each client. On the one hand, C-reg is trained using pscudo labels generated by the local model in a supervised manner. On the other hand, the parameters of the local model are further rectified according to the feedback from C-reg. Specifically, at training iteration t, the coarse-grained regulator searches its optimal parameter ø" by minimizing the cross-entropy loss on unlabeled data with pseudo labels. We formulate it as:
Φ- = =rgminn Eu Fon (S (()
w.r.l (m)
(2)
where (u) is the strongly augmented unlabeled image The optimal parameter ø' is related to the local model's parameter 0: via the generated pseudo label, where we denote the relationship x²(()) (0.). In practice, it requires heavy computational costs explore the optimal parameter by training the coarse-grained regulator, so we design a strategy to approximate $"
Conceptually, we approximate o by performing one gradient step based on the parameter training iteration (i.e., (()). We establish the meta learning process between and 0 as followed:
(0(0(()) & (1+1) (0(1) 6 - n, (00) Eu
(y. fa
To O ((()))))))))) (()))
(3)
Practically, we update C-reg by utilizing the updated fine-gratn ane-ggrined regulator to measure the adaptive weight for each unlabeled instance, where the updated fine-grain finegrriined regulator is obtained based on one gradient step of C-reg (Φ in Eqn. 6). The formulation to optimize C-reg is as followed:
(1+1) = $ (() 1/s H.Wl(w (++1), V Lee (s. (T.(u): (())
where H(w((++1; o ( fw (fa (T): (()) ; w ((+1)), fw is the fine- ane-grained regulator (F-reg), and (1++) is the parameters of F-reg updated by Eqn. thhat we present in the following subsection.
Next, quantify the learning effect of the local model with the C-reg using labeled samples by computing the entropy difference (t++1) of C-reg between training iterations l and / + 1:
((++1) =
1(t+1)==xx Exy [(coe (x: fax; Lee (xxx
(5)
The learning effect is further used as reward information to optimize the local model by regulating the importance of local training unlabeled data. In particular, the cross-entropy differences signify the generalization gap for the C-reg updated by the pseudo labels from the local model. We provide detailed derivation in Appendix A.4 for the optimization of the local model with C-reg.
Fine-grained Regulator (F-reg). F-reg regulates the importance of each unlabeled instance in local training. It addresses the challenge that the fa is substantially hindered by corrupted labels or class imbalance, especially the early period of training rounds. This challenge could further negatively impact the optimization of local model fi. Furthermore, previous methods usually utilize
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fixed threshold to filter noisy pseudo labels in all clients. It is infeasible for clients with heteroge- neous data when the skewed data distribution across clients is unknown.
To tackle the challenge, construct F-reg/ fu parameterized by It learns adaptive weighting scheme tailored for each client according to the unlabeled data distribution characteristics. A unique weight is generated for each unlabeled image measure the contribution of the image to the overall performance. We first perform one gradient step update of C-reg & to associate F-reg and C-reg with the following formula:
77 )(w((()
( Volli Lee (g. (To(u): (((()))(())) )ie)
(6)
where one gradient step of C-reg x depends on the F-reg w(t) Next, we optimize F-reg in local training iteration as follows:
w
w Tww V wits Cxe fa(x; (xxxx ()
where fa(x; Φ (w(+)) is the output of fa on labeled data. We then introduce a re- re-weighting scheme that calculates a unique weight m; for i-th unlabeled sample:
mi fm (T..
(((+
(8)
Note that my is scalar re-weight the importance of the corresponding unlabeled image.
3.3 BI-LEVEL OPTIMIZATION
In this section, we present optimization processes for the dual regulator and local model 0. We alter- natively train two regulators, which approximate gradient-based bi-level optimization procedure
Finn et al. 2017: Liu et al. 2018). Then, we update the local model with fixed C-reg and F-reg.
Update F-reg. Firstly, we obtain one gradient step update of C-reg o using Eqn. 6
After that, the
supervised loss Lee fax
guides the update of the F-reg with Eqn. 7
Update C-reg, After updating the parameters of F-reg, we update C-reg by Equ. regarding local model (0) and the updated F-reg w ((+1) as fixed parameters.
Update Local Model with F-reg, We use the updated F-reg w(++1) to calculate a unique weight m; for i-th unlabeled sample with Eqn. 8. The gradient optimization is formulated as:
=
E.
m V
VoLur Lee
f (T.()):)())
Update Local Model with C-reg. We then use C-reg to calculate entropy difference d(++1) using Eqn. 5 The entropy difference d(f++1) adopted reward coefficient adjust the gradient update of local model unlabeled data. The formulation is as followed:
(++1)
oED E. Lee ($ (T((w):(()))
(10)
where the learning process can derived by meta-learning strategy shown in Appendix A.4
Update Local Model with Supervised Loss. Besides, we compute the gradient local model on labeled data as followed:
V ofn ExyLoo (y. (xx((x)))))
(1I)
On this basis, we update the local model's parameter with the above gradient computation in Eqn. 9 and [I] which defined as:
0 0e++1) 0 17 (9.) g + + +
(12)
where 1/ denotes the learning rate of the local model. Finally, after T local epochs, the local model is returned to the central server. The server updates the global model 0g r+1 by weighted averaging the parameters from these received local models in the current round, and the round is conducted by sending 0=+11 to the randomly selected clients as initialization. Alg. presents the pipeline of the overall optimization process.
F-rg ML. architecture with fully connected layer with 128 filters and Sigmoid function.
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Algorithm Federated Semi-supervised Learning with Dual Regulator (FedDure)
Require: K: number of clients; S: number of selected clients in each round; R: number of training rounds;
T: number of local iterations;
1: RunServer
Initialize dg and w each client
3: for each round r from 0 to H do
4: Randomly select {Ca] ) from K clients;
5: for cach l [] in parallel do
6:
0f
RunCliien(()))
7: end for
9: end for Σ (DE (PI+PPE) (i=i( (DE)) 0
05++11
A Aggregation
10: return BR:
RunClient(
000)
f%:: (0)) + 0g
13: for each local iteration from to T do for minihatch D E DD and D E Dj do
14:
15:
Y.A. <- Generate pseudo labels for unlabeled data Dj with Eqn. I DE
(u
16:
Update the mne-graiedd regulator with Equ. 7
Compute the instance weight m, Eqn.
18:
Update the coarse coarse-grained regulator é with Egn.
19:
Compute the entropy difference with Eqn.
20:
Compute local model's gradient (6) 94 9-
following Eqn.
10 and
21:
Update local model O: with Eqn. 12
22:
end for
23:
end for
24:
return OF
3.4
CONVERGENCE OF OPTIMIZATION PROCESS
In this section, we further analyze the convergence of the coarse- soasee-rriied and the fine-graines regu- lators and derive the following theorems. The proofs are provided in Appendix A.5
A.5
Theorem Suppose supervised loss Cee falx; (((++(((((()))))) (0(2)) is L-Lipschitz and has p-bounded gradients. The Lee (f, fa (T,(H;; (11) has p-bounded gradients and twice differential with Hessian bounded by B. Let the learning
1/s min(1, +} for constant
O, and n min (
for some e. > O, such that vT 2 L. Thus, the optimization of the local model using coarse-grained regulator achieve:
min
(13)
OSIST
VT
Theorem Suppose supervised and unsupervised loss functions are Lipsehitz- smoohh with constant L. and have p-bounded gradient. The HH(-) is differential with e-bounded gradient and twice differential with its Hessian bounded by B. Let learning rate ns satisfies = min [, #) for constant k > O, such that &/ < 1. Ahe = min(t, ) for constant > such that vT 2 L. The optimization of the coarse gaarse-grained regulator can achieve:
lim (111) (.) Lae (s. (Ta()):( (1)) ++00
=
(14)
4 EXPERIMENTS
In this section, demonstrate the effectiveness and robustness of our method through comprehen- sive experiments in three benchmark datasets with multiple data settings. More details and additional experiments can be found in the supplementary material.

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Performance comparison of our proposed FedDure with ofte-offthheart methods on three different data heterogeneity settings. FedDure outperforms all other methods in all settings.
Table 1:
MNIST
CINIC-10
Methods
(II. ID))
(ID. DIR)
[DIR
DIR)
(II.
II))
(II.
DIR)
(DIR
DIR)
(ID.
I13)
(II. DIR)
(DIR
DIR)
FedlAvg
55.88 + 1.144383
4133
0.36
40
85.50
0.09
84, X4
0.00
1107
40.73
0.50
99.00
0.31
2X.09
0.53
FodAvg-SL
15.47
66.70
0.86
58.38
0.4
89,87
0.25
86.95
1.12
67,97
0.50
46.21
1.06
Fe.Prox-SI.
14.67 + 0.556666666
66.78
0.87
59.55
0.61
89.53
0.23
88,35
0.02
87.32
0.84
63.13
0.96
1.04
52.09
0.20
HoJAvg+UDA
47.47 0.67
43.89
0.19 35.52
85.35
81.07
0.56
0.31
39.93
29/27
FodProx+UDA
46.49 0.74
42.82
0.79 37.38
84.78 0.43
84,50
82.94
0.39
41.81
= 0.94
39.40
0.18
33.26
0.98
FodAvg-Fixmatch
46.71 2.49
46.67
0.56 39.95
86.46
85-42
81.07
0.56
40.40
0.61
39.66
31.99
FedProx-Fixmatch
47.60 +: 1:05
43,39
- 0.71
41.85
1.32
86.31
85.18
0.79
83.68
0.78
41.46
0.35
10.02
0.61
32.21
1.03
FodMatch
51.22 0.50
51.59
0 0.32
45.56
0.91
85.71
85.55
0.09
0.15
43.73
41.82
0.23
35.27
FedDure (Ours)
67.69 - 0.23
66.85
0.65
57.73
0.31
88.69
0.16
88.21
0.07
86.96
1
0.12
56.36
55.10
0.25
46.43
0.13
10
Dal Labels
Data Labels
5 Client ID
5 Client ID
22345677 910
2 6 910 Client ID
Client ID
(a) FedMatch: Labeled
(b) FedMatch: Unlabeled
(c) FedDure: Labeled
(d) FedDure: Unlabeled
Comparison of data distribution between FedMatch (Jeong et al. 2021 and our (DIR, DIR) setting: (a) and (b) are labeled and unlabeled data distribution used in FedMatch, respectively; our data distribution in (c) and (d) present external imbalance across clients and internal imbalance between labeled and unlabeled data inside client.
Figure 2:
4.1 EXPERIMENTAL SETUP
Datasets. conduct comprehensive experiments on three image classification datasets, including CIFAR-10 10 (Krizhevsky et al., 2009), Fashion-MNIST (Xiao et al.) 2017) and CINIC-10 (Darlow al. 2018). We provide the simulation of different data heterogeneity for external and internal imbalance below and present more details of these datasets in the Appendix A.1
Data Heterogeneity. We construct three data heterogeneity settings with different data distribu- tions. We denote each setting (A, B), where A and B are data distribution of labeled and unlabeled data, respectively. The settings are as follows: (1) (IID, IID) means both labeled and unlabeled data 5 instances per class to build the labeled dataset for each client. The
IID. By default, remaining instances of each class are divided into clients evenly to build an unlabeled dataset. (2) (IID, DIR) means labeled data is the same (IID, IID), but the unlabeled data constructed with Dirichlet distribution to simulate data heterogeneity, where each client only contains a subset of classes. (3) (DIR, DIR) constructs both labeled and unlabeled data with Dirichlet distribution. It simulates external and internal class imbalance, where the class distributions across clients and within client are different. Specifically, we allocate 500 labeled data per class to 100 clients us- ing the Dirichlet process; The rest of the instances are also divided into each client with another Dirichlet distribution. Figure 3 compares the data distribution of FedMatch (Batch NonlID) (Jeong et al. 202T and ours. Our (DIR, DIR) setting presents class imbalance both across clients (external imbalance) and between labeled and unlabeled data within client (internal imbalance).
Implementation Detail. We use the Adam optimizer with momentum = 0.9, batch size 10 and learning rates = 0.0005 for 7)., 17 and Tu.. If there no specified description, our default settings also include local iterations T 1, the selected clients in each round S 5. and the number of clients K = 100. For the DIR data configuration, we use Dirichlet distribution Dir(t) to generate the DIR data for all clients, where y 0.5 for all three datasets. We adopt the ResNet-9 network the backbone architecture for local models and the coarse- -rreerrrindd regulator, while an MLP is utilized for the fine-grained regulator. More details refer Appendix A.2
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90
(DIR, DIRI (ID, DIR)
(DIR, DIRI (ND, DIR)
65
TedMatch
Baseline
55
reaMatch
Baseline
80
92
Accuracy (%)
60
FedDurelours)
Accuracy(%5
FedDurel
Accuracy
70
Accuracy
55
50-
60
88
50
45
50
86
45
40
82
40
2
10
20
2
4
10
15
20
30
20
Label Ratio (%6
Label Ratio (%)
Num of Clients
Num of Clients
(a) Setting: (IID, DIR)
(b) Setting: (DIR, DIR)
(c) CIFAR-10
(d) Fashion-MNIST
Figure 3: Analysis of the impact of the number of labeled data and the impact of the number of selected clients. (a) and (b) illustrate that FedDure consistently outperforms FedMatch and Baseline different percentages of labeled data. (c) and (d) show that FedDure scales with increasing numbers of selected clients on CIFAR-10 and Fashion-MNIST datasets.
Table 2:
Quantitative analysis of components of FedDure on CIFAR-10 and Fashion-MNIST datasets.
Sacdite
Accuracy
60
55
CIFAR-10
Pashion-MNIST
Methods
0.3
0.5
0,7
1.0
(DIR, DIR)
(IID, DIR)
(DIR, DIR)
(ID,, DIR)
Dirichlet Coefficient
Baseline
39.95 + 1.85
46.67 + 0.56
81.07 F 0.56
85.42 0.19
Impact of dif- ferent Dirichlet coefficients under (DIR, DIR).
Figure 4:
w/o C-reg
54.79 + 0.59
64.98 = 0.58
86.18 + 0.13
87.45 = 0.23
w/o F-reg
56.79 1 0.63
66.75 1 0.23
86.79
1 0.17
88.14 0.12
FedDure
57.73 + 0.31
66.85 = 0.65
86.96
- 0.12
88.21 + 0.07
Baselines. We compare FedDure with the following state-of-the-art methods. FedAvg-SL (McMahan et al., 2017) and FedProx-ST. (Li et al., (020b) denote the supervised algorithms with corresponding FL methods and have fully labeled data in each client. FedAvg+UDA, Fed- Prox+UDA, Fedavg-Fixmatch, and TedProx+Fixmall supervised method (Sohn et al. 2020, Xie et al. 2020) and FL. Although both labeled and unlabeled data are utilized in these methods, they need to specify predefined threshold on pseudo labels across decentralized clients. FedMatch (Zhang et al. 2021b) adopts inter-consistency loss and disjoint loss for model training, which can reflect state-of-the-a performance in FSSL. Note that, we set equal hyper-parameters for FedDure and other state-of-the-ard methods in all experiments.
naive combination between semi-
4.2 PERFORMANCE COMPARISON
T reports the overall results of FedDure and other state-of-the-art methods on the three datasets, where all results are averaged over independent random trails. Our FedDure achieves state-of-the- art FSSL performances
all datasets and data settings. (IID, IID) setting: compared with naive combination FSSL methods and FedMatch, our FedDure significantly outperforms them on all three datasets. Specifically, when evaluated on CINIC-10, which is more difficult dataset and may encounter a larger amount of unlabeled samples, we observe that other methods suffer from the performance bottleneck and inferior to the evaluation on CIFAR-10 with fewer unlabeled sam- ples. This phenomenon verifies that our FedDure alleviates the influence of mass unlabeled data and prevents performance degradation when the imbalance between labeled and unlabeled data increase rapidly. (IID, DIR) setting: our FedDure is slightly affected by weak class mismatch on unlabeled data, but our FedDure makes a rapid performance boost by 16.17% compared to FedMatch on CI- FAR10. Also, competitive performance is achieved compared to the supervised method FedAvg-SL. on Rishion-MNIST' (DIR, DIR) setting: to simulate the federated semi-supervised scenario real- world applications, we formulate a severe scenario where labeled data and unlabeled data come from different data distributions and suffer from extreme data imbalance. Under this setting, our FedDure significantly outperforms others by at least 10% on CIFAR- 10 and CINIC-10. In partic- ular, we observe that the performance of other approaches degrades sharply and is even inferior to FedAvg* which is only trained divided labeled data. That is say, extra unlabeled data might
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even have negative effect model performance due to the distribution mismatch between labeled and unlabeled data. Therefore, these quantity results demonstrate that our method is well suited for this real-world scenario since the dual regulator effectively and flexibly provides real-time feedback for local model updating.
4.3 ABLATION STUDY
Effectiveness of Components. To measure the importance of proposed components in Fed- Dure, we conduct ablation studies with the following variants. (1) baseline: the naive combination of FedAvg and Fixmatch. (2) Ours w/o C-reg: this variant removes the C-reg (i.e. Ia in Eqn 12) and updates F-reg with local model. (3) Ours w/o F-reg: this variant replaces the dynamic weight (i.e. Iu in Eqn 12) and utilizes the fixed threshold to filter low-confidence pseudo labels. Table shows that adopting the C-reg improves the performance from 54.79% to 57.73% under (DIR, DIR) setting on CIFAR-10. The F-reg can further make remarkable performance boost under almost all data sets on CIFAR-10 and F-MNIST. These evaluations verify the effectiveness of our components. The local model can flexibly optimize parameters according the complementary feedback from coarse and fine- iineggraind regulators.
Number of Label Data per Client. We evaluate the performance of our method when tuning the proportion of labeled instances in each client in (2%, 4%, 10%, 15,, 20%]. As illustrated in Figure (3a) and 3(b] we find that our framework gains steady performance improvements with the number of labeled data increases both in two data settings. Interestingly, after the labeling ratio reaches 10%, the performance of the baseline is basically unchanged in (IID, DIR), while we find substantial performance fluctuations for FedMatch and baseline in (DIR, DIR). This phenomenon proves that our regulators can more properly extract valuable knowledge from labeled instances with imbalanced distribution to help local model optimization.
Number of Selected Clients per Round. We also investigated the performance impact of the number of selected clients per epoch, which varies in (2, 5, 10, 20). As illustrated in Figure 33c) and (rd) significant improvements can be achieved by increasing the selected clients. However, there would be limited impact on performance when the selected clients reach certain amount. We argue that although the number of the selected clients has positive correlation with overall performance, our framework can fully explore the underlying knowledge of each client promote overall performance improvement in the central server. In this case, when there are enough clients, our method has learned comprehensive knowledge such that the performance becomes saturated.
Impacts of Data Heterogeneity. As illustrated in Figure 4, our FedDure is the only method that robust against different levels of internal data imbalance characterized by Dirichlet distribution. FedMatch and baseline (FedAvg-Fixmand higher data heterogeneous (small Dirichlet Coefficient). These results demonstrate that our FedDure is more flexible and can alleviate diverse inductive bias across clients when accounting for severe data heterogeneity in worl-world applications.
suffer from the rapid performance degradation in the
5 CONCLUSION
In this paper, we introduce a new federated semi-supervised learning framework with dual regulator, FedDure, to address the challenge of external and internal imbalance of data distribution. Particu- larly, we propose a coarse-grained regulator to regularize the gradient update in client model training and present a fine-grained regulator to learn an adaptive weighting scheme for unlabeled instances for gradient update. Furthermore, we formulate the learning process in each client as bi-level op- timization that optimizes the local model in the client adaptively and dynamically with these two regulators. Theoretically, we show the convergence guarantee the regulators. Empirically, ex- tensive experiments demonstrate the significance and effecttieness of FedDure. In the future, consider designing and integrating other client selection strategies for FSSL. Future work also in- volves extending our method from image classification to computer vision tasks.

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6 REPRODUCIBILITY STATEMENT
We provide the datasets, experimental settings, and implementation details Section 4.1 More details of the experimental setup are provided Appendix A.I and A.2 Besides, we summarize our proposed FedDure in Algorithm The source code will be released in the future.
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A APPENDIX
A.1 DATASET
CIFAR-10 10 is a dataset containing 60,000 RGB images of 32 resolutions for image classification tasks. We follow the official guidance and involve 50,000 training images and 10,000 test images. The data set contains 10 categories: "airline", "automobile", "bird", "cat", "deer", "dog", "frog", "horse", "ship", "trunk".
CINIC-10 is drop-in replacement for CIFAR-10 and is an extension of CIFAR-10 via the addition of downsampled ImageNet images. CINIC-10 contains 270,000 images and is equally split into three subsets: train set, validation set, and test set. In each subset, there are 10 categories like CIFAR-10 and each class involves 9,000 images. In our FedDure training, apply the training subset for training and allocate them to K clients for uniform or Dirichlet distributions while the global model tests in the test subset.
MISIIO consists of 60,000 training examples and 10,000 test examples. Each example is 28 x 28 gray-scale image, associated with label from 10 classes. We implement training in divided training examples and test test set.
A.2 IMPLEMENTATION DETAILS
Network architecture. Follow the conventional methods Jeong et al. (2021), we employ the official ResNet-9 to local model on all these datasets, i.e, CIFAR-I0, CINIC-10 10 and Fashion-MNin Our coarse-grained regulator is a deep copy version of initial local model. Our fine-grained regulator is an MI.P architecture, which contains one fully connected layer with 128 filters and follows Sigmoid function to normalize the output.
Naive combination methods. For all reimplement SSL algorithms FixMatch Sohn et al. (2020) or UDA et al. (2020), we fix the confidence threshold 0.85 for all FixMatch and FedMatch methods following their official implementation. To achieve federated semi-supervised methods, the plain FedAvg and FedProx are separately equipped with these SSL methods. For data augmentation, we apply the same strong (RandAugment Cubuk et al. 2020) and weak (flip-and and-shift) augmentation for unsupervised loss on unlabeled data.
A.3 ADDITIONAL ABLATION STUDIES
100
80
(DIR, DIR)
(DIR, DIR)
80
(IID, DIR)
75
(ID,, DIR)
Accuracy
Accuracy
70
60
65
40
60
20
55
0
50
2
4
5
1
10
50
100
Local iteration
Local iteration
Figure 5: Visualization analysis in terms of different local iterations, where the total number of local iterations training rounds is fixed.
Number Local Iterations. Finally, to qualitatively analyze the impact of local iterations on performance, we consider two different cases: (1) The total number of local iterations is fixed, where we reduce training rounds with the increase of local iterations to maintain invariant computation set local iteration 2, the number of training rounds is 100. As shown in the
cost. For instance, part of Figure [5] our methods suffer from accuracy degeneration with increasing local iterations. We analyze that while few clients could receive adequate training, many other clients with valuable
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information have chance be learned, especially with only 40 training rounds. (2) The total number of rounds is fixed, which means we can increase local iterations regardless of computational costs. It can be seen in the right part of Figure by increasing local iterations. These results indicate that enhancing the local model training in each client can promote the overall performance improvements of the central server.
method achieves steady performance gains
A.4 DERIVATION OF COARSE- GRAINED REGULATOR
Our C-reg tries to correct the pseudo labels generated by the local model and the local model tries to update its parameters by the feedback from the coarse-grained regulator (C-reg). The cross-entropy difference is applied to quantify the learning effect, it can be derived by gradient-basee meta-learning method. We now present the derivation, which theoretically verifies the effectiveness of our coarse- grained regulator. We first formulate the one-step update of the regulator (it) using the sampled soft pseudo label y ~ (u(TTo());:) 01) generated by local model as follows,
Φ (1+1) (0)))) = Eg~
(0(0) V a10 Lea (s (1)
(15)
Then, CE loss on labeled samples Lee (y, fa(x: (((+))(())) utilized to characterize the quality of pseudo labels from the local model. Since ((++1) has dependency on 0(t) we can minimize the CE loss to update the local model 0 according to the real-time feedback of regulator.
0C = 11 (
a
Lao o
(0(")
(16)
2
Loo (y, (x((x ((tt1)
00(0)
We focus on the first term in Equation
16 Since the (1+11) has no dependency on 8 while only
depends (())_ Note that here is the soft predictions of the local model fi. Therefore, utilize REINFORCE to achieve,
16 a
17 Var Lee (s (T(()): [(010]
00(0) a0(t) (g>(((T))))))))
a
Oei( Rgn (Fve (T((u): (T
-1 00(()
Lce (v.fa (T((w):((0))
0
log (gu; o())
=- - ((-
o0
(17)
Then Monte Carlo approximation is applied for the term in Equation pected value with the same using ÿ. Finally, we rewrite the Equation 16 according to the Equation
17 We approximate the ex-
17 as follows,
00 = T) a Loe (g. fal(xxx((tt])
Oc
a Loe (b. (T.()):(())
log P
i ul (1)
(0
(18)
Due to the heavy computation cost, we apply the first-order Taylor expansion to approximate the first two factors. Given that (((+1)- ((t) iلاn) Lee (y fa (Ta()); (())), we achieve
Lee (xx -Lon
Loc (y, Sa (1+)))
Len (y, [xx(xx (6 (((11)
a0((+1)
1/ 0b Lee
(y (xxx((i
θ J Lee (s: (To(
(19)
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Now, rewrite the Equation 18 as follows,
Oc
(oce (a(x fee (xx
a0 log P (()):
00(")
(20)
= (Coe (v.f((x(((t) Loe (xfa(xi(((t1)
(0 Lee (0. (To(w):)()))
The Equation T0 is equal to Equation 20 and the difference between the coarse-grained regulator characterizes learning difficulty from the perspective of the feedback and learning process of the regulator labeled samples.
A.5
CONVERGENCE OF OPTIMIZATION PROCESS
Our FedDure involves a bi-level optimization, so we demonstrate the convergence of these objectives theoretically.
Theorem Suppose supervised loss Ly, ((())))()))) is L-Lipschitz and have p-bounded gradients. The Lee (f. sian bounded by B. Let the learning rate Tls min(1, 1, + for constant > O, and 1j = min v
have p-bounded gradients and twice differential with Hes-
for some e > O, such that VTT 2 L. Thus, the optimization of the local model using a coarse-grained regulator achieve,
min OSIST
BII Sa(x; 6 ()) O
(21)
The CE loss Lee (y, (x Φ5 ( (1(+1(((00))) ()())) minimized update the local model 0 Let
((((++); g()) Lee (y, (x ((++1)) (8()))), the update of 0₂ in each step follows,
((+1)) g( VoL ((0)
(22)
In coarse-grained optimization process, the updating for (()) to (++1) is.
(1()()-)) g((+1)) - i(t) = - o(++1))- ((t(++1); (((+1))) ((+11)) ( :(0(++1):000))
(23)
For the first term, since we have (((+1) = $11) 7s V Votes Buher (8. Sa (T) let yeaarse (d())) = EuCee (f. (Tx( (1)), we achieve,
[ (++2) ((t+1)) -
L + (t -
S (V (1 yenarse (e (tt1))
- 1) yeoarse (11)))
(1+1))11
2
L
VV 1(++ ycoarse (((0are((((+11)))
. - yeearse ((+1)))
17 V 3(++)) yeaarse ( (1+1) |
1/1 + 2
|
s(e+1) yeaarse ( (1
2
(24)
Since V Vite=1) Decarse ((+1)) S so Equation 24 satisfies,
(o
(((((++)) - 1( p(+t)) < (1% (-16- +
ne2
12
(25)
2
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For the second term, we have, 21 L(b(+t);(())
S Voic ) - - + L
- -10(++1)- - 11
2
1)(1)) + I.
(26)
Vow ((p -17 のw [(
|| - -n ocl ((
2
-(-n+ 2p 1 vio (( (()) 0(
Combining these two terms we have,
L
(-m++
1²L)
( 1 - (-7
p²
Vooc ((b(++2,
2
2
(27)
Summing up all iterations, we can obtain,
T
T
12L
L ( - 0(0)) - Σ
11 +
p² +
-1] +
11 pie) L(b ((1)))
2
2
t=l
T
LL 2
T
no
|V Vove ove ((0)))));
0² (26 + ((0(2))
11
- 1/ss +
2
t=1
T
n
0² + +1(0
1/s +
2
[=1
(28)
Furthermore, we deduce that,
T
min B|ll gco 1(6( (((()+)));;)))1113
0²+
12 + ((012)
1/s
+
Σ/=1 17 2
1
2
1=1
1
21 + :1= L) p² + 22) ((1)))
Σ
T
21=1 17 [=1
E
(-2m, + +1 2 p² + 21 (0:0011
Σmm
Σt
2m + no L) p²
22 0(1)
1
T'
VT } + 2))
max(L, VT
= (-2n, + n1 p² max(L,
T
(L 2) p² min (1i () L. L VT }
2
2((
T max ,, VT
e(L 2)p² + 22(
0 ( c
cVT
eVT
VT
(29)
The proof has been completed.
Let the & is optimized with the loss in (b()) ((()) = (t((( (1)) Lcc (f Sa (To (())
of") (w((tt)) indicates the adaptive weight for samples where (( = fw (fa (T=(u): (()))
u.
Theorem Suppose supervised and unsupervised loss functions are Lipschitz-smool with constant L and have p-bounded gradient. The H()) is differential with a e-bounded gradient and twice dif- ferential with its Hessian bounded by B. Let learning rate ns satisfies ns min(1, 1 4 } for constant
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mintt: (r for constant such that LT O, such that 1. Yj can achieve
L. The method
V aie fime "om w 2121 =0 20000
lim
(30)
The proof. The optimization from (t)) to ((++1) is,
w (()) nw Vwit Lee fy fw (fa(x: w(
1 2 (m (1) wn(
(31)
We know the updating of is.
((++1) = 6 H(w (6(")) ( V Loe (s. fa (rc)
(32)
Observe that,
sime ( (1+2)) - L fine (Ø'; w(+11))
= (om ( - L fime ( (b(1+)), ( + (nn w Line
(s" (d2:0((++)))
(33)
For the first term, we have
( (0(22) [ fine (d(t)( ()
(34)
= (c+1)) () H((w((+1); (g(t)11))) ((((t(+t)):(((t11))) Lee fa (T((w):)l(ti)))
In the first factor, we achieve
H(w
(++2) ((+() ((+1)) H(w ( (((11)
< (V Wo (((1)) wl(+2) - w((2))) + | - -w((+))
I.
(V Weeen ((n ((++)) - winnn L (x; (e+1), (((+l)))) + _
- Twe V
w ((x (((tt(),,,,))+)))) (t++)))
-/ Vuatn H( (++1), ((+1)) V Lx ((+1) ( ((+1))) + 7/0 2
||
wi (x;
(1+1)
w (++ ||
2
(35)
For the second term, we have
L fine [++). ((t)))) Line (0(00)0)0))))))
I ste Line (1)) w (++1)) (1+1) (1)) (++1)) - -61013 -
stos Tine (1): -16 V VoL ( (t), ((++)))} - 7/ VoL" (
((++)))13
--%//VV L" (t), (+1))1 n, L
V s0o) (1) 11
2
(36)
18

---

Under review as a conference paper at ICLR 2023
Combining these two terms have,
Fine ; (((+))) - 1 f,me (6 w
$ - V p(o)) (u:
(1(2)))) (1) +
210) L" (u: , w((+)))
2
+ Loe (R (T((u); (To()):(((t1)))) 1-1 Vi(+ts) ((w ((tti))) V ( ((tt)) w(++1)
2 L
(i (x; & (1+1), w (++)))))))
2
(37)
Rearranging the inequality, we obtain,
Nw w)(+1) H(w ; ()+))) Vii+t) (x: (z: ( Lee (x. (To(u):
L |1 / 20e) (u: (()) w 11
1/ss 1///lV $010 (u: (0) (1+ S
2
The L
2 VV L 2f (e+1)) (((+ Lee (3. (T((u):((+)))
L. fime ( ;
fime (++ (((+2))
(38)
Summing up the inequalities in T iterations on both sides, we achieve
Bw V H(w ((1)) V Wiiet (x; (=;; (1+1)) w(tt)) Lec (s, ((())))))+t))))
T
n T I
nall pro) (w: w ((+))
V polt) C (u: (u: (10) w (1+1))1
Tu
L
V Lx ( (1+1), w (++ )12 1 Lee (s. (T(
L fine
(2)) fine (T+))))
ns L
T
V (lie) Ld (t,) 11
2
t=1
Nu 2
1) (x: (1t1), ()("),,(()))) (++1))1 Loe (s fa ((tt)))((tt)))
F.fine
(2)
1/8 PT
Tho pT
Σ
T
Lee (s (T((w): + I, sine (6
2
2
(39)
When T + oc, we can obtain.
((a wt Lee (3. fa (To()): (T((w))((t1i))) (((+1)))
nw V H(
nal V Lut (1+
lim
Ep Lee (g.fa (T((w):((++11))
lim Σ noll V 2is) Lu; (t) (t+1))]1
T-0
n/ PT
The pT T
< lim
lim
Σ
Lee (s. (((()):)(++1))) + L (1)) s 00,
T-000
2
T +00
2
(40)
19

---

Under review as a conference paper at ICLR 2023
since Lce (T (T) (() is bounded for limited number of unlabeled samples, supervised loss function have p-bounded gradient and the H() is differential with e-bounded gradient. There- fore we deduce that
T
lim T-+00
1/
L (u: (00 w (++ 11 < xc.
(41)
According to the Lemma A.5 Mairal 2013), prove co B|ll elt) L (w; (10), w (1 0, we should prove
B (in) (" (u; (1+1) w (++2
B (00) (" (0),
w )1 S QTa
(42)
where Q represents constant. Consider the Equation
41 we have
E su (w: ((+1)) w (1+)2)
)121
(u:
(I oi (1+2)
(+2)
||
|
acc
222)
(1+2)
1|2
|
のج 4* u;
writt))) [|2]]
(IV ge 1) uu (1+1) (++2)) (++2))
w
V
(2:
w
((++))) l1l)
(43)
scc L"
(u:
((+))
S 2h V [B[ V dro L" (u: 6(1), w (((())))
B with L (r: ( (1)]
22/2Lp2na na7
Thus, has proved. Since ( = (z s((), (((+)), therefore, the proof has com- pleted.
20


Reviews:
[{"review_id": "Gk9bDctSAWl", "reviewer": "Reviewer_yeCB", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper studies federated semi-supervised learning and propose a new method with a dual-regulator which can handle the heterogeneity of labeled data and unlabeled data from each client. The main contribution is the proposed dual-regulator where the first regulator updates local models  in an meta-learning based way by accessing the updating effect, the second regulator assigns weights to unlabeled instances. Experiments shows that the proposed method significantly outperforms existing methods for different data distribution scenarios. ", "summary_of_the_review": "I am not an expert in this field,  my assessment is based on educational guess. Overall this paper looks good: it studies a problem which was overlooked by previous method, proposes a method which is technically sound, and produce significantly better performance. ", "strength_and_weaknesses": "### Strength\n1. The proposed method is technically sound. \n2. Experiments show that the proposed method significantly outperforms existing methods for different scenarios. \n3. The paper is overall well presented. \n\n### Weakness\n1. The proposed dual-regulator is now very new; we can see similar techniques in many learning problems, e.g., semi-supervised learning, few-shot learning, learning with noisy labels. etc. With that being said, I still appreciate the value of introducing and tailoring these techniques to the federated learning scenario.\n2. Many federated learning works evaluate different data types, images, texts, etc, which would definitively gives more comprehensive evaluation of the proposed method. I do not see the proposed method has an assumption for the data type and thus would be better if such experiments can be conducted.\n3.  There are a few typos and inconsistency of using capitalization in the paper, which should be corrected in the future: sometimes all the words are capitalized for the first letter for the title and sometimes not. The language use is not very professional and should be improved. ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "GQtocNFsNAQ", "reviewer": "Reviewer_JdwN", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This work proposes FedDure, a method for semi-supervised learning (SSL) in federated learning. FedDure employs two “regulators” in order to improve performance in SSL scenarios. The first regulator is the C(oarse) reg(ulator); its job is to regularise the local model training by taking into account the pseudo-labels the local model assigns to unlabelled data. It is a network (initialised to be the network received from the server) which is trained on the pseudo-labelled dataset, where the pseudo labels are obtained from network received from the server. The authors perform a single step of training for the C-reg and then use the difference of the predictive entropies on the actual labelled data as a weight for the gradient of the local model on the cross-entropy loss of the pseudo-labelled data.  The second regulator is the F(ine) reg(ulator); its job is to learn an instance specific weight for the loss that models the impact each unlabelled datapoint should have in training. The training signal for this weight is the cross-entropy loss of the C-reg on the labelled data. The authors alternate between optimising the F-reg, optimising the C-reg for a fixed F-reg and then updating the actual local model using gradient contributions from the labelled data and gradient contributions from the unlabelled data that depend on the C-reg and F-reg. The overall architecture is evaluated on cifar10, cinic10 and fashion mnist, using various split settings that lead to data heterogeneity in both the labelled and unlabelled data. \n", "summary_of_the_review": "While the concept of the F-reg and C-reg are novel and the experiments seem to show improvements upon the baselines (although without error-bars so their significance is a bit unclear), I cannot recommend acceptance given the aforementioned concerns. ", "strength_and_weaknesses": "Strengths:\n- Good performance on the tasks considered \n- An ablation study was performed \n\nWeaknesses:\n- Paper is not clearly written and can be hard to follow \n- Theory seems to be disconnected from the actual method\n- FedDure has a lot of moving parts\n- There are no error bars on the performance metrics, so it can be hard to determine the significance of the results", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "BGUgEN-UsI", "reviewer": "Reviewer_DPn5", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "In this work, the authors propose a new method for federated semi-supervised learning relying on a coarse grained regulator and fine grained regulator. This work handles scenarios where the labeled data and unlabeled data share different distribution. Empirical results show that the proposed method is able to outperform prior baselines.", "summary_of_the_review": "This work tackles an interesting case where the labeled data and unlabeled data comes from different distribution. This problem is conceptually realistic and interesting. The proposed method also shows strong empirical performance.", "strength_and_weaknesses": "Strengths:\n- This work proposes a novel method that handles a realistic scenario that haven't been studied before.\n- This work provides formal convergence guarantee.\n- The empirical results look promising.\n\nWeaknesses:\n- It is unclear what is the motivation for having both coarse-grained and fine-grained regulator. From figure 1 and Section 3, it's hard to follow what is the purpose of having each of them.\n- Is there any theoretical guarantee on how the proposed method handles imbalanced data distribution between labeled and unlabeled data?\n- I'm curious how the method performs in cross-device setting where the number of clients is large and each client has low probability to be selected at each round for scalability. The results would be more convincing if such results are provided.\n\nNit:\n- In Equation (2), should it be argmin over $\\phi$ rather than argmax?", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject