Self-Aware Personalized Federated Learning
Authors: Huili Chen
Jie Ding
Eric William Tramel
Shuang Wu
Anit Kumar Sahu
Salman Avestimehr
Tao Zhang
Venue: NeurIPS 2022 Accept (2022)
Keywords: Federared Learning
Personalization

Abstract: In the context of personalized federated learning (FL), the critical challenge is to balance local model improvement and global model tuning when the personal and global objectives may not be exactly aligned. Inspired by Bayesian hierarchical models, we develop a self-aware personalized FL method where each client can automatically balance the training of its local personal model and the global model that implicitly contributes to other clients' training. Such a balance is derived from the inter-client and intra-client uncertainty quantification. A larger inter-client variation implies more personalization is needed. Correspondingly, our method uses uncertainty-driven local training steps an aggregation rule instead of conventional local fine-tuning and sample size-based aggregation. With experimental studies on synthetic data, Amazon Alexa audio data, and public datasets such as MNIST, FEMNIST, CIFAR10, and Sent140, we show that our proposed method can achieve significantly improved personalization performance compared with the existing counterparts. 

potentially Self-Aware Personalized Federated Learning
Huili Chen, Jie Ding, Eric Tramel, Shuang Wu, Anit Kumar Sahu, Salman Avestimehr, Tao Zhang
Alexa AI, Amazon
(chehuili, jiedi, writramm wushuan, anitsah, avestime, taozhng) @amazon, com
Abstract
In the context of personalized federated learning (FL), the critical challenge is balance local model improvement and global model tuning when the personal and global objectives may not be exactly aligned. Inspired by Bayesian hierarchical models, we develop a self-aware personalized FL method where each client can automatically balance the training of its local personal model and the global model that implicitly contributes to other clients' training. Such balance derived from the inter-client and intra-client uncertainty guantification. A larger inter-client variation implies more personalization needed. Correspondingly, method uncertainty-driivn local training steps and aggregation rule instead of conventional local fine-tuning and sample size-based aggregation. With experimental studies on synthetic data, Amazon Alexa audio data, and public datasets such as MNIST, FEMNIST and Sent140, we show that our proposed method achieve significantly improved personalization performance compared with the existing counterparts.
Introduction
Federated learning (FL) Koneveny et al. 2016 McMahan et al. 2017) ) is transforming machine learn- ing (ML) ecosystems from "centralized in-the-cloud" "distributed across-clients." leverage the computation and data resources of billions of edge devices (Lim et al., 2020), without raw data leaving the devices. As a distributed ML. framework, FL aims train a global model that aggregates gradients model updates from the participating edge devices. Recent research in FL has significantly extended its original scope to address the emerging concern of personalization, broad term that often refers to FL system that accommodates client-specific data distributions of interest (Ding et al. 2022).
In particular, each client in personalized FL system holds data that can be potentially non-identically and independently distributed (non-Ill IID). For example, smart edge devices at different houses may collect audio data (Purington et al. 2017) of heterogeneous nature due to, c.g., accents, background noises, and house structures. Each device hopes to improve its on-device model through personalized FL without transmitting sensitive data.
While the practical benefits of personalization have been widely acknowledged, its theoretical understanding remains unclear. Existing works on personalized FL often derive algorithms based on pre-specified optimization formulation, but explanations regarding the formulation its tuning parameters rarely go beyond heuristic statements.
In this work, take different approach. Instead of specifying optimization problem to solve, we start with toy example and develop insights into the nature of personalization from a statistical uncertainty perspective. We aim to answer the following critical questions regarding personalized FL.
(Q1) The lower-bound baselines of personalized FL can be obtained in two cases, iee, each client performs local training without FL, or all clients participate in conventional FL training. However, the upper-bound for the client is unclear.
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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(Q2) Suppose that the goal of each client is to improve its local model performance. How to design an FL training that interpret the global model, suitably aggregate local models and fine fine-tune each client's ' local training automatically?
Both questions Q1 and Q2 are quite challenging. Q1 demands a systematic way to characterize the client-specific and globally-shan training process being used. To this end, instead of studying personalized data in full generality, we restrict our attention to simplified and analytically tractable setting: two-level Bayesian hierarchical models, where the top and bottom level describes inter-client and intra-client uncertainty, respectively.
information. Such characterization is agnostic to any particular
The above Q2 requires FL updates be adaptive to the nature of the underlying discrepancy among client-specific local data, including sample sizes and distributions. The popular aggregation approach that uses sample size-based weighting mechanism (McMahan et al., 2017) does not account for the distribution discrepancy. Meanwhile, since clients' data is not shared, estimating the underlying data distributions unrealistic. Consequently, is highly nontrivial to measure and calibrate such a discrepancy in FL settings. Addressing the above issues is a key motivation of our work.
1.1 Contributions
We make the following technical contributions:
Interpreting personalization from hierarchical model-based perspective and providing theoretical analyses for FL training.
Proposing Self-FL, an active personalized FL solution that guides local training and global aggregation via inter- and intra-client uncertainty quantification.
Presenting novel implementation of Self-FL for deep learning, consisting of automated tuning for clients and an adaptive aggregation rule.
Evaluating Self-FL on Sent 140 and Amazon Alexa audio data. Empirical results show promising personalization performance compared with existing methods.
To our best knowledge, Self-FL is the first work that connects personalized FL with hicrarchical modeling and utilizes uncertainty quantification to drive personalization.
1.2 Related work
Personalized FL. The term personalization in FL often refers to the development of client-specific model parameters for a given model architecture. In this context, each client aims to obtain local model that has desirable test performance on its local data distribution. Personalized FL is critical for applications that involve statistical heterogeneity among clients.
A research trend is to adapt the global model for accommodating personalized local models. To this end, prior works often integrate FL with other frameworks such multi-task learning (Smith et al.
2017), meta-learning (Tiang el al.) 2019; Khodak et al., 2019 Fallah et al. 2020a b Al-Shedivaa et al.
2021). transfer learning @Wang et al. 2019 Mansour al. 2020), knowledge distillation (Li and
Wang 2019) and lottery ticket hypothesis (Li et al. 2020a). For example, DITTO (Li et al. 2021)
formulates personalized FL as a multi-task learning (MTL) problem and regularizes the discrepancy of the local models to the global model using the &a norm. FedEM B0cdEM/Mrrfo Marfoq et al. (2021) uses the MTL
formulation for personalization under a mnite-mixture model assumption and provides federated EM-
like algorithms. We refer to Vanhaesebrouck et al. (2017); Hanzely et al. (020)): Huang et al. (2021) for more MaLeb approaches and theoretical bounds on the optimization problem. From the perspective of meta-learning, peedMe (Dinh et al., 2020) formulates a bi-level optimization problem for personalized FL and introduces Moreau envelopes as clients' regularized loss. PerFedAvg (Fallah) et al. 2020b) proposes method to find a proper initial global model that allows quick adaptation to local data. PFedHN Shamsian et al. (022)) proposes to train a central hypernetwork for generating personalized models. FedFOMO Zhang et al. (2020) introduces method to compute the optimally weighted model aggregation for personalization by characterizing the contribution of other models to one client. Later on, will focus on the experimental comparison of Fe with DITTO, pFedMe, and PerFedAvg, since they represent two popular personalized FL. formulations, namely multi-task learning and meta-learning
limitation of existing personalized FL methods is that they do not provide a clear answer to question QI. Consequently, it is unclear how to interpret the FL-trained results. For example, in the extreme case where the clients are equipped with irrelevant tasks and data, any personalized FL methods that
require a pre- presseccfeeed global objective (c.g.. Ditto (Li et al. 202I), pFedMe (Dinh et al. 2020 may cause significant biases to local clients.

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2 Bayesian Perspective of Personalized FL
We discuss how Self-FL approaches personalized FL with theoretical insights from the Bayesian perspective in this section. The notations are defined as follows. Let N (W, σ²) denote Gaussian distribution with mean μ and variance o². For a positive integer M, let [Ad] denote the set {L...., M.
Let Em/i denote the summation over all m E [M] except for m = i. We summarize frequently used notation in Table Bof of Appendix and the derivation for general parametric models in Section D
2.1 Understanding personalized FL through a two-level Gaussian model
To develop insights, we first restrict our attention to the following simplified case. Suppose that there M clients. From the server's ' perspective, it is postulated that data 21: 21..... 2M generated from the following two-layer Bayesian hierarchical model:
mm 00 H (6o, oō), 1m.6. 6m HD (6m,, mm)
(I)
for all clients with indices m = 1..... M. Here, of is constant. and 9, is a hyperparameter with con-informative flat prior (denoted by πT). The above model represents both the connections and heterogeneity across clients. In particular, each client's data are distributed according to a client-specific parameter (0m). which follows a distribution decided by parent parameter (0o). ). The parent parameter is interpreted as the root of shared information. In the rest of the section, we often study client I's local model as parameterized by 0, without loss of generality. Under the above model assumption, the parent parameter 8g that represents the global model has a posterior distribution p(0o 21:M) N(((()) ((O),, where: g(w) A Σ Eme(an + + 2m
(())
(2)
Emejar --
mm My + ob.)
The 2m in Eqn. may also be denoted by 0% for reasons that will be seen in Eqn. 3 From the perspective of chennt m, we suppose that the postulated model is Eqn. (T) for m 2............................... M, and
0, = 8g. It can be verified that the posterior distributions of 0₁ without and with global Bayesian
learning are p(0) 21) No(O e(1)) and p(0, 21.M) ~ Ar(e(T)) ((m)),, respectively, which can be computed
0 A
(1) A oi
21:
0 20(h) Σ mzt1 (0) + o²h) -10
((m))
(3)
01 2 + Σ moti 1 (0) + o2a)
[AL] A
+ EmEmi +
The first and the second distribution above describe the learned result of client from local data and from all clients' data in hindsight, respectively. Using mean square error as risk, the Bayes
estimate of 0 or 6g the mean of the posterior distribution. namely 0 and f( as defined above.
The flat prior on Og can be replaced with any other distribution to bake prior knowledge into the calculation. We consider the flat prior because the knowledge of the shared model is often vague in practice. The above posterior mean (( can regarded as the optimal point estimation 0 given all the clients' data, thus is referred to as "FL-optimal". g(a) can be regarded as the "global- optimal." The posterior variance quantifies the reduced uncertainty conditional on other clients' data. Specifically, we define the following Personalized FL gain for client 1 as:
(L)
GAIN
1 11++f of
Σ (o0 -
[FL)
m
Remark 2.1 (Interpretations of the posterior quantities). Each client, say client 1, aims learn 0 in the personalized FL context. Its learned information regarding 91 is represented by the Bayesian posterior of 01 conditional on either its local data 21 (without communications with others), the data 21:M in hindsight (with communications) For the former case, the posterior uncertainty described by ( depends only the local data quality of. For the latter case, the posterior mean (( is weighted sum of clients' local posterior means, and the uncertainty will be reduced by factor of GAIN1. Since point estimation of 0, is of particular interest in practical implementations, we treat g(IL)) as the theoretical limit in the FL context (recall question Q1). To develop further insights into
(BL) we consider the following extreme cases.
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As o + meaning that the clients are barely connected, the quantities ol and (BL) reduce to 0(4) and oj respectively; meanwhile, the personalized FL gain approaches one, the global parameter mean ((G) becomes a simple average of 0% (or 2m.. and the global parameter has large variance.
When of = 0, meaning that the clients follow the same underlying data-generating process and the personalized FL. becomes standard FI., we have (/T)) (((), which is weighted sum of clients'
local optimal solution with weight proportional to omm (namely client m's precision).
When of much smaller than all other o and of: and M is not too large, meaning that client has much higher quality data compared with the other clients combined, and GAIN, R 1. In other words, client 1 almost learns on its own. Meanwhile, client 1 can still contribute other clients through the globally shared parameter 0g. For example, the gain for client 2 would be GAIN2 2 o./ which is much larger than one.
have @!mh) ~ o(
Remark 2.2 (Local training steps to achieve (()))). Suppose that client 1 performs & training steps using its local data and negative log- ligellooo loss. We show that with a suitable number of steps and initial value, client can obtain the intended 0(+2)) The local objective
0 (0 /(2o)) = (0 00000)))((((
(4)
which coincides with the quadratic loss. Let 17 E (0, 1) denote the learning rate. By running the gradient descent:
0f t 0.- à (0 0(0)) /200)
00
= 09 n0
(5)
for steps with the initial value 0N client will obtain:
of (1 (1 or em + (1 (1-oj or (n) 0!TT.
(6)
It can be verified that Eqn. becomes ((t))) in Eqn. 3D if and only if:
Σ Emyr (a ) -1
(7)
Σ mx (08 + +
E mz (0) om)
(1 oj m))
(8)
o7 + Emwz (oā + o%
other words, with a suitably chosen initial value OINIT, learning rate y,, and the number of (early- stop) steps e, client can obtain the desired o(m)
3 Proposed Solution for Personalized FL
Our proposed Self-FL framework has three key components as detailed in this section: (i) proper initialization for local clients at each round, (ii) automatic determination of the local training steps. (iii) discrepancy-awart aggregation rule for the global model. These components are interconnected and contribute together Self-FL's effectiveness. Note that points (i) and (iii) direct Self-FL to the regions that benefit personalization in the optimization space during local training. which is not considered in prior works such as DITTO Li et al. (202T) and pFedMe (Dinh et al. (2020). Therefore, Self-FL. is more than imposing implicit regularization via early stopping.
3.1 From posterior quantities to FL updating rules
In this section, we show how the posterior quantities of interest in Section 2 can be connected with FL, where clients' parameters suitably deviate from the global parameter, and the global parameter is a proper aggregation of clients' parameters. For notional brevity, we still consider the two-level Gaussian model in Subsection 2.1 For regular parametric models, mentioned in Subsection D that one may treat zm as the local optimal solution o(() and variance a2 as the variance of 0!!) due to finite sample.

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Recall that each client can obtain the Fl Fl-ootimal solution 0 with the initial value ON in Eqn. and tuning parameters 7/, in Eqn. Also, it be shown that O connected with the global-optimal ((0) defined in Eqn. through:
(oā +
ON (
(0m) o(0)).
(9)
kettm (o + o2)
The initial value ONNe in Eqn. 9 is unknown during training since 0% o(a) are unknown. A natural solution is to update gINIT, 0 and g(a) iteratively, leading to the following personalized FL rule.
Generic Self-FL: At the t-th (t = .. round of FL:
Each client m receives the latest global model 0- from the server and calculates:
(oū + to0)
O INIT 0--1
Σ ke ( + + (0th 0²-
(10)
where 0i-11 is client m's latest personal parameter at round t- 1, initialized to be 8 Starting from the above gf,NI client performs gradient descent-based local updates with optimization parameters following Eqn. ( or its approximations, and obtains a personal parameter 6m.
Server collects On m I,..., M, and calculates:
6º Emejyy (o) + +m) 20
(11)
Σme(M (0g + -
In general, the above où o2 represent "inter-client uncertainty" and "intra-client uncertainty," mn respectively. When oj and m. 's are unknown, they can be approximated using asymptotics of M-estimators or using practical finite-sample approximations (elaborated Subsection 3.2
We provide a theoretical understanding of the convergence. Consider the data-generating process that al (0m, ) are independent, and o... up (fo: a.) where of is fixed constant and each of may or may not depend on M. Let Op denote the standard stochastic boundedness. The following result gives error bound of each client's personalized parameter and the server's parameter.
Proposition 3.1. Assume that maxme[ad] on upper bounded by a constant, and there exists constant q E (0, 1) such that:
Ens ( + o0)
mE M 6m + En ( og) 5q
(12)
Suppose that 0, the gap between the initial parameter and each client's FL-optimal value
satisfies 00 - - < C for all m E [M]. Then, for every positive integer t, the quantities max 10 0!/h) 1, 10 g(o) are both upper bounded by C. .g' + Op(M11/2 as M oc.
Remark 3.2 (Interpretation of Proposition 3.T. The proposition shows that the estimation error of each personalized parameter 6t and the server parameter 6 can uniformly go to zero as the number of clients M and the FL round t go to infinity. The error bound involves two terms. The first term q' corresponds to the optimization error. Typically, every om is small value. If each client has sample size of N, will be at the order of M/ + M). The second term (M--222) is a statistical error that vanishes as more clients participate. Intuitively, the initial model each client and the global model at each round are averaged over many clients, so a larger pool leads to a smaller bias. The proof is nontrivial because the averaged terms are statistically dependent. For the particular case that each of is at the order of N-1 can that the error is tiny when both M and N/M grow.
3.2 SGD-based practical algorithm for deep learning
For the training method proposed in Subsection 3.1 the quantities og and o2 are crucial as they affect the choice of learning rate 7mm and the early-stop rule. For many complex learning models, we do not know of and o2 and the asymptotic approximation of og and o may not be valid due to a lack of regularity conditions. Furthermore, one often uses SGD instead of GD to perform local updates, so the stop rule depends on the batch size. this subsection, we consider the above aspects and develop practical algorithm for deep learning. Following the discussions in Subection D
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can generally treat on as "uncertainty of the local optimal solution 0 of client m", and où as "uncertainty of clients' underlying parameters." We propose a way to approximate them.
Assume that for each client m, we had u independent samples of its data and the corresponding local optimal parameter 0m.1...... mm, We could then estimate oe by their sample variance. In practice, we can treat each round of local training as the optimization from a bootstrapped sample. In other words, at the round t, let client m run sufficiently many steps (not limited by our tuming parameter E) until it approximately converges to a local minimum, denoted by mm..- To save computational costs, client does not necessarily wait for its local convergence. Instead, we recommend that each client use its personal parameter as a surrogate of m, at each round t, namely to use 8% In other words, at round t, we approximate of with:
a empirical variance of (0m....., J...
(13)
Likewise, at round 1, we estimate o by:
of empirical variance of (0i,.... p-
(14)
parameters, counterpart of the derivations in earlier sections will involve matrix multiplications, which does not fit the usual SGD-based learning process. We thus simplify the problem by introducing the following uncertainty measures. For vectors Fiy...,Ta. their empirical variance is defined as the trace of Eme[Ar]
For
(Xmm (Nm (Im z)², which is the sum of entry-wise
empirical variances. 22 and of will be defined from such empirical variances, similar Eqn. 13) and 14 In practice, for large neural network models, we suggest deploying Self-FL. after the baseline FL training runs for certain rounds (namely warm-start) so that the fluctuation of local models does not hinder variance approximation.
propose our personal- ized FL solution in [ We include the implementation details of Self-FL in Section M and
Combining the above discussion and the generic method in Subsection
Appendix. We derived how to learn ((9) and (FLL) for parametric models in Subsection D The key motivation of Algorithm is that client often cannot obtain the exact 0% (especially in DL), so we interweave local training and personalization through an iterative FL procedure. Note that the
computation of g(() and !!!h) requires uncertainty measurements approximated from communications between the clients and the server. In the case where a client does not have sufficient labeled data, this client's 's intra-client uncertainty value of tends to be large and the local training step computed via Equation K will be small. This means that Self-FL. will suggest a client with limited labeled data train only few epochs on their local dataset, thus alleviating over-fitting.
Algorithm Self-aware Personal FL (Self-FL)
Input: A server and M clients. Communication rounds T, client activity rate C, client m' 's local data Dm and learning rate 7m
for each communication round f = 1, 1....... do Sample clients: M,, <- max(1c M). 1) for each client m E M, in parallel do
Distribute server model gt-1 to client m72 Estimate o² using Eqn. (3)
Compute local step mm from Eqn. (8) and local initialization @INIT via Eqn.
6', <- LocalTTriin (fiIT .mmm mm; Dm)
Server estimates of using Eqn. 14
Server performs global aggregation and updates global model 0 via Eqn.
The proposed Self-FL framework (described in Alg. I requires the selected clients to send their updated local models 0r, and the intra-client uncertainty values of to the server. After uncertainty- aware model aggregation. the server distributes the updated global model and the inter- client uncertainty oă to the clients. Therefore, the communication cost of Self-FL is the same level as the standard FedAvg except for the additional cost of transmitting the uncertainty values (which are scalars). Compared to baseline FedAvg, Self-FL requires additional computation to obtain the inter-client and intra-client uncertainties via sample variance shown in Eqn. (3) and (4). The extra computation cost of Self-FL. is small since these sample variances are updated in an online manner as detailed in Appendix Subsection B It is worth noting that our proposed personalization method for balancing local and global training in FL is applicable to other tasks involving auxiliary data since Self-FL does not depend on particular formulation of the empirical risk.
Discussion.

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Experimental Studies
4.1 Experimental setup
We use AWS p316 instances for all experiments. To evaluate the performance of Self-FL, we consider synthetic data, images, texts, and audios. The loss in Alg. [ can be general. For our experiments on MNIST, FEMNIST, CIFARIO, 10, Sent1 40, and wake-word detection, we used the cross-entropy loss. Our empirical results on DL problems suggest that Self-FL. provides promising personalization performance in complex scenarios.
Synthetic Data. We construct a synthetic dataset based on the two-layer Bayesian model discussed in Subsection 2.T where each data point is scalar. The FL system has total of M 20 clients, and the task is to estimate the global and local model parameters. The heterogeneity level of the data can be controlled by specifying the inter-client uncertainty og and the local dataset size Nm for each client m. We construct two synthetic FL datasets, one with high homogeneity and one with high heterogeneity, to investigate the performance of FL. algorithms in different scenarios. The empirical results are provided in Appendix Subsection G.1
MNIST Data. This image dataset has 10 output classes and input dimension of 28 28. We use a multinomial logistic regression model for this task. The FL system has a total of 1, 000 clients. We use the same non-IID MNIST dataset FedProx (Li) 2020). where each client has samples of two-digit classes, and the local sample size of clients follows a power law (Li et al. 20205).
FEMNIST Data. The federated extended MNIST (FEMNIST) dataset has 62 output classes. The FL system has MM- = 200 clients. We use the same approach as FedProx (Li et al. 20206 for heterogencous data generation where ten lower-case characters ('a"-"j") from EMNIST are selected, and each client holds five classes of them.
CIFARIO Data. This image dataset has images of dimension 32 x 32 x 3 and 10 output classes. We use the non-i.i.d. data provided by the pFedMe repository [anh T. Dinh (2020). There are a total of 20 clients in the system where each user has images of three classes.
140t140 Data. This is text sentiment analysis dataset containing tweets from Sentiment 40 Go cet al. 2009). It has two output classes and 772 clients. We generate non-i.id. data using the same procedure as FedProx Li (2020. Detailed setup and our experimental results on Sent140 are provided in Appendix Subsection G.3
Private Wake-word Data. We also evaluate Self-FL. on private audio data from Amazon Alexa for the ware-word detection task. This is a common task for smart home devices where the on-device model needs determine whether the says a pre-specified keyword to wake up the device. This task has two output classes, namely 'wake-word detected' and 'wake-word absent.' The audio stream from the speaker is represented as a spectrogram and is fed into convolution neural network (CNN). The CNN is a stack of convolutional and max-pooling layers (11 in total). The number of trainable 1 The heterogeneity between clients comes from the intrinsic property
parameters is around of different device types (e.g.. determined by hardware and use scenarios). We use an in-house far-field corpus that contains de-identified far-field data collected from millions of speakers under different conditions with users' content. This dataset contains 39 thousand hours of training data and 14 thousand hours of test data.
To support practical FL systems where only a subset of clients participate in one communication round (also known as client sampling), Self-FL can update the global model 0' with smoothing average. Particularly, given an activity rate (i.e., ratio of clients selected in each round) C E (0, 1), we first obtain the current estimation 0f by applying Eqn. 11 to the active clients. Then, the server updates the global model using 0² = (1 C) 0²~1 + C' 0¹. Updating the global model with smoothing average allows us to integrate historical information and reduce instability, especially for small activity rate.
4.2
Effectiveness on the image domain
Results on MNIST and FEMNIST. A description of MNIST and FEMNIST data are detailed in
Subsection 4.1 The activity rate is set to C' = 0.1. For MNIST, we use learning rate 17 = 0.03 and batch size 10 as suggested in FedProx Li 2020). For FEMNIST, we use = 0.01 and batch size 10. The FL. training starts from scratch and runs for 200 rounds. For comparison, we implement FedAvg and three other personalized FL. techniques, DITTO (Li et al. 202T), PFedMe (Dinh et al. 2020), and PerFedAvg (Fallah et al. 2020b with the same byper--arameete configurations.
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0.8
Test Acc
0.6
0.6
0.4
FedAvg
0.4
FedAvg DFedMe
PFedMe
PerfedAvg
PerFedAvg
DITTO
DITTO
SelfFL
SelIFL
0.0
25
50
75
100
125
150
175
50
75
100
125 150 175
Rounds
Rounds
(a) MNIST
(b) FEMNIST
Figure 1: Weighted client-level test accuracy in different rounds (with 0.1 activity rate).
For real-world data, the theoretical value of the local training steps in computed using Eqn. (66 might be too large for the client (due limitation of client's computation/memory budget). this ex- periment, we determine the actual local training steps for Self-FL framework as im min f mmax) where mmx is a pre-defined cutoff threshold. We use fixed local training step of 20 for other FL algorithms and set mmxx = 40 for Self-FL. Note that o represents the variance Om (i.e., model parameters such as neural coefficients) In our experiments, oz is approximated using the empirical variance of On across rounds.
Figures la and lb compare the convergence performance of different FL algorithms MNIST and FEMNIST, respectively. The horizontal axis denotes the communication round. The vertical axis denotes the weighted test accuracy of individual clients, where the weight is proportional to the sample size. We observe that: (i) Self-FL. algorithm yields more stable convergence compared with FedAvg and the other three personalized FL methods due our smoothing average aggregation; (ii) Self-FL achieves the highest personalized accuracy when the global model converges.
To corroborate that the performance advantage of Self-FL does not come from larger potential local training steps (we set Lmax = 40 for Self-FL), we perform an additional experiment where we use a local step as 40 (instead of 20) for DITTO, pFedMe, and PerFedAvg the FEMNIST dataset. In this scenario, the test accuracy these three FL algorithms is 71.33%, 68.87%, and 71.08%, respectively. Our proposed method achieves test accuracy of 76.93%. Furthermore, it is worth noting that other FI. methods do not have a principled way to determine the value of l. The adaptive local steps in Self-FL. also address this challenge.
Results on CIFARIO. We also perform experiments on the CIFAR-10 dataset (from the pFedMe repository Canh T. Dinh (0200) with the CNN model from PyTorch example (Py Torch (2022). In each round, we randomly select out 20 clients to participate in FL training. We use a learning rate of 0.01 for all FL algorithms and set the local training step as 40 for the baseline methods. Figure 2a visualizes the test accuracy comparison, showing that Self-FL achieves a higher accuracy.
1.0
1.0
FedAvg
PFedMe
0.8
PerFedAvg
DITTO
Test Acc.
0.6
SeltFL
Test Acc.
0.6
0.4
0.4
SelfFL Adjustinit
0.2
DynamicSteps
VarWeighted
0.0
50
100
150
200
250
0.0
25
50
75
100
125
150
175
Rounds
(a) CIFARIO
(b) FEMNIST
Figure 2: Weighted client-level test accuracy.

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Ablation study on Self-FL. Recall that Self-FL consists of three key components: (i) Adjusting local initialization; (ii) Dynamic local training steps; (iii) Variance- -eeighed global aggregation (Section E To investigate the effect of each component, we perform an ablation study where we apply the full deployment of Self-FL. and only only component of it. Figure 2b compares the test accuracy of the global model on FEMNIST benchmark in these four settings. We can observe that adjusting the local
initialization at each round (Eqn.
(TC) gives the highest contribution to Self-FL's performance.
To characterize the distribution of personalized performance across clients, we define two new metrics to evaluate different FL algorithms: (i) weighted test accuracy of clients that have top 10% most samples; (ii) worst 10% clients' average test accuracy. The evaluation results on FEMNIST (where the client sample size ranges from 1 to 206) are shown in Table I (standard errors in parentheses). We can observe that Self-FL outperforms other FL algorithms in terms of these auxiliary metrics. In addition, we visualize the distribution of Self-FL.'s personalization performance in Figure 3 by plotting the histograms of the user-level test accuracy. This user-level accuracy is obtained by evaluating the final local model (acquired by Algorithm [ of each client on his local dataset. The same metric is measured for the baseline FedAvg. We can see from Figure 3 that the user-level test accuracy distribution under Self-FL is shifted toward the right side of its counterpart under baseline FedAvg, suggesting that Self-FL effectively improves the local model performance for individual clients and achieves the goal of personalization.
Table 1: Test accuracy comparison on FEMNIST.
FL Alg.
FedAvg
DITTO
pleddMe
PerFedAvg
Self-FL
Top 10%
70.48%
70.58%
72.76%
74.95%
76.24%
most samples
(0.07%)
(0.14%)
(0.28%)
(0.56%%
(0.07%)
Worst 10%
0%
0%
17.97%
24.51%
37.01%
user avg acc
(0%)
(0%)
(1.23%)
(1.55%)
(1.57%)
100
Solt-FL
80c
Self-FL
SLlf-FL Fed/vg
40-
Fed/vg
700
Fed/vg
5c0
4:0
40-
300
20
200
150
02 0.4
Tex: Act.
(a) FEMNIST
(b) MNIST
(c) CIFARIO
Figure 3: Distribution of the user-level personalized performance on the test set.
4.3 Effectiveness on the audio domain
In this section, we evaluate the performance of Self-FL on an audio dataset (Subsection 4.1 for wake- word detection. Particularly, we use CNN that is pre-trained on the training data of different device types (i.e., heterogeneous data) as the initial global model to warm-start FL training for all evaluated FL algorithms. The personalization task aims to improve the wake-word detection performance at the device type level. In this experiment, we assume there are five clients in the FL system. Each client only has the training data for a specific device without data overlapping. Furthermore, all the clients participate in each communication round. Note that FedAvg (McMahan et al. 2017) and DITTO LLi ct al. 2021 I) typically use the sample size-based weighted average to aggregate models, which do not take data heterogeneity into account. For comparison, we implement FedAvg and DITTO with both equal-weighted and sample size-based weighted model averaging (denoted by the suffix "-e" and '-w", respectively) during aggregation. For metaaleermnngg based PerFedAvg (Fallah et al., 2020b), we use its first-order approximation and equal- weighted aggregation. We did not report pFedMe on this dataset because we found it did not converge with various pepeer-prameters..
Evaluation metric. One can control the trade-off between false accepts and false rejects of wake- word detection by tuning the threshold. Since we use a pre-trained model to warm-start FL., we first evaluate the detection performance of this pre-trained model as the baseline. To compare the

---

performance of different FL algorithms, we use the relative false accepr (FA) value of the resulting model when the corresponding relative false reject (FR) close to one the metric. So relative FA smaller than one is preferred. Here, the relative FA and FR are computed with respect to the baseline. We detail the results two scenarios below.
Table 2 summarizes the results of the updated global model. Recall that a smaller relative FA indicates better performance. Each column reports the relative FA for a specific device type. The results show that Self-FL achieves the lowest relative FA. Several updated global models have worse performance than the baseline model, e-g.. for FedAvg-w and DITTO-w in Table 2a This is due to the setting here that local models are initialized from pre- pre-trained model, and the comparison relative that warm-start Because clients' data are highly heterogeneous, a sample size-based aggregation rule used in FedAvg-w and Ditto-w w results in a deteriorated global model compared with the original start. We provide ablation studies the client sampling setting the Appendix Subsection G.4, which show Self-FI. still performs well.
Table 2: Detection performance (relative FA) of model on a test dataset.
Device Types
FL methods
B
C
E
methods
Device Type
C
D
E
Self-FL.
0.91
FedAvg-w
8.39
4.00
12,80
8.61
10.62
Self-FI.
0.93
0.91
0.90
0.90
0.99
FedAvg-e
0.97
0.96
1.00
0.92
1.00
FedAvg-e
0.95
0..55
0.93
0.91
0.98
DITTO-w
8,38
4,00
12.75
8.61
10.23
DITTO-e
0.97
0.96
0.93
0.91
0.96
DITTO-e
0.97
0.95
1.00
0.93
0.99
PerFedAvg
1.02
1.08
1.00
0.93
PerFedAvg
1.06
0.98
1.08
0.93
1.01
(b) Personalized model.
(a) Global model.
We further compare the personalization performance of Self-FL with FedAvg-e and two personalized FL algorithms, DITTO-e and PerFedAvg, on each device type's s test data and summarize the results in Table 2b We do not consider FedAvg-w and DITTO-W in this experiment since they result in performance degradation, as seen from Table 2a One can see that Self-FL outperforms the other methods across all device types, thus demonstrating better personalization capability.
5 Concluding Remarks
In this paper, we proposed Self-FL to address the challenge of balancing local model regularization and global model aggregation in personalized FL. key component is using uncertainty-driver local training steps and aggregation rules instead of conventional local fine-tuning and size-based weights Overall, Self-FL connects personalized FL with hierarchical modeling and utilizes uncertainty quantification to drive personalization. Extensive empirical studies of Self-FL show its promising performance. We do not envision any negative societal impact of the work.
The Appendix contains further experimental studies, remarks, related works, and technical proofs.
Acknowledgments and Disclosure of Funding
This work was done when Huili Chen worked as Applied Scientist Intern at Alexa AI, Amazon.
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Checklist
1. For all authors...
(a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? [Yes] Our empirical results in Section ijjustffy ours claims.
(b) Did you describe the limitations of your work? [Yes] We discuss our limitations in Appendix Section G.7
(c) Did you discuss any potential negative societal impacts of your work? [Yes] We do not envision any potential negative societal impacts of this work and mentioned that in Section 5
(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
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(a) Did you state the full set of assumptions of all theoretical results? [Yes]. . We state the full assumptions in Section 2 of the main body and Section D in the Appendix.
(b) Did you include complete proofs of all theoretical results? [Yes]. We provide complete proofs in Section 2 Appendix Section D and Section
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(a) Did you include the code, data, and instructions needed to reproduce the main ex- perimental results (either in the supplemental material or as a URL)? [Yes] We have included the codes the supplementary material.
(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes]. We specify the training details in Section 4. and Appendix Section G
(c) Did you report error bars (e.g., with respect to the random seed after running exper- iments multiple times)? [Yes]. We report the standard error of our experiments in
Section gl and Appendix Section
13

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(d) Did you include the total amount of compute and the type of resourees used (e.g.. type of GPUs, internal cluster, or cloud provider)? [Yes]. We provide the computing resources in Section 4.1
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(a) If your work uses existing assets, did you cite the creators? [Yes]. We use the open-
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(b) Did you mention the license of the assets? [Yes]..
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14


Reviews:
[{"review_id": "PQTKmMw9Rux", "reviewer": "Reviewer_b7BG", "summary": "In this paper, the authors study an important problem in federated learning, i.e., personalized federated learning, where the goal is to balance the training of the local model of each client and the global model shared by all the clients. In particular, the authors do not follow previous works on model fine-tuning in each local client and size-based weighting in global aggregation, but propose to address the balancing challenge from a statistical uncertainty perspective. Specifically, the authors design a novel solution called Self-FL, which uses uncertainty-driven approaches for the training of the local models and the global model. Empirical results on some well-known datasets show the effectiveness of the proposed Self-FL.", "questions": "1 Can the proposed approach be applied to other tasks, e.g., classification/recognition with some auxiliary data such as knowledge graph, federated recommendation?", "limitations": "The authors do not include sufficient discussions about the communication and computational cost, which are suggested to be included.", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n1 The authors address an important challenge in personalized federated learning, i.e., balancing of the training of each local model and the global model.\n\n2 The authors propose a novel perspective for the studied problem and design some novel uncertainty-driven approaches.\n\nWeakness:\n\n1 The authors may include more discussions and quantitative analysis about the communication cost.\n", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "DktHwh83K-", "reviewer": "Reviewer_rRk4", "summary": "The authors present a self aware personalized FL system which uses Bayesian hierarchical modeling to balance training of local versus global models. This helps to quantify inter and intra client uncertainty quantification. The authors present both theoretical justification and empirical analysis of the proposed technique - Self-FL.", "questions": "- The motivation for using Bayesian hierarchical modeling for personalization needs to be better explained. \n\n-  How exactly is personalization quantified and how is the notion of \"personalization\" different from learning parallel algorithms where local models are updated by information from global models?\n\nMinor comments\nSection 2.1. to bake prior knowledge -> to take prior knowledge \n\n", "limitations": "- The use of local versus global training  is extensively used in literature. It is unclear how this idea is different from the notion of \"personalization\" introduced here. Infact, the basic premise seems to be the construction of a generative model at the client side and update its parameters using a global counterpart (assuming a generative model for global training).\n", "rating": 3, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths\n- The authors identify an important problem -- that of personalizing federated learning problems\n- The paper is well written\n- A reasonably well written Related Work and Experimental Studies section\n\nWeakness\n- The problem of tuning local versus global models has been studied extensively in literature and therefore the novelty of the proposed approach is questionable. ", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "DQ6G0wOFqiO", "reviewer": "Reviewer_jvSV", "summary": "The paper is on personalized federated learning, where the critical challenge is in balance of local and global model tuning. More specially, the goal of global model tuning and local personalized model tuning are not fully aligned.  Toward this problem, the authors develop a self-aware personalized FL method to balance the personal model and global model update based on the inter-client and intra-client uncertainty quantification. The paper recognized and clearly defined critical research questions. To answer the questions, the authors formulate  personalization from a  hierarchical model-based perspective and propose Self-FL, an active personalized FL solution that guides local training and global aggregation via inter- and intra-client uncertainty quantification. The experimental results confirm the effectiveness of the proposed method from task performance and training stableness. ", "questions": "One of the challenges in personalization is how to achieve good performance while clients do not have enough data and prevent overfitting.  Could authors provide some intuitions to explain how the model handle the case when the labeled data is limited on some clients?", "limitations": "The authors propose to characterize the performance by weighted accuracy. Even though this is a good way to show the performance, the detailed performance distribution is also suggested. For example, a violin plot could depict the distribution of performance. \nAnother suggestion is to uncover the relationship between performance and other factors including data size and class distribution on client sides. ", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "The authors clearly defined the challenging questions and work on the fundamental research questions. The proposed methods are derived  in a principal way with theory. The performance is promising and experiments are pretty comprehensive. The personalization naturally puts more requirements on evaluation and analysis due to involving performance evaluation across clients. I include my suggestions in the following sections and encourage authors to provide more analysis to uncover personalization challenges in term of data dimension. ", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Accept