FedTrans: Client-Transparent Utility Estimation for Robust Federated Learning
Authors: Mingkun Yang
Ran Zhu
Qing Wang
Jie Yang
Venue: ICLR 2024 poster (2024)
Keywords: Federated Learning
Primary area: societal considerations including fairness, safety, privacy
TL;DR: Client-transparent utility estimation for Federated Learning

Abstract: Federated Learning (FL) is an important privacy-preserving learning paradigm that plays an important role in the Intelligent Internet of Things. Training a global model in FL, however, is vulnerable to the noise in the heterogeneous data across the clients. In this paper, we introduce **FedTrans**, a novel client-transparent client utility estimation method designed to guide client selection for noisy scenarios, mitigating performance degradation problems. To estimate the client utility, we propose a Bayesian framework that models client utility and its relationships with the weight parameters and the performance of local models. We then introduce a variational inference algorithm to effectively infer client utility, given only a small amount of auxiliary data. Our evaluation demonstrates that leveraging FedTrans as a guide for client selection can lead to a better accuracy performance (up to 7.8\%), ensuring robustness in noisy scenarios.

Published as a conference paper at ICLR 2024
FEDTRANS: CLIEN--TRANPPAEENT UTILITY ESTIMATION FOR ROBUST FEDERATED LEARNING
Mingkun Yang, Ran Zhu, Qing Wang, Jie Yang
Department of Software Technology
Delft University of Technology
mm.yang-3, zhu-1, q ging...nn. wang, J. -yaagggeeeeedllfee
ABSTRACT
Federated Learning (FL.) is an important privacy-preserving learning paradigm that plays an important role in the Intelligent Internet of Things. Training global model in FL, however, is vulnerable to the data noise across the clients. In this paper, we introduce FedTrans, a novel client-transparent client utility estimation method designed guide client selection for noisy scenarios, mitigating perfor- mance degradation problems. To estimate the client utility, we propose a Bayesian framework that models client utility and its relationships with the weight param- eters and the performance of local models. We then introduce a variational in- ference algorithm
effectively infer client utility at the FL server, given only small amount of auxiliary data. Our evaluation results demonstrate that leveraging FedTrans to select the clients can improve the accuracy performance (up to 7.8%). ensuring the robustness of FL in noisy scenarios
INTRODUCTION
We live in a world with billions of Internet of Things (IoT) devices deployed to perform various tasks. These devices sense the surroundings and upload the collected data to servers, where tech- niques such as deep learning are used to perform various tasks such as sensing human activities. The data transfer to cloud edge servers raises privacy issues. Federated Learning (FL), a distributed training paradigm, has thus been proposed to preserve privacy (McMahan et al., 2017). In FL, a cloud or edge server coordinates the training of local models in connected devices, i.c., clients, to learn a global model. The clients only update the server about the weights of their local models. Based on many rounds of the updates from the clients, FL learns the global model gradually by aggregating clients' weights. Since there is no need for the clients to upload their sensed data, FL. has become a popular privacy-preserving learning framework and is being heavily studied for many privacy-sensitive application scenarios such as disease diagnosis (Yang et al. 2021). monitoring (Wul al. 2020), and object detection (Liu al. 2020)..
A key challenge of FL is the data utility of the involved clients. The widely accepted norm in FL that the server adopts the random selection strategy and treats each client with the same selection probability. This is based on the assumption that all the clients with heterogeneous distribution can acquire high-quality labels/data and have equal contributions to the model learning. reality, this assumption does not stand. Studies have reported that existing datasets could easily have more than 30% label errors (Konovalov et al.. 2017 Ren et al.) 2017). FL server inevitably aggregates the updated local weights from unreliable clients which could degrade the performance of the global model trained at the FL server. The issue further complicated by the compounded relationship between noisy data and the heterogeneous local data distributions (non-iid), which affects the vergence and final performance of the model. To demonstrate this, we conduct an experiment, using the CIFARI 10 dataset and without loss of generality flipping the labels the clients, with average label flipping rate of 16.5% across the noisy/corrupted clients, and show the results in Figure (the results under more types of noise can be found in Section 3}. We have the following observation: unreliable clients -the clients with noisy data- slow the learning of the global model and reduce its
"Equal contribution
Code available at httt:p:://ithub..om//eaate http

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accuracy. This can be observed clearly in the non-iid setting by comparing the dash-red curve and solid-red curve. Randomly selecting clients under the non-lID setting with/without noise, fails to account for the potential variations in data characteristies across clients, leading to suboptimal per- formance in terms of the model convergence and the final accuracy. This performance degradation also exists under the IID setting (dash-green curve vs. solid- -rreeen curve).
The above observation validates the importance of selecting reliable clients for training the global model at the FL server. To achieve this, a critical step assess the client utility in a way that can reflect the quality of updates uploaded by clients in the most practical non-IlID scenarios. How-
1.2
Global Model Loss
iid w/o noise
non-idd wlo noise non-lld w/ naise
1.1
lid w/ noise
1.0
0.9
0.8
ever, it is nontrivial to infer client utility due to FL server's lack of accessibility to clients' local data. Therefore, the key problem is how to infer client utility without compromising privacy. Ide- ally, the estimation of the client utility should be transparent to the clients, i.e., no additional oper- ations are required on the client side.
0.7
0.6g
25
50
75
100
125
150
175
200
Round
Figure 1: The noise impact on the global model performance shows different patterns under two data distributions illustrating that data hetero- geneity and quality are tightly coupled issues.
In this work, we design FedTrras (Figure a novel client utility evaluation framework that enables client selection guidance for heterogeneous and noisy scenarios to ameliorate performance degrada- tion. We exploit small but high-quality auxiliary data to explore two complementary strategies for client utility inference: 1) creating synthetic clients based on the auxiliary data build a discrim- inator that distinguishes high-utility clients from lower ones based on their weight parameters, and 2) evaluating the performance of local models as an indicator of client utility. We propose a unified Bayesian framework that seamlessly couples these two strategies and further introduces a variational inference algorithm that allows the inference based on these strategies to benefit from each other, therehy reaching an effect where the whole is greater than the sum of its parts. We execute experi- ments on two public datasets under the Dirichlet distribution, using six different label/feature//hybri noise types. The results demonstrate that our FedTrans delivers better accuracy performance (up to 7.8%) and significantly faster convergence speed (a reduction of over 56% in time consumption, refer to Appendix Eb compared to competing FL methods in noisy heterogeneous settings.
2 FEDTRANS DESIGN
To overcome the data noise issue, it important to precisely estimate the utility of parameter up- dates from clients for updating the global model. For this problem, previous work mainly takes an approach that estimates utility by comparing weight updates among local models and treating updates that disagree more with those from other clients as less useful (Li et al. 2021 Xu et al. 2022]. The effectiveness of such methods depends on the validity of two assumptions: 1) that the majority of local updates are high-quality, which is not necessarily always true in real applications; and 2) that data noise is the only factor of the quality of local updates, which largely overlooks the intertwined effect heterogeneous local data distributions bring on the resulting weight updates in local clients. An alternative approach is to infer the update utility by evaluating participating clients against a certain benchmark, by including high-quality auxiliary data with correct labels and a dis- tribution representative of the data distribution that the global model encounters in the application. We note that in the real applications. it feasible for the service provider to obtain a small amount of auxiliary dataset (Teong et al.) 2018 Tuor et al.) 2021 Yang et al.] 2022a) (e.g., by soliciting data from paid, anonymous workers). Such an approach does not compromise user privacy provided that the auxiliary data is hosted on the server and the computation is also carried out on the server. A practical limitation of such an approach, however, is that the auxiliary data comes at a cost - as it requires human labor for labeling and thus the data can only be of limited size. It, therefore, remains an important open question how to best leverage a limited amount of auxiliary data in a cost-effective way for estimating the client's 's update utility for robust FI.
Problem Definition. The i-th round of FL involves a set of participating clients J that report their local updates (Wr,, Ie to the server. Given set of well- and balanced data D., the server has infer the utilities of local updates (0, (0gre to guide the selection of subset of clients
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Inference
Variational Inference
Hlund Repetation Matrit
0.9
0
Cleat
0
0
W Weight based Discrimination
Boyedian Framswwart
Paranttirs
lnvelrod Cliests
Wolgh-baasd
fratorue
Diurisisane
Figure 2: FedTrans pipeline: it leverages a small, auxiliary data on the server to infer client utility, using Bayesian framework that considers both the weight parameters and performance of local models. A learnable discriminator outputs the client utility while the training lacks labels. To tackle this, we apply a variational inference algorithm update the parameters of the discriminator.
J T' for global model aggregation. The process of utility estimation the server is transparent to all the clients; in other words, no additional operations are required on the client side.
In this way, the model aggregation performed at the server can be formulated as:
W arg min
Σ 9,Cr, jEJ
(I)
where W refers to the weight parameters of the global model; D, is the weight the local client ý in aggregation satisfying |131 pÚ I, e.g. the fraction of local samples; LD, (-) is the corresponding training loss. In this paper, we mainly focus on the estimation of client utility; that means, Pú and CD,( (-) can be arbitrary existing aggregation and local training schemes.
Privacy Guarantee. As a client-transparest approach, auxiliary data Da resides in the central server. In this way, FedTrans retains the same level of privacy protection as FedAvg other SOTA frame- works, since the local data and the training process remain unchanged from the user's perspective. An additional advantage of including auxiliary data is that it makes FL more resilient to adversarial attacks: becomes more challenging to disguise malicious behavior since the performance of the local model be easily evaluated the auxiliary data.
2.1 MODELING THE CLIENT'S UTILITY
FedTTrans makes use of the auxiliary data to infer client utility 8y by fusing two kinds of information: 1) the weight parameters from clients and the clients" performance on the auxiliary data. We illustrate the full pipeline in Figure and introduce details in this subsection.
To start, we denote the utility of client j as 0, [0, 1]. 0, parameterizes Bernoulli distribution that generates the selection decision s, of client j:
8y (0r)
Weight-based Utility Estimation. The auxiliary dataset allows us to simulate a few clients with the known utility using the auxiliary data and based on that, train an additional machine learning model to discriminate clients with low utility by their weight parameters from the rest. To this end, we build secondary machine learning model, denoted as fWa,, and client utility 0g is conditioned on the parameters of local updates, through the weight- weight-based based discriminator fWa:
0, f W (x)).
where the x, refers to the top-layer of local model Wi, in i-th round. We specifically consider the weights of the topmost layer of the models from clients, since those weights most relevant for the given task (Li & Zhan 2021) and hence most discriminative for utility inference. Note that any DL model for the discriminator can generate 0, [0, 1] with sigmoid function.
To train the discriminator, we utilize the auxiliary data D, to generate the synthetic clean and cor- rupted weight parameters, which provides discriminator labeled training samples. Given set of
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clean, well-labeled, and balanced samples Da, first construct clean dataset D Da and a corrupted dataset D where all the labels are manually flipped to incorrect classes. FedTrans then assigns D DD/"" to K pairs of synthetic positive/negative clients {D (1-,,,....
spectively, where each pair possessed | auxiliary samples. For each synthetic client, we obtain synthetic weight parameters by initializing it with the global model from the last round, and then train the model as we would do for normal clients. Training discriminator benefits from such a set of top-layer weight parameters (xx x }x=(1....KK) with known labels.
Weight- baseht discrimination, however, is intrinsically limited by the size of the auxiliary data, which may only cover a small fraction of the weight patterns of clean and corrupted clients. This espe- cially concern given we only consider synthetic clients with all correct all incorrect labels in reality, clients may hold labels with a different mixture of correct and incorrect labels.
based Utility Estimation. To address the issue, we also leverage the auxiliary data with correct labels for evaluating the performance of clients and use such performance as an indicator of client utilltyy To this end, we propose create round-reputation matrix R that keeps track of the local model performance of clients involved in different rounds. In such a matrix, the entry R in the i-th row and j-th column records the performance of client in round We devise the following way for determining values in the matrix: R 1 if the performance of the local model from client exceeds an empirical threshold, and R 0 otherwise. Note that the threshold should be dynamic with the FL progress, thus we take the performance of the local models (i.e., average accuracy) in i-th round on the auxiliary dataset as the threshold.
Performance-
The round-repph repuuattottti matrix R constructed above is a sparse matrix because only a relatively small proportion of candidate clients could be activated in each round. The value assignment for the round- reputation matrix in a certain round is severely affected by the randomness of client involvement, which means that for those R 's that are not blank, the entries cannot be directly treated as the selection decision 85- A more sophisticated way would be to consider the consistency of client performance across different rounds and only consider the clients whose performance consistently exceeds threshold in multiple rounds high-utility ones. A further consideration is to account also for the informativeness of different rounds, c.g., client performance in the first few rounds of FL might be less informative due to the randomness of weight initialization in the local models.
We denote round informativeness as 9, E [0, r; = means the i-th round provides sufficient information for inferring client utility, r; = 0 otherwise. To account for the uncertainty in estimating r; and hence to make Fed- Trans more robust, we take a Bayesian view and model the prior probability distribution as a Beta distribution:
A
Round
rs (eta(a B.):
(4)
Client
where og and 33 are the parameters of the distribution.
Figure 3: Graphical model of FedTrans. Nodes denoted with circles represent random variables where single circled nodes correspond hidden variables and doubly circled nodes correspond to observed variables. Nodes denoted with squares refer to the parameters of the model. Edges represent conditional re- lationships when generating the round- reputation matrix.
Overall Framework. Combining these two ways of leveraging auxiliary data, we now define the likelihood of observed client performance in different rounds, i.e., the round-reputation matrix, as the probability conditioned on the informativeness of the round r; and the client se- lection decision 8, (determined by the client utility 0,):
p( (R..Iris
r, (e, + +(1 -11-10 (1) (e, (5)
where 1(-) is the indicator function. The informativeness of the round is higher if there are more tags {R.j satisfying the actual client utility. The overall framework is depicted in Figure 3 Model updating constitutes parameter learning for Wa and posterior inference for latent variables sy and r;.
2.2 CLIENT-TRANSPAREN UTILITY ESTIMATION
Parameters of the Bayesian framework are learned by maximizing the likelihood function:
p(R) = / /ppp R, r, s|x Wa)dr,s,
(6)
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where and the latent true informativeness of all rounds and the selection decision for all clients, respectively; X is the set of topmost layer of all local models.
We train the discriminator f by maximizing the likelihood function in Equation 6 To solve this optimization problem, we transform Equation to the log-likelihood function
log / q(,, s) log( RR
g(r,))
/ /q(1. s) log( p R, & Wa) )dr,
dr,
R, X; Wa)
(r.
[[(g]IpWa)
2(Wa.
where q(, s) is any probability density function and KL(-) is the Kullback-Leiblee (KL) divergence between two distributions.
Maximizing the above function computationally unfeasible due to the two latent variables in the integral (Tzikas et al. 2008). We solve this problem by Variational Expectation Maximization (variational EM) that iterates between two steps: 1) the E-step where we approximate the distribution of latent variables p(r, s) RJ, X; Wa) with the variational distribution q(r,s); ; 2) M-step where we update the estimate for the parameters of the discriminator Wa by maximizing the evidence lower bound (ELBO) (Blei et al. 2017) of the Equation @ the updated latent variables.
E-Step. We use the mean-field variational inference approach by assuming that q(r factorizes over the latent variables:
q s) = II ((;;) II ((5)).
(8)
We further assume each factor function as:
(r.)) Beta(a4: 3:),
(9)
( = Ber(0,),
(10)
where 0j. C2, and 3, are the variational parameters that can be tuned to minimize the KL-divergence- We use the coordinate ascent to search the optimal parameters, that is, iterating Og (a,, and 3,) until convergence while keeping ag, and B (03) fixed.
To update ((3)), first keep only the terms that depend on 8j simplify the K LLgglpPWy
g(3,) x p(s; Xy; Wa) II #EZi
exp s1)),,
(1I)
where p(sy)x Ky; Wa) is the variational distribution of 8j from last iteration, It is the set of rounds containing j-th client, and (-(-) refers to the expectation term Eg [log()) with x being a variational
distribution. Based on Equation II we can derive the update rule for ((s,) in Equations I3 and 14
Following the same idea, we keep only the terms depending on ry (qllp))))) update the variational distribution g(r:), and the KL-divergence is simplified as
a(rs) p(r.) II JET'
explgg P(R,, s;)).
(12)
where p(r:) ) is the variational distribution of ry from the last iteration, and 6' is the estimation of true label distribution in the current iteration. We can derive the update rule for g(r;) in Equation 15
The updating rules for q(r,s) s) in E-step are given by the following theorems.
Theorem 2.1 (Incremental Client Utility) q(8)) can be updated based on the output of discrimi- nator oj and the parameters of round informativeness from the rounds containing the j-th client and B3 (i E D) ) in the previous iteration. We can derive the update rule
(0, IIEES exp( (Ba) (aa + B,)3
(Ry, = 0)
q(5; 1) x (0, Ilie exp( Vaa;; + {:)}
(13)
(Ri,) = 1),
(1 I1 TIETO exp(V((a)) v(a; + {.}}
(Rij = 0)
a(,== 0)
(14)
(11 0,) TiE (BB)) V(a; + {.))
(Ri, = 1),
where V.) is the Digamma function..
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Algorithm Variational Utility Inference
Require: Local updates (Wigh global model WT-1, Round-Reputation Matrix R, Server aux- iliary dataset D.
1: initialize Wa
2: {Xy]eTJ &- top-layer of (Wijhee
3: [xt,x]] f- top-layer of weight parameters of synthetic clients initialized by Wi trained on D.r and D
4: while Equation has not converged do
b Variational EM D. E-Step
5: while not converged do
6: for j E I do update ((8,) following Equations 13 and
7:
8: end for
9:
for each round = 2, . do
update ((ra) following Equation 15
11:
end for
end while
13: while not converged do
& M-Step
14:
Wa < training on {xylser* with label g(s,) and {x7, (xTxx) x
with known labels
15:
end while
16:
end while
17:
return Parameter of the discriminator Wa
Theorem 2.2 (Incremental Round Informativeness) The informativeness distribution of i-th round q(ra) can be updated based parameters a, and Br from the last E-M iteration and true distribution of client utility in current iteration 0'
Beta(os + Ejer. (1-01)-) (1-0,(1-0),,) ((rs)
00),
+ E)
(Raj = 00
(15)
Betala, Σjey: E1 60)) (Ri, =
Detailed proof of Theorem 2.1 and Theorem 2.2 can be found in Appendix
M-Step. Based on the utility of selected clients and rounds quality inferred by the E-step, the target of the M-step the maximization of the first term Equation 7
Q(Wa, 4) = f g(ri, 8,) log (R.j, Rij. 83 X; Wa)dr;; 85 + const
Σ / (r 8,) log p ddr +
E((0)
logp(s; Wa) + const, (16)
M1
M2
where const = (e) [og q(r..,,) is constant. From the derived equation, only M2 depends on the parame- ters Wa that M-step aims at learning. Obviously, M₂
Ublity
the inverse of the cross-entropy between ((s;) and
p(s,|X X: Wa). which is used as the loss function for our discriminator. M3 can, thus, be optimized using standard mack-propagation in the case of training the discriminator.
0.5 Figure 4: Client Noise Rate case study on CIFAR10: utility inference of 30% noisy clients with random local corrupted samples in participating clients in normal FL settings, well a proportion from 10.1,
Algorithm describes the entire process of clients' util- ity inference and Appendix B provides the convergence analysis. In each round, the server receives updates from
simulates the local training on the auxiliary dataset D. (row 2-3). It then goes through multiple iterations until convergence (row 4); in each iteration, incrementally updates the latent variables sj and r; in the E-step (row 5-10) and updates W2 in the M-step (row 11-13). Figure shows an example result of client utility inference where 30% of clients corrupted by random label flipping

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with local noise rates ranging from 0.1 to 1. We observe that FedTrans can effectively estimate the utility of clients, inversely proportional to the actual local noise ratios.
EXPERIMENTAL RESULTS
3.1 EXPERIMENTAL SETUP
Datasets and Models. We use two widely-used image datasets: CIFARIO (Krizhevsky et al. 2009) and Fashion-MNIST (FMNIST) (Xiao al. 2017). We implement the commonly used neural model for each dataset: LeNet-5 (LeCun et al. 1998) for FMNIST; MobileNetV2 (Sandler et al. 2018) for CIFARIO. We construct the auxiliary dataset by randomly selecting [Dol samples from the test set.
Heterogeneous Data Distribution and Noise Construction. Inline with recent studies (Kairouz al. 2019 Li et al. 2022b Hsu al. 2019), we create the non-IID data distributions by as- signing to the i-th client local data that follows the distribution E R. where is the number of classes and qi sampled from a Dirichlet distribution Dir(ap). The concentration parame- ter a controls the divergence of q: with respect to prior distribution that we set to uniform distribution. We add noise to local data in both label and feature spaces, as shown in Figure
The first row illustrates three types of label noises constructed in different ways: Random Flipping constructs random noise by flipping a label to other classes with equal probabil- ities (Han et al., 2018 Patrini et al.] 2017); Pair Flipping constructs structural label noise by assigning labels to the most often confused classes (Rolnick et al. 2017). as determined by confusion matrix from a centralized training on CIFARIO; Open-set constructs label noise by introducing data (features) from another source while keeping the labels unchanged, for in- stance, a ship image in CIFARIO is replaced by a bicycle image in CIFAR100 (Tuor et al. 2021 Wang et al. 2018). Feature noises are shown in the bottom row of Figure These include Gaussian random noise (with mean 0.2 and variance 1.0), Corruption noise where 50% of an image is set to black, and Resolution distortion where images resized to 4x 4 and then dilated back to 32x32. We set the above parameters following (Wang et al. (2018).
Random Fllpping
Fllppiing aipllone
Noiso
Label: automobile
Label:
Clean Labat ship
Corruption
Gaussian
Resolution
Figure 5: Illustration of data noise in both label and feature space.
Baselines and Metric We compare FedTrans with SOTA baselines that: 1) selectively aggregate
clients, i.e., FLDebugger (Li et al. 202T), FedCorr (Xu et al.] 2022). Oort (Lai et al. 2021) and DivFL (Balakrishnan et al. [022]; g 2) adopt robust local objective function, i.e., Robust-FL. (Yang) ct al. 2022b) and RHFL (Fang & Ye 2022). Besides, we also compare the commonly used vanilla FL framework FedAvg (McMahan et al. (017) in all settings. For fair comparison, we evaluate FedTrans and baselines on the same test set excluding the auxiliary samples Da, and further intro- duce new baselines by fine-tuning FedCorr and DivFL on the auxiliary data. We run all the methods under each setting five times, considering the randomness during model training, and report the aver- age Top-/ accurucy within 500 communication rounds. For further evaluation of training efficiency, we also calculate the wall-clock training time and energy-to-accural in the Appendix P and
3.2 PERFORMANCE EVALUATION
Resilience to Data Noise. To evaluate the resilience of FedTrans to data noise, we compare the FedTTrans and baselines on the non-iid of Dirichlet distribution with concentration parameter a = 0.5 and inject noise to e = 30% clients by applying the six label and feature noise creation strategies on the random fraction (from 10% to 100%) of local samples. In each communication round, the server randomly selects 20 participating clients from 100 active ones. We construct the auxiliary dataset D. by randomly selecting 200 samples from the test set while keeping balanced data distribution.
Table reports the results of the compared methods in different noise configurations. We observe that Fed Trans consistently outperforms other baselines in all noise configurations on both two tasks. This signifies the ability of FedTrans to deal with noisy clients by providing the server with pre- cise utility inference for client selection. Among the baseline methods, Oort and Fl.ebugger
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Table I: Global model accuracy under six types of noise configurations. Label noise integrates three label corruptions, Image noise integrates three image corruptions, and Hybrid noise covers both label and image corruptions, each of which includes two settings: across- refers to noisy clients only preserving one of the specified noises, while intru- refers to a mix of specified noises in all of the noisy clients. The size of auxiliary data [Da|= 200. Distribution of the local data is followed by Dir (0.5), and = 30% of active 100 clients are corrupted. We report the average and standard derivation on five trials under each experimental setup.
CIFAR-10, MobileNerV2 Dirl0.5)
Hybrid (arrors-)
Hybrid (iurro))
Label (ormoss))
Label (lema-)
Image (ocmes-)
Image (Intre-)
FedAAg
McMahan at.l.
2017
69.3%
0.6%
68.3% + 0.6%
66.4%
0.8%
66.4%
0.3%
71.0% + 0.4%
69.25% + 2.4%
Fe.beuugger (1ac ci mi. 2
65.0%
0.5%
64.3% + 1. 5%
66.3%
0.2%
61.2%
0.4%
67.2% + 0..6%
66.1% + 0.5%%
Oort
al
63.1%
0.5%
56.2% 0.3%
1.4%
56.8%
0.8%
67.6%
65.8%
Robist-FF.
Yang ci
2022h
73.1% 0.3%
70.66 + 0.8%
62.3%
0.1%
73.4%
0.4%
72.5%
+ 0.1%
70.8% + D.11%
RHFL
Fang Yo P1M
71.5%
0.2%
70.1% 4: 0.15%
69.4%
0.1%
68.8%
0.4%
72.9%
4: 0.5%
73.0% 4: 0.11%
2022
73.4% 0.2%
70.1%
0.2%
70.7%
0.3%%
72.7%
72.7%
FedCor
Xu al. 2122
77.0%
0.3%
73.7% + 0.4%%
72.8%
0.1%
75.7%
0.1%
73.4%
+ 0.33%
73.7% + 0.6%%
Fine- tone-tnedll DivEL.
70.6%
0.3%
70.6% 4: 0.4%
69.7%
0.35
68.7%
0,258
71.8%
+: 0.3%
70.0%
:: 0..4%
Fine- toneetteeddde FodCor
71.1%
0.3%%
68.2%
0.2%
0.3%
69.2%
68.0%
67.0%
FedTrans
77.1%
0.3%
76.9% 1 0.3%
76.3%
0.2%
75.7%
0.4%
77.3% 1: 0.11
77.0% 1: 0.2%
FMNIST, LoNet-5, Dir(
FodArg (MMMhhnn ct
2017
84.9%
0.3%
84.1% 1: 0.2%
83,9%
0.2%
53,0%
0.1%
85.3%
0.3%
85.1% 1: 0.3%
FeDebugger (Li et al. 2021
85.1% 1: 0.1%
85.3% 1: 0.11%
84.9%
1: 0.2%
84.8%
0.11%
84.8% 1: 0,2%
85.1% 1: 0.11%
Oort Lai
2011
82.6% 0.4%
80.0% 0.4%
80.9%
0.9%
77.0%
0.25%
85.1% 0.2%%
85.5%
Robus-FF Yime
20226
85,0% 0.4%
85.3% 1: 0.2%
84.9%
0.1%
84.8%
0.2%
85.1%
0.3%
85.3% 1: 0.1%
RHFL Fang & Yo 2022
84.5% 0.0%6
84.6% +: 0.1%
83.6% :: 0.1%
84.1%
0.1%
84.5% + 0.00%
84.2% +: 0.5%
DivFI. Halakmshhin
86.1% 0.4%
85.0% 0.0%
85.0%
0.0%
84.8%
0.3%
86.2% 0.1%
86.2% 0.0%
FedCorz Na al. 2023
87.3% 0,2%
87.6% 1: 0.1%
87.3%
0.1%
87,4%
0.1%
86.8%
0.8%
86.1% a: 0.9%
Fin--tuned DivFL
84.3% 0.25%
83.9% 4: 0.11%
83.8%
0.1%%
83.5%
0.2%%
84.9% :: 0.0%%
84.7% :: 0.1%
Fine-runed FedCorr
84.9% 0.1%
84.4% + 0.15%
83.9%
0.0%
44.6%
0.25
83.9%
0.1%
84.8%
0.1%
FedTrans
88.7% 0.3%
88.0%
0.3%
88.2%
0.2%
88.2%
0.5%
88.6%
0.3%
88.6% 0.5%
outperformed by vanilla FedAvG. Their relatively low performance shows that neither the training loss of local models used in Oort nor the difference between the local model weights and global model weights (i.e., [Wr,- - D used in FLDebugger can approximate utility. In comparison, DivFL shows an improvement by encouraging diverse and representative clients for aggregation (via submodularity based client selection); FedCorr achieves also a relatively better performance by measuring the local intrinsic data manifold dimensionality (LID) for utility approximation and further clustering data into two subsets (i.e., clean set and noisy set). Most importantly, FedTrans outperforms all comparison methods, including all the above methods and Robust-FL. and RHFL whose local objectives are designed to be resilient to the local noise. Furthermore, unlike FedCorr which requires all clients to calculate and report their LID score before FL, FedTrans is flexible to take in new clients during the FL process without extra operations on the client. FedTrans is therefore more favorable in terms of both its transparency and flexibility.
To investigate the ability of FedTrans to exploit auxiliary data, we compare it to the fine-tuned ver- sions of FedCorr and DivFL global models using auxiliary data and report the result also in the table. We conduct multiple trials, considering several epochs of the auxiliary data for fine-tuning the global models in all rounds, and report the best results of the new baselines. We observe that the performance after fine-tuning is notably weaker than before fine-tuning. This highlights the impor- tance of effective strategies to leverage limited amount of auxiliary data for model improvement. We report further results under different local data distributions in Appendix G
Ablation Study. We conduct it on CIFARIO with Dir(0.5) and hybrid noises across clients, to evaluate each component of FedTrans in client utility estimation. We compare FedTrans's variants with 1) using entries in the i-th row of round-reputation matrix R for client selection, and 2) using outputs of the discriminator, in each round trained on topmost layers of synthetic clients with known labels, for selection. Figure 6 shows the results. We observe FedTrans as a whole, outperforms both variants, verifying the effectiveness of integrating both components for clients' utility estimation.
Impact of Auxiliary Data Size. Figure 7 shows the performance of FedTrans given increasing sizes of auxiliary data [Pa], corresponding to different data partition of K pair(s) of synthetic pos- itive/negative clients (see Section 2.I). We observe no significant accuracy drop until the size of data on the synthetic client becomes too small (i.e., |Da = 50 and K = 3). The result signifies the cost-efficcency of FedTTran in making use of auxiliary data. We also experiment with a Misaligned situation where the noise type in the local data (hybrid noise) is different from that in the manually
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0.000
0.71
Accuracy
Accuracy
0.775
Accuracy
120
ee
800
Round
0.700
0.5
0.69-
Pactrars
Round Recutstin Mailx
0.725
sol
pal para
0.68
100
2013
300
400
300
0.700
50
100
200
500
06 0.7 Inclusion Ratio
Round
Figure 6: Ablation study on ef- fectiveness of coupling valida- tion & weights discrimination.
Figure 7: Performance
Figure 8: Accuracy and conver- gence speed when using varied inclusion ratios (0.1 to 0.9).
der varied configurations of the auxiliary dataset D..
corrupted D (kept random flipping noise), and observe similar results: significant performance drop even when the local noise is agnostic.
Clients Inclusion. Figure & shows the evolution of FedTTrans performance under varying number of clients included in the aggregation (e = 60% clients having noise). The global model performance first increases and then decreases with an increasing number of noisy clients involved, which is in line with our previous observations on the effect of noisy clients. This reveals the interesting fact that the global model may benefit from selecting appropriately low-utility updates for aggregation. This phenomenon can be attributed to the benefit of including more training data even with a certain level of noise (e.g., in countering biases of the learning) and can leveraged for better design of aggregation strategies in the future. In addition to the performance evolution, we also observe similar trend of the effect of including more noisy clients on the convergence speed.
4 RELATED WORK
Learning from noisy data is a critical issue in deep learning (Khetan et al., 2017 Han et al., 2018 Li al., 2019 2020), especially for cross-device FL with restricted access the local data. In the following, we provide succinct overview of existing literature addressing data noise in FL.
The majority of the work focuses on selecting clean clients. (Lai et al. 1 Li al., 2022a mea- sure the client data utility by the training loss and select clients with large loss. Div (Balakrishna al., (022)) dynamically clusters clients at each communication round according to the modular score and selects the representative client from each cluster for aggregation. (Cho et al., (222)) pro- vides a theoretical convergence analysis of biased client selection in FL. and proposes a selection strategy for trade-off between convergence speed, solution bias, and communication/comppiii overhead. Our work close to (Li et al. 2021 Xu et al. 2022) that propose two-step strategies where the server first identifies the corrupted clients, and then guides the clients to rectify the local noisy samples. Note that our FedTTrans provides a precise identification of defective clients a client-transparent way and shows compatibility with the existing sample-level rectification methods.
A few papers propose to design robust local objective functions. Robust-FL (Yang et al. 2022b) introduces into the local loss function a local centroids term to represent and reduce the effect of noisy data on model training. (Fang & Ye 2022) combines the cross-entropy loss with a reverse term to prevent overfitting noisy labels. In experiments, we have shown the better performance of FedTrann over the above methods; note though, that FedTrans can further benefit from the calibration of local objective functions. Finally, our work related adversarial attacks (Fung et al.) 2020 Tolpegin et al. 22200] Nguyen et al.] (2022). The scenarios considered in this work are, however, FL with the presence of natural issues with the local data, instead of those caused by adversarial attacks.
5 CONCLUSION
In this paper, we observed that FL clients with noise data slow the learning of global model and reduce its accuracy. To help the server select the most suitable clients for global model aggregation, we proposed a unified Bayesian framework FedTrans to estimate the utility of clients. Our FedTrans transparent clients and thus does not require any modifications to clients. Extensive evaluations validate the effectiveness of FedTrans. Our client utility estimation strategy could be leveraged to design better aggregations at the server, make FL more robust in practical deployments.

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ETHICS STATEMENT
We have read the ICLR Code of Ethics and ensured this paper follows it. Our work does not involve dataset releases; all benchmark datasets are publicly available. We anticipate that our work yields positive societal impact by recognizing corrupted and noisy clients during model aggregation within the Federated Learning framework.
ACKNOWLEDGEMENT
This work partly funded by the EU's Horizon Europe HarmonicAl project under the HORIZON- MSCA-2022-SF-0) scheme with grant agreement number 101131111 The work is also part of the ICAI GENIUS lab of the research program ROBUST (project number KICH3, 2T1.3LTP..0000000. 2,000),, partly funded by the Dutch Research Council (NWO). We also thank the support provided by Samenwerk- ende Universitaire Rekentaciliteiten (SURF) with their HPC Cloud infrastructure.
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A PROOFS OF THEOREM 2.1 AND THEOREM 2.2
A.1 PRELIMINARIES
FedTrans integrates (wo client utility estimation strategies: weight-based estimation and performance-bast based estimation. We formulate a Bayesian framework shown in Figure 3 wherein the parameters are estimated by employing the maximum likelihood estimate (MLE) approach. We first briefly introduce MLE under latent variables settings, and from that derive the parameter esti- mate rules for our framework. The general MLE problem formulated as follows:
arg max pl (0: ΦE
MLE
(17)
where & are the parameters of the probabilistic model and O are set of observations.
When infeasible to directly model the likelihood function p( (0; (as our problem), we introduce latent variables L to connect the observations to unknown parameters. In this way, the likelihood function is transformed into
p0: の) = / O)),L
(18)
The expectation maximization (EM) algorithm employed for MLE with latent variables. The algo- rithm iteratively updates the elements in the likelihood function. Specifically, the E-step iteratively optimizes the latent variables L, and the M-step iteratively optimizes the parameters Φ
For the problem in this paper, the observations refer to the round reputation matrix R conditioned on the weight parameters of top-layer X; the latent variables are and s; and the parameters are (Wa, A, B), hereafter denoted P. A detailed expression of the likelihood function is follows:
PR P)
R P):
p Te: P)dr:
(19)
p R. r. r, Wa)dr,s.
We first decompose the likelihood function in Equation 6 into terms shown in Equation of Section 2.2 We then employ variational EM to optimize variables in the Bayesian framework, wherein the E-step and M-step are designed iteratively update the variables related both the two modules. The reason for choosing the variational EM instead of the closed-form EM will also be discussed in the following section.
After applying the logarithm on Equation
19 we get
log (
log
= log
p(R.,, T1, P)dri,
log (K P(Ri,,. P P)dre 8j
Σ Σ
(20)
3
Σ log (Vr ((r), 85)
p1 (Riij xz; q(r,, 83)
Σ
dr
where the approximation term g(ri, 85) can be any probability density function.
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According to Jensen's 's Inequality, we have described the entire process of
(/ (1..e)
P 8,13,333
log
((ri 83)
dri, 8j
(9)))89)
p( R .. Ti, 8y P2):P)
= log
E
a(rin 8j)
(21)
p p. 88 Pxj:P)
2 E
log
q(Tir 84)
p Mi, (2;P))
(rit, log
dri, 83-
((r..)))
rs.83
Therefore, we have
logp(R(X:P) 2 ΣΣ/. g(r,, 8y) log
( 8x1;;;)
dr.. Sy.
(22)
((r),
The difference between the two sides of the inequality is
A (R(x;
ΣΣ
((T:.))) log
p R R.ji. 89 P); (Trr 83)
dr;; 83
Xy: p): ΣΣ I
p (R
log(
((rr)))) log
dr 8j
((1))8))
log(p(R:,j)) Xz; P)) ΣΣ / g(r., log
p(R Si
dr.. 8j
(((),)))
Fri8;
ΣE J...,, (arr 83) log (p (R. (y;; P)) - g(r2, log
dri; 8j
((r,,)))
ΣE Lr g(r,,,)) log
p (R xy;; ()(((
dr:,
p(Rijs rss 83 s|1x; P)
ΣΣ J a(rs, log
p( Rig Mxy; P P)a(riss))
dri,sj 8j
p(r,, Rs Ny; P))((R.)))
Ri, (xy; P))
I g(rr,,8))oo log
85)
ΣΣ Tusy
dri, 8j
p(ri, 85
Ri.j. Xj; P))
= ΣΣ KL(gllp(re, (R,.,x;
(23)
The gap A refers to the first term in Equation 7 which we need to minimize in the E-step. However, the closed-form EM updates do not work in the case of discrete-continuuus variables. We develop mean field variational inference, following the idea of approximating the posterior distribution of
latent variables p(r., sy RR Xy; P) with the variational distribution q(r.s) = II. II, ((r,,,)).
In the mean-field approach, we assume that
q s) (())(()) = 9(r. ((:)) (s..,
(24)
where q(r.) = (et B,) (i.e., Equation 9 and q(s;) = Ber(O,) (i.c., Equation 10
Next, will derive the update rule of q(s) and (r) corresponding to Theorem 2.1 and Theorem 2.2
A.2 PROOF OF THEOREM 2.1
For qs), we have
((s) exp(())())) (og(p(r R, X:P))))
(25)
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For the j-th client, there is set of rounds T' involving the j-th client. In other words, R, is not blank for E It. Equation 25 is formulated as
((3)) & exp(eatra) & exp(
p(r,, 8j X P))))
Σ
log(p(r; 8j. Rij xy; P))]}
iET
(26)
expl
E B (ogg()))g((rr.. 8y. Ri xy; P))l}
iET
II iEz
sy Xy; P))]}.
After applying the chain rule on p(r:, 8j: Rij Xy; P), we can get
p(r;, Sj. Ri X3; P) p(r: P) p X;; p(R.. Fi;
(27)
= p(r)) x p( x P) p(R., (T.
This is because only depends on xj and P, and R does not depend on and P given sj and
Tx.
Substituting Equation 27 into Equation 26
we have
((3)) x II
(Bp(BBrr)llog((m x p(s) iEZ)
x II
exp (
(5)(Ber))ooo(((( Bytr) (ow.::))oopsss))) P)) + (ogt))oo((((RR...o 8;))]}-
iE
(28)
We remove the irrelevant term related to q(s)). i.c., [lo((p(T)) then we get
((3,) x II
(o P)) + + (o.
(29)
o II
exp
( (0g P))]} x exp
(E
Since log(p(s; Ny; P)) dose not contain the variable qr::), we have
exp (Bg (og(p(s))))))))))))) xy; P))]] = exp(log(p(s)Mx; P))} p())1x;;))
(30)
Substituting Equation 30 into Equation 29
we have
((s)) II 1x;
Dog(p( s;))
NET
(31)
x p(s p(3
KEZI
Equation 31 is equivalent to Equation of Section 2.2 when we define Eg(r.) (lo(() (g(r.)
now derive the update rule of q(s,) given the variational parameters 0z. ag and 3g from last iteration. We first show the proof for = 1; the proof for 0 follows similarly.
Based on Equation 31
Equations 2 and of Section 2.1 parameterize the latent variable with the utility 05: the selection 8y of j-th client Tollows Bernoulli distribution parameterized by client utility Oy that is the output of machine learning model f (-)) with input topmost layer x, in the j-th local model. We have
p(aj 1 |x;; P) 03-
(32)
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In Equation 5 connect the round informativeness r, and client selection s, under the assumption that rounds with higher informativeness have more entries Ra., satisfying actual client utility, which can be formulated to
(Rgl r. (11s R.D (1 1 r:)) R.sl
(33)
In the case when 8, = 1, Equation
33 equivalent to
p (R 8,) (1
ri (Rij = 0) (Ri, = 1).
(34)
ri
After substituting the probabilities p(s,|xş; P) and p(R;, (iil 85) into Equation 31
we get
q(s; = 1) x { HER expl (1- - r:)) RR. = 0) 0 IEr explea(r))
(35)
RR. = 1).
By computing the geometric mean of the beta distribution, evaluate the expectations (-) as follows:
Oetre) - r;) v((3.) (ax; + 3c), In(ra) V((a,) (a, [B)).
(36)
(37)
Substituting Equations 36 and 37 into Equation 35 we can obtain the update rule ((s) = 1), as
given in Equation 13 of Section
as well as shown below:
0
Va + Bi) 6, Hig exp( (a;) V(a, + B()
ILE exp (B:) exp(V(B.)
(Rij = 0) (R:j = 1).
q(s 1)
Similarly, for 8, 0, we have
p(s; = 0|xy; P) - -0z.
(38)
and
ri
(Ri, = 0)
(R,y)rs,)) = (1 1 (Rij = 1).
(39)
Equation 31 is then equivalent to
(1- 0,) llees expldg(n)Ts)
(R.; 0)
s(s) 0) x
(40)
(11 0,) Niezs exp( (1)))
(R., = 1).
Again, substituting Equation 36 and 37 into Equation 40 we can obtain the update rule of g(s, 0)
as Equation 14 of Section 2.2
(Raj = 0) (1 - 03) TheT exp ((,) Va + 3:) (Ri,' = 1).
(1 - 03) HliT exp( V(a + }:)}
gss 0) x
We now conclude the proof of Theorem 2.
A.3 PROOF OF THEOREM 2.2
For q(r), we have
(() xc exp(E [log (p(r, R, P:))))
(41)
In the i-th round, there is of participating clients J' corresponding to entries in the i-th row of matrix R. Equation 41 is formulated as
((r)) x (B ) [log( II
p(r., Ry;,, P))]].
(42)
JE5
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Following the transformation of q(3)), can also get simplified version of Equation 42 similar to Equation 31
a(re) x p(r.)
II JEJ
(43)
Since g(5,) Ber(0,), we have
B (oog))log(((.....)) 8;))] = - (13}) log(p(Rs,)
8j
q(3) 0) log(p( R / 85)) g(s; 1) x log(p(Re,lra:s5))
= (1 (,-8,) x log(p p R,,, ris (5) + 8, x (og(
def Ee, (log(p(R.,
(44)
Therefore, Equation 43 is finally transformed into
a(r;) x p(r:) II
exp( [log(p(R, 8y))]}.
(45)
je3r
Equation 45 is equivalent to Equation of Section 2.2 when we define Eg, [log(-)] = Io' (+).
Based on Equation 45 we now derive the update rule of ((rx) given the variational parameters 8 ar and 8, from last iteration.
We replace the probability p(r;) in Equation 45 by the Beta distribution with parameters and 3 from the previous iteration:
a(ri) x Betalas, 3.)
II
(46)
JEJ
According to Equation 33 the exp( Be, [log(p(R 85)]]} in Equation 46 can be reformulated to
exp(Ea,
8,])]}
BBo, [log(;; (1-le,-R,,)) R, x (1 r.) 8, +;-R.ss)]]
exp((1 0,) log(r, (1-1R.,l) x (1 (1-r;) [R.,]] 03 log(r, (1-11- x rr:) 11-B111)
= exp((1 - 0;) x log(r, (1-R,,) x (1 - r;) (R.)) ) 0, x log(r; (R.,) x (1 - -r) (1-,,))))
exp((1 0,) log(r, (1 R.,) (1 rr)) [(s) exp log(r, (R.,)) x (1-1 r₂) (1-
(ri (1 x (1 rú) R..) R (1-8,) x (re Ri,, (1 - r; (1-
r, (1+2R;, , -0, B (1 -r) (Ra.- - 2R, 00,+0)
(47)
Therefore, the expectation term in Equation 46 can be evaluated as follows:
(1,(1-0)(11 rz)
R 0)
Ex, log(p(R, s,)]]
(1-))11 (1-00 (Ryj = 1).
(48)
In the case when R., Equation 46 is equivalent to
a(ri) Beta(a,, 3,) II r: (1-r)) JE31
(49)
The probability density function of r:'s distribution is given by: Beta(os, 3.) ri (a.-1) rz) (0.-1)
(50)
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Published as a conference paper at ICLR 2024
Substituting Equation 50 into Equation 49 get
g(ri) x r (a-
(1 r:) r.: (81111 T: (1 - (1-r:) (-0))
FEI
II ry (a--1))(1 r2:) (0:-))))))) r, 01 r:)) (1)(1)))))
jE.
II JETi
(au -1 (1 - r;) (:))0(+11-0))---
x
ri
(51)
rr, Prllatt),e E5J1 2) - ri) 1:) (Br+t (1 11-0))-1)
Bela
+
Σ JEJ
0z Bi + Σ (1 (1-0,)
JE
Similarly, for R,j = 0, we have
((r)) x Beta (3)) II
r2 (1-0)) - rr:)
(52)
jEji
Again, substituting Equation into Equation 52
complete the proof of Theorem 2.2 as follows:
g(rs) x ri la (1 - r,) (8=-1
II r (1-8;) (1 rz))*
JEJ
II r3 () - ria) ( () re 01) re) JETi
II (1,) 0,0 1) rz) r;) 011+
(53)
JET
ri (a: Je5r (1-0))-1) (1 r,) 1:)(0tt (#:+2iscrr 13-1)
a, a E (1-0,)
(1- 0,), + Σ 0,
Beta
JEJ
jEJ
B CONVERGENCE ANALYSIS
B. PRELIMINARIES
Before the convergence analysis on FedTrans, we first provide detailed formulation of the local training and global aggregation in FedTrans with selective client participation.
In the i-th communication round, the cloud server randomly selects of participating clients J Each client j E J' performs the stochastic gradient descent (SGD) on the local data instances:
D(F, -
Σ NEEi
101 :x),
(54)
W,-1==W = - V (
(55)
where indexes the local SGD step on the objective L(-) regarding the loss function I(-) (e.g.,
cross-entropy loss). E/ a batch of samples randomly selected from local data D, at step T. Client updates local model to pWetts after one-step gradient descent with the learning rate n,. Suppose that client reports the model updates every E' E z steps, and we have the update rule
Weiss Ejegs Pi Wi
+ # iE
Wr+1J
(56)
++1 1 i
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We define the local updates of client offloading the cloud server in round i as
W WEE.
(57)
Under the guidance of client utility estimated by FedTrans, the server aggregates subset of updates from clients J C J for the global model
W
E D, Σ DiW.E.. jES
(58)
jEă
In the following section, we simplify the objective function as (W, = [(S)" and gradients as (W,E) = V2,WW, E) for a more concise expression. Specifically, L,(W) = L(2 D2) and By (W) VL,(W).
B.2 CONVERGENCE GUARANTEE
rigorous convergence analysis of FedTrans is non-trivial since the tendentious selection of clients with high utility compared with random client selection (e.g.. FedAvg). Borrowing from the theo- retical analysis in (Cho et al. 2022) that considers the effect of biased client participation on con- vergence, provide the convergence guarantee of FedTTran under assumptions
Assumption L,,-... Giss are all L-smooth, for all W and W
L (,(W) S (,(") + (VL,(W)) W W") + 2 IIW W
(59)
Assumption LD.... DD are all p-strongly convex, i.e., for all W and w
C,(W) 2 (,(") (VL, W W + # ~/ lI 1w
(60)
Assumption For mini-batch E uniformly sampled at random from local data j- client Dj, the resulting stochastic gradient is unbiased, that is, B[gg(W+.j. :. =9; Also, the variance of the stochastic gradient bounded, ie., for all j = -,..., ,[T] and VT,
([l,,, 9j (Wrr))l1 0z
(61)
Assumption 4 The stochastic gradient's 's expected squared norm is uniformly bounded, i.e., for all j = T and VT,
Ellg, (W 22)1 < G².
(62)
In line with (Cho et al. 2022), we then define two metrics: local-global objective gap and selection skew. The local-global objective gap formulated
M
Σ
(63)
where refers to the fraction of data at j-th client to the overall data volume. The W and Wj are the optimal weight parameters of the global objective 2(-) and local objective 2,(-) respectively. To be more specific,
Wj arg min C,WW),
(64)
W
W arg min [(W) arg min Ep(cs()).
(65)
W
w
Further, denote 2j -2)33) and L L(VV))
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Published as a conference paper at ICLR 2024
The selection skew is formulated as
E ()) c,) ((W) Σ, P
P(S
(66)
where STz,, W) is a set of selected m clients given selection strategy ा according to weight param- eters W, and W is the observing point where we evaluate the local objective (y(W) and global objective L(W)).
We then define two related metrics
- min ((S(TT, W), W")
(67)
W.W.
max W), W
(68)
Under the above- mentiondd three assumptions, for learning rate 7) m(++)) the convergence with any selection strategy т after local steps as
and y
we have
1 AL /2/m) T+T
SL2T 1
W
12
SLT 0 (2-1) (69)
B[(((V)))
3p²p
3p p
where is is the local SGD interactions, and G is the upper bound of the stochastic gradient's expected squared norm in assumption (3).
Similarly, for fixed learning rate 7) & min 2pB } where is + gence with any selection strategy π as
3p 8
we have the conver-
43 + o.) (6PLT)
SLT p) p(8 + +3))
B[C(W]]] L-
118+ +p)
+ 1 - mu(1 + 30) r
L
4 (n132)2
a²
m + (pLL) 2D p)
11
((WV) - c--
8 8+ 3p
(70)
For a small 7j. both fixed-learning rate case and decaying lecaying-learnigg rate case have the same upper bound by ALT 3r ( 1).
In FedTrans, the selection strategy Tutil chooses clients Fr C J't from the participating clients based on the estimated utilities. Therefore, in Equation 66 S(T, W) f and m = 1 Vi I. According to the analysis in (Cho et al.] (202)). larger selection skew results in faster convergence. We provide the lower bound convergence rate ( where T denotes the accumulated local SGD steps, since f calculates the minimum of the selection skew, as shown in Equation 667 In practice, the varying weights parameters of the global model W." and the local model Wi,, cause the selection skew p(S(zz W;), Wi,) change with the FL proceeding while maintaining convergence rate of at least of p.
C MORE EXPERIMENTAL DETAILS
Implementation Details. The parameters of variational utility inference and those for discriminator
fWa training are empirically set. We adopt fWW with Multi-Layer Perception (MLP) having hidden layers of 128 and 64 dimensions respectively. In discriminator training. select the learning rate as le 3, and we set the priors A and B by sampling from a uniform distribution ~ [0, 10) and update them in E-step according to Theorem 2. and Theorem 2.2
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Comparison Methods. We implement all the comparison methods in Python and the neural net- works with PyTorch, running on an NVIDIA 2080Ti GPU. In local training, local epochs are set to 5 and the learning rate is le - 2. We use SGD with momentum factor 0.9 as the local optimizer.
To evaluate the resilience of FedTrans to data noise, we compare it with SOTA baselines. RHFL (Fang & Ye, 2022) considers symmetrically using cross-entropy loss and reverse cross- entropy loss to ameliorate the negative effect internal local model noise. Robust-FL. (Yang et al.) 2022b) copes with the noisy federated setting by interchanging additional information called class- wise centroids. FLDebugger (Li et al.) 202T) utilizes the 2-norm distance between local weight parameters and global weight parameters to distinguish noisy clients. FedCorr (Xu al. 2022)
calculates the average Local Intrinsic Dimension (LID) of local prediction vectors for each client. The server applies a Gaussian Mixture Model on received LID scores to partition involved clients into two subsets: noisy clients and clean clients. As a client selection method, Oort ([.i et al. 2021) achieves enhanced tineuu--ccurrcy by constructing both statistical utility and system utility for clients. DivFL (Balakrishnan al. 2022) selects subset of clients whose weight updates closely mimic the information gained from aggregating updates across all clients, to improve learning ef- ficiency. Note that FLDebugger and FedCorr are sample-wise noisy correction methods where partially compare two baselines with regard to the identification of noisy clients. We implement the component about data utility in Oort for comparison.
Observation details. Figure | illustrates the negative impact of noisy clients under two different local data distributions, emphasizing more severe degradation in global model performance when local data is non-llD across clients. For the completeness of experiments, we also explore the per- formance of the global model varying with learning rates other than 10-2 in Figure | Compared with results in Figure P under both IID and non-lID settings, the global model achieves the best performance when the learning rate is 10-2 as used in Figure [ Furthermore, we observe a more pronounced degradation of the model performance introduced by data noise in non-IID data com- pared to IID) data across all learning rates ranging from 10-1 to 10-1, which necessitates inferring client utility in more realistic non-Ill scenarios.
(lobal Model Loes
2.0
2.0
1.9
Giecal Model LODE
2.2
wis nose Ron-Ed u/o nove nonc
wio noise roise
non rid who roine
JR wio Foise
non w/ race
1.
50
75
12.
125
150
375
200
125
1.9
136
200
25
35
75
200
325
150
375
250
(a) Learning rate = 10
(b) Learning rate 10
(c) Learning rate 10
Figure 9: Global model performance of FL with noisy clients (in Hybrid (across-) local noise). We consider two data distributions and three different learning rates.
0.9
client detecting
0.90
0.9
Accuracy
Recall
0.8
0.80
0.8
0.7
0.70
0.7
0.6
23
75 Round
100
125
150
0.60
2.5
50
75
100
125
150
0.6
100
Round
Round (c) Accuracy
(a) Recall
(b) Noisy client detecting rate
Figure 10: The client selection performance in the presence of 6 30% noisy clients.
Client selection performance. In the experiments, we adopt a threshold based selection strategy, excluding the updates of the clients with the utility 0 below 0.5 from the global model aggregation. As shown in Figure 10 we evaluate the client selection performance in the setting where = 30% clients cornupted by Hybrid (across-) noise. We observe the high recall performance, stabilizing
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approximately 99% after 50 communication rounds. It indicates FedTrans's effective recognition of clean (positive) clients on the server side. The success rate of detecting noisy clients (true negative rate) reaches average of 85% as the rounds progress. Furthermore, the overall accuracy of client selection according to the utilities estimated by FedTraan around 95%, given that the clean clients the majority participants (at approximately 70%) in each communication round.
Correlation between utility and noise rate. As inferring client utility is the main focus of this paper, we investigate the performance of utility estimation by FedTrans across commu- nication rounds. contrast evaluating the success rate of detecting noisy clients, our assessment measures the strength of the monotonic relationship between estimated utility and actual local noise. Disregarding the specific selection strat- egy (e.g., the threshold-based method) according to client util- ities, we employ Spearman's 's rank-order correlation coefficient (PROCC) to quantify the statistical dependence between two variables (i.e., f, and local noise rate). As shown in Figure the utility exhibits a negative relationship with local noise, and this relationship becomes progress. This observation indicates that utility estimation be- comes more accurate and aligned with the client noise degree, primarily attributed to the incremental updates on the discriminator rounds.
Speaman correlation
-0.8
-0.9
-1.0
25
50
75
100
125
150
Round
Figure 11: The correlation be- tween estimated client utility and its actual local noise rate varies with the communication rounds.
significant along with FL
fW across communication
D TRANSPARENT CLIENT UTILITY ESTIMATION IN FEDERATED LEARNING
Here, we provide the pscudo-code of the overall FL process with FedTrans as general algorithmic framework (see Algorithm[2] 22 In each round, local models participating clients first updated as in standard FL settings (rows 3-6). The server then updates the round-reputation matrix and infers client utility (row 8-11) by calling the variational utility inference algorithm (see Algorithm T. After that, it can perform arbitrary client selection strategy guided by estimated client utility (row 12- 14). It finally obtains the global model by aggregating the weight parameters from selected clients (row 15). FedTTaas,, can be coupled to any existing aggregation and local training schemes.
module that does not require any additional information from the client,
Algorithm 2 Federated Learning with FedTrans
1: Require: A set of clients with self-contained data: C; Server auxiliary dataset: Dai Client
selection rate: 7/
1,........ do 3: T +- randomly select [C] x 1) clients from C
2: for each round
4: for j J' in parallel do
Local Training
5: W CliinttUpaate (CN, W;-)
6: end for
7: Server Executes Fed FedTrans:
8: R, + MatrixUpdatte (Wishees R;-1, Da)
9:
Wa +- Variational
(Wryhers W (_...R) R.)
Utility Estimation
10:
{xybier= + top-layer of (Wr, (Wr,hee
11:
{0, f ((x))jer1)
12:
for j E J' do
13:
8, f- client selection guided by 0
D Client Selection
14: end for
15: W Aggregattio ((Wi))eed (sy
Server Aggregation
end for
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E
TIME CONSUMPTION
Although the FedTTrans is running on the server with relatively rich computing resources, this in- evitably incurs extra training time overheads. We present a detailed time consumption analysis un- der noisy clients (i.e., Hybrid (cross-)) on the CIFARIO dataset with distribution Dir(0.5), as shown in Table Z Note that FedCorr Xu et al. (2022) requires involving all clients estimate a set of noisy clients before Federated Learning (FL) training starts. Therefore, we do not investigate the per-round time consumption of FedCorr in this context.
Table 2: Time consumption per round or when achieving the target accuracy for each method.
CIFAR-10 10, MobileNetV2. Dir(0.5)
FedAvg
FLDebugger
Oort
Robust-FL
RHFL
DivFL
FedTrans
Per round (scconds)
113 =
115 2 114
129 2
IIS 1
114 1
173 =
Tirget accuracy (minutes)
118.7
3.2
280.8 + 4.9
385.8 + 10.2 60.9 + 3.3
63.3 + 1.7
49.4 + 0.9
21.7 0.4
In Table we provide the maximum time consumption for single round of FedTrans and other baselines across 300 communication rounds of Federated Learning (FL) communication. Addition- ally, it includes cumulative time consumption when reaching the target accuracy of 63% (i.e., the maximum accuracy achievable by all methods). The results reveal that, although FedTrans requires more time for each round compared to the baselines, the overall time consumption to reach target accuracy with proposed FedTrans is the shortest, showing an impressive speedup of more than 56%. This is primarily because FedTrans requires fewer rounds to attain the targeted accuracy.
Discniminator teration
EM time (seconds)
Iteration
18
600
100
50
0
25
50
75
100
125
150
75
Round
Round
(a) EM optimization time
(b) EM ileration
(c) # Discriminator iteration
Figure 12: The varying optimization overhead in FedTrans across communication round. From left to right: total optimization time, total EM iterations, and the Discriminator iteration required in variational inference.
Furthermore, we also explore the optimization overhead of the variational EM algorithm that changes as FL proceeds. Figure shows the EM optimization time, EM iterations, and Discrim- inator (i.c., M-step) iterations varying with communication rounds. The overall optimization time significantly decreases as FL progresses, attributed the diminishing trend observed both EM iterations and discriminator iterations. Moreover, the time cost of training the discriminator takes a larger proportion of the total optimization time. As a result, the overall optimization time across communication rounds exhibits similar trend as the discriminator iterations.
F EVALUATION ON PRACTICAL RESOURCE- CONNNCREICNNTTAINEEDD TESTBED
We also build a testbed consisting of 21 Raspberry Pi 4B embedded devices, as shown in Fig- ure 13(a), to evaluate the performance of FedTrans in practical resource-constrained scenarios.
HAR Dataset. We conduct the experiments on the Human Activity Recognition (HAR) dataset col- lected from onboard inertial sensors (accelerometer and gyroscope) for distinguishing six activities of daily living: walking, walking upstairs/downsttarrs sitting, standing, and laying. HAR dataset shows inherent suitability for the FL scenarios since the data is naturally split by different partici- specific, HAR contains data collected from 30 different users, and we take 21 users as the training data and augment the number of clients from 21 to 42 by assigning the data of each user to two clients. We the FedTrans testbed and each Raspherry Pi simulates
pants. To be
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0.9
Agcuncy
Aquuracy
Acerncy
0.8
8.7
Fedi FedAvg
FodAng
FolAvg
0.0
200
408
600
500
0.5
200
400
200
M00
Round
Round
Round
(a) Our testbed
(b)
0.2
(c)
0.3
(d)
0.5
Figure 13:
Evaluation of FedTrans on the HAR dataset implemented on resource-constrained de- vices, across three settings of client flip rate (e, 0.2, 0.3, 0.5). Our built testbed: 21 Raspberry Pi 4B embedded devices connect to an FL server wirelessly via a TP-Link WiFi Router.
two clients and connects to the laptop wirelessly through TP-Link WiFi Router. Here, we em- ploy shallow CNN with two convolutional layers for the HAR task and only consider the Random Flipping noise with three different proportions of corrupted clients ranging from 30% 50%.
Results in Figure 13 show FedTTrans can already outperform FedAvg by margin from the beginning. We notice that the gap becomes larger when the number of corrupted clients increases. While FedAvg performance increases when the training proceeds to later rounds, it remains lower than FedTrans. This shows the advantage of selecting clean clients even though number of much fewer than the clients selected by FedAvg.
Energy-to-accuracy. We report the energy consumption (measured by the power meter) when the global model achieves the same performance (i.e,, the best accuracy of FedAvg) utilizing the CIFARIO dataset on our testbed shown Figure 9(a). FedTrans is more energy-efficient even with the extra overhead the server: it reduces the energy consumption by up 66.1% This is mainly due to the fewer training rounds required when FL is training with FedTrans: it requires only 52.2%, 79.2%, and 74.1 % rounds to reach FedAvg's 's best performance for three client noise ratios, respectively.
G PERFORMANCE ON OTHER DATA DISTRIBUTIONS
IID setting. We conduct experiments under the IID setting using the CIFAR10 and FMNIST dataset, evaluating the performance of baselines mixed noise scenarios, The results are presented in Ta- and
and Table 4 The data reported in the tables is based on five trials.
Table 3: Global model accuracy under six types of noise configurations using CIFARIO dataset. Distribution of the local data is followed by IID setting, and 30% of participating 100 clients are corrupted.
MobileNetV2.
Hybrid (acress-)
Hybrid (intro-)
Label (acrese-)
Label (intra-)
Image (acroxz-)
Image (intra-)
FodAvg
FeDeuereer Li
2021
82.1% 1 0.0%
81.5%
0.3%
82.0% 1 0.2%
$1.4% 1 0.4%
81.9%
0.1%
$2.2%
0.2%
Oart Lai ct 2021
66.7% +: 0.4%
63.4%
0.5%
64.7% + 0.7%
64.8% 4: 0.0%
70.2%
0.3%
69.2% + 0.5%
Ro Yang et
2022h
78.4%
77.5%
0.6%
0.0%
RHIF
Fang &
83.1% 1: 0.2%
82.3%
0.1%
83.4%
0.11%
83.4%
0.2%
82.9%
0.5%
82.1%
0.1%
DivFL Balammimma
2022
79.4% +: 0.11
78.4%
0.2%
71.5% 1 0.2%
77.6% 1: 0.0%
80.1%
0.0%
78.7% + 0.2%
FedCor
79.1%
79.6%
0.1%
0.1%
78.3%
0.3%
78.9%
0.2%
FedTrans
0.1%
0.2%
Table 4: Global model accuracy under IID setting with varying ratios of the corrupted clients using FMNIST dataset.
The Ratio of Coruupted Clients
30%
40 %
50%
60%
70%
FedAvg McMahan et
2017
91.2%
91.2%
0.0%
91.2% + 0.0%
91.2%
91.2%
FedAvg McMahan 2017
90.4%
90.3%
90.0%
0.1%
89.7%
87.6%
0.0%
FedTrrans
0.1%
90.4%
0.0%
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Results in these two tables demonstrate that the negative of unreliable clients could be exacerbated by the complexity the task. Even with mixed noise, a significant accuracy drop only becomes dis- cernible when the ratio of corrupted clients surpasses 60% in the relatively straightforward task (i.e., FMNIST dataset). FedAvg suffers from significant performance degradation under mixed noise on the complex task (i.e., CIFARI6 dataset), while FedT'rans outperforms other baselines in effectively mitigating the effects of such complex noise.
H2C setting. We also explored more severe non-IlD experimental setting where each client holds only two classes of data, denoted as H2C. Table S reports the results of the compared methods in different noise configurations under 30% corrupted clients.
Table 5: Global model accuracy under six types of noise configurations. Distribution of the local data is followed by H2C setting, and e = 30% of participating 100 clients are corrupted.
MobileNetV2.
Hybrid (ocrows))
Hybrid (inrr-))
Label (acrnre)
Label (intro-)
Image (across-)
Image (intra-)
FodAvg
0.5%
FLDebucerr Li ctal. 2021
37.7% 1 0.1%
40.7%
0.7%
37.1% 1 0.7%
37.7% 1 0.2%
38.2% 0.9%
40.2%
1.0%
Oori (Lai et 2021
33.2% + 0.2%
18.7% +: 0.7%
34.9% + 0.4%
28.3% = 0.7%
44.6%
0.8%
41.1% +: 0.1%
RobustPl Yang
1.0%
RHIF Fanz & A0re
43.8%
0.5%
36.0%
0.8%
46.6%
1.1%
43.7%
1: 0.8%
44.9%
0.8%
43.2%
1. 0.33%
DivEL Balakrsmmon ot m 2022
45.1% + 0.9%
40.4% + 0.4%
42.64% +: 0.2%
41.3%
= 0.0%
44.1% 0.1%
45.4% +: 0.2%
Xi
0.5%%
0.38
Fed
0.7%
0.8%
FMIISTT LeNet-5, H2C
FodAvg
75.7%
0.2%
FLDebuceer Li
2041
68.2%
0.2%
69.3%
0.2%
72.1%
0.1%
69.0%
0.3%
57.9%
0.2%
56.8% 0.2%
Oori Lai al 2021
72.3% + 0.3%
48.0% +: 0.7%
66.2% +: 0.9%
45.7%
+: 0.8%
0.1% 78.9%
78.1% 8%
Robast.F. Yang
79.9%
79.3%
0.34%
R1IF
Fanz & 1023
80.7%
0.1%
81.2% 0.2%
80.6%
0.2%
80.0% 1: 0.3%
80.8%
0.2%%
80.9% 0.2%
DivFL Balakrislmon d ml 2022
76.8% + 0.7%
76.4% + 0.9%
75.1%
0.4%%
75.2% -: 0.2%%
76.0%
0.3%
71.3% +: 0.5%
et
0.1%
0.4%
81.3%
79.3%
0.22%
79.3%
FedTrans
82.4%
0.2%
84.2% 0.6%
84.3% 1: 0.1%
84.7%
0.33%
83.5% 0.2%
83.2% 0.2%
25


Reviews:
[{"review_id": "OVnxGddC3E", "reviewer": "Reviewer_DCr1", "summary": "The paper considers the problem of performance degradation caused by the presence of noisy clients in federated learning. In order to mitigate this degradation, the paper proposes a client selection policy based on  FedTrans, a Bayesian framework for client utility estimation. The paper constructs a probabilistic graphic model determining the relationship between the client utility, the round reputation matrix, the round informativeness, and some other parameters of the problem (e.g., clients models weights, discriminator model weights, and prior distributions parameters). The paper uses Variational Expectation Maximization to infer the parameters of this probabilistic graphical model. Finally, the paper conducts numerical experiments on FEMNIST and CIFAR-10 datasets with different types and levels of noise. The numerical experiments lead to the following conclusions: 1) FedTrans outperforms other methods. 2) Other methods cannot take advantage for small auxiliary dataset, as opposed to FedTrans. 3) Combining both the round-reputation matrix and the discriminator model is crucial for FedTrans to achieve good performance. 4) The performance of FedTrans is robust to variation in the size of the auxiliary dataset, however, the performance drops if the auxiliary dataset is scarce.", "questions": "- Could you, please, discuss the fairness implication of FedTrans? \n- Could you, please, clarify if the evaluation r2eports the performance of benign clients only, or includes the performance of noisy clients?\n- Could you, please, report the success rate of FedTrans in detecting the noisy clients?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- The paper effectively motivates the problem of performance degradation under the presence of noisy clients. \n- The paper clearly justifies the feasibility of accessing an auxiliary dataset.  \n- The definition of the probabilistic graphical model, and the execution of Variational EM are overall correct. \n- The proposed method does not require the clients to perform any additional computation. \n- The numerical experiments, although being restricted to only two datasets, are fair, and evaluate all the important aspects of the proposed approach.", "weaknesses": "- The paper relies on the availability of an auxiliary public dataset at the server.\n- The clarity of the probabilistic graphical model explanation is lacking, and the rationale behind the modeling choices is not consistently elaborated upon. \n    -  It is unclear what \"the top-layer\" means.\n    - $x_j$ is obtained using $W_{i, j}$.  It raises the question of why the paper opts not to employ $x_{i, j}$ instead.\n    - Further clarification is needed to justify (5).\n- I am surprised by the drop of DivFL and FedCorr after 2the fine-tuning. My guess is that the fine-tuning employed a large learning rate, or a large number of epochs. \n- Figure 6 highlights a limitation of the proposed method: relying solely on the round-reputation or the discriminator model results in inferior performance compared to alternative methods. It is plausible that the superior performance of FedTrans stems from its stacking of two learning methods.\n- The evaluation criteria is unclear. Are the reported results evaluated only on \"good\" (i.e., mot noisy) clients, or on all the clients. \n- Similar to most robust federated learning approaches, FedTrans might raise fairness concerns, as it may eliminate benign clients from the training if their local data distribution is very different from the majority of clients. \n- Other minor issues: \n    - The conclusions of Figure 1 might be due to a poor choice of the learning rate. \n    - I am not sure that Figure 1 brings any significant value to the paper. My understanding is that the main conclusion obtained from Figure is that it is important to select reliable clients for training the global model. This conclusion is obvious. \n    - In the first sentence in Section 1; lives -> live.\n    - what is the meaning of \"without loss of generality\" in Section 1. Does it mean that the same results hold if we vary the flip rate? \n    - As opposed to the paper claim, I think that the calibration/computation of the weights $p_j$ in (1) is crucial. Please, note that $p_j$ in (1) is different from $p_j$ used in Appendix B.\n    - I think that $\\Theta$ is missing in the probabilistic graphical model depicted in Figure 3.", "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": "", "extra_scores": {}}, {"review_id": "jSGIchBEU9", "reviewer": "Reviewer_kySo", "summary": "In this paper, the authors propose a novel Bayesian method designed to achieve robust aggregation on the server side within the framework of federated learning, effectively addressing the challenges posed by heterogeneous and noisy data. Central to this methodology is the use of a small yet pristine and balanced dataset, which resides on the server side and plays a crucial role in approximating the utility of each client. The experiment results validate the efficacy of the proposed approach, showcasing its potential practical benefits.", "questions": "See the weakness above.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The paper addresses a significant issue in the federated learning (FL) environment, presenting a clear and well-founded motivation.\n \n2. The clarity and simplicity of the writing style make the content accessible and easy to understand.", "weaknesses": "1. The novelty of this paper appears somewhat limited. There have been extensive prior studies on federated learning focused on client utility. It would be beneficial if the author could provide further clarification regarding the unique contributions of this work.\n\n2. The proposed method appears to have a high dependence on the server dataset, which significantly limits its potential use cases. This limitation substantially reduces the generality of the proposed method.\n\n3. While the authors do provide a convergence analysis in the appendix, it lacks a proper derivation of the convergence rate. In comparison to random sampling, the theoretical advantages of the proposed method remain unknown.\n\n4. The proposed method introduces additional computational overhead per round, which could potentially increase the time required for each round when compared to the baseline methods.", "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": "", "extra_scores": {}}, {"review_id": "o3zr3qlLla", "reviewer": "Reviewer_PLVU", "summary": "* This paper proposes a Bayesian framework to estimate the client utility on different levels of noisy data. \n\n* Two metrics, i.e., weight-based utility estimation, and performance-based utilization estimation are applied into the Bayesian framework. \nFor the first metric, last-layer weights are trained on a server-owned clean auxiliary dataset/and the noisy dataset is provided as a label. For the second metric, the inference results over the selected model in the auxilliary dataset are used for labeling.", "questions": "As I am not so familiar with the EM framework, I am wondering why the weight-based utility estimation is only involved in the M step, while the performance utilization estimation is involved in the E step. Is that because the performance-based utility label is binary?\n\nIt is shown on page 6 that Algorithm 1 is run in each round of the federated learning process. Will the discriminator weight be inherited from that obtained in the previous round? Will utility inference become more accurate when rounds in the federated learning process increase? If so, can the authors demonstrate how the utility curve evolves with the rounds go?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* The paper is very well-written and the motivation for proposing a utility estimation method is clear. \n\n* The addressed problem is important and addresses the pain in the deployment of federated learning.  \n\n* The method looks technically solid, and the formulation/description is concise but rigorous, but I couldn't check their correctness because of a lack of background in the Bayesian framework.   \n\n* The experiment is also comprehensive, which demonstrates the effectiveness of the utility estimation. Ablation study and analysis of different simulation settings are also provided.", "weaknesses": "* The Bayesian inference part is difficult to read through for readers without related knowledge. The authors may want to  introduce the framework of EM updates in the Appendix for readers without such background,\n\n* The authors may discuss and contrast their Bayesian-based solution and multi-arm bandit-based client selection framework,  (Lai et al,2021), (Huang et al,2020), (Xia et al,2020)， as both frameworks aim to balance exploration and exploitation by providing some label signal for the client selection process. \n\n\n* Minor: the margin of the headers of Section 4 and Section 5 are modified. It is suggested the authors obey the author's guidelines and keep the original format. \n\n\nLai F, Zhu X, Madhyastha H V, et al. Oort: Efficient federated learning via guided participant selection[C]//15th {USENIX} Symposium on Operating Systems Design and Implementation ({OSDI} 21). 2021: 19-35.\n\nHuang T, Lin W, Wu W, et al. An efficiency-boosting client selection scheme for federated learning with fairness guarantee[J]. IEEE Transactions on Parallel and Distributed Systems, 2020, 32(7): 1552-1564.\n\nXia W, Quek T Q S, Guo K, et al. Multi-armed bandit-based client scheduling for federated learning[J]. IEEE Transactions on Wireless Communications, 2020, 19(11): 7108-7123.", "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": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (poster)