PRIOR: Personalized Prior for Reactivating the Information Overlooked in Federated Learning

Summary

This paper targets injecting personalized prior knowledge into the global model, which attempts to mitigate the introduced incomplete information problem in PFL. The idea is to decouple the personalized prior from the local objective function regularized by Bregman divergence. The mirror descent (RMD) is used to extract the prior. The authors presented convergence analysis and showed many experimental results.

Strengths

1. The authors conducted many experiments and show improved results. For example, the proposed method has a higher deviation in missing classes in local testing and a lower deviation in global testing. 2. The idea seems to be interesting.

Weaknesses

1. Unclear motivation and literature review. 2. Lack of an explainable summary of the main idea. Given the abstract, I think the idea seems to be interesting, but I got lost in the details and symbols when reading Section 4 and Section 5. 3. The writing requires to be improved.

Questions

**Background** 1. In Lines 43-46, "Most of the insightful works [17, 50] propose assumptions for recovering this incomplete information, but these assumptions are implicit, which limits the way to use the information to develop personalized strategies. To address the former issue above, ...". What is the exact problem/issue of the previous assumption? Can the authors explain more about the motivation? What is "limits the way to use the information" exactly here? I did not catch the exact challenge that the authors target here. 2. In lines 46,47, the major contribution comes from "we propose framework pFedBreD to inject personalized prior knowledge (PPK) into the one provided by a global model." Is there a research line for injecting personalized prior knowledge? What is the advantage of pFedBreD compared with them? I see the authors elaborated on "Ablation Analysis of Personalized Prior" from Line 269 to Line 283. Can authors explain more about PPK-relevant research line in a more intuitive manner? **Method and Framework** 3. In lines 103,104, "Exponential Family The regular exponential family (X-family) is a relatively large family... Therefore, to yield the prior, we employ the X-family..." Is the employment of X-family due to "large family"? Is there any other special advantage for X-family? 4. I can follow the equations of Section 4 from a math view. Would the authors elaborate the intuitive logic of combining these equations? 5. Section 4 is "methodology", meanwhile, Section 5 is "framework". Does the designed framework belong to the proposed methodology? Or, what is the relation between the two sections? 6. In Line 156, "Inspired by the aforementioned motivation," What is the "motivation"? I tried to search "motivation," but "motivation" appears only once in the paper...What is the "motivation" here? Is it relevant to some types of math objective functions? 7. In Line 163 and Line 164, "To solve the optimization problem in Eq. (12), we use gradient-based methods to solve the global problem ..." Based on my knowledge, the conventional method is "gradient-based methods." Is there any other special optimization in your framework? **Experiment** 8. In Line 220, "The results of average accuracy per client are shown in Table 1." Could the authors summarize the insight conclusion of Table 1 in the main text? 9. What is the relation between "RMD" and "mh"? Are any experiments relevant to "RMD"? **Minor** - In Line 85, "a expectation" - The clickable indices of reference/table/equation/etc do not work, which are not convenient for searching the relevant contents. - In Line 113 - Line 115, long sentence with grammar error. "In this section2, we introduce missing client-sampling information based on classic FL use EM to reduce the computational cost of the information-introduced FL problem, and propose RMD, a class of prior selection strategies, based on the E-step in EM" - Equation 5 requires to introduce "KL" function before usage. - In Line 168, T,R,N appear suddenly by following the main body.

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

The authors try to empirically address the limitation of instability in the global model with aggregation noise.

Summary

The authors of the paper consider the problem of personalized federated learning. The main problem the authors attempt to tackle is the information on sampling of clients being overlooked. Specifically, they attempt to introduce two major steps in the training of personalized models: the first one is the injection of personalized prior knowledge into the global model before training, the second is the extraction of the prior before sending the global model updates. The authors formally present the problem of overlooking client-sampling information, then they utilize a framework for the problem called pFedBreD. Additionally, they provide extensive theoretical examination of the framework, as well as numerous experiments to validate the superior performance of their solution compared to a handful of baseline algorithms.

Strengths

- The paper is very well-written. It is clear and comprehensive, and its structure is sound. - The authors motivate the problem very well, and provide a sound formulation of it. - The theoretical examination of the problem, especially the results are well-presented. - The extensive experimental results, especially the comparisons with various baselines are useful for the completeness of the evaluation of the proposed framework. A number of datasets as well as different models are considered. Moreover, the analysis of the results is insightful.

Weaknesses

I have a couple of comments on the weaknesses of the paper: - I think the main body of the paper is well-written as I mentioned in the weaknesses, but I also think it lacks fundamental parts that can be added to improve the readability of the paper. For example, the pFedBreD algorithm is not included in the main body but it is an important part that needs to be presented in the main body of the paper for completeness of the presentation. Similarly, the authors refer to Theorem 1 in the paper but it is not mentioned until the Appendix D. The paper should be self sufficient for the reader. - The authors use acronyms in the paper before mentioning what they are, for example the use of **mh**, **lg**, and **meg** before explicitly defining them or mentioning what they stand for. This can be confusing for the reader and needs to be rectified.

Questions

The mentioned weaknesses need to be addressed. The main body of the paper should be improved to include the missing parts as well as the acronyms should be clearly defined. Further, the paper needs to be checked for typos. For example: line 85, "pFedBreD is a expectation" -> "pFedBreD is an expectation", line 95 "Bregman divergencee" -> "Bregman divergence", line 213: "we choose following" -> "we choose the following".

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

2 fair

Contribution

3 good

Limitations

The authors present the limitations of their work.

Summary

This paper proposes pFedBreD, which decouples the personalized prior from the local objective function regularized by Bregman divergence for greater adaptability in personalized FL. Extensive experiments validate the effectiveness of the proposed method on 5 datasets.

Strengths

S1. The problem of overlooking client-sampling information at prior knowledge being transferred is important. S2. A novel framework, pFedBreD, is proposed for computing the Bayesian optimization problem. The theorem is provided to analyze the convergence. S3. The experiments validate the effectiveness of pFedBreD on five widely-used datasets.

Weaknesses

W1. The problem is not well-motivated. To be more specific, the shortcomings of existing PFL methods are not well explained. The client-sampling information should be clearly illustrated, and the reason why the prior knowledge extraction is challenging is missing. W2. The problem should be formally defined. It would be better to add a subsection to provide the statement of the research problem of this paper. W3. The efficiency of the proposed methods is not well analyzed.

Questions

Q1. The assumption this paper makes is the uniform sampling of clients. How about other sampling methods? Is the proposed method applicable to other sampling scenarios? Q2. In Table 1, the accuracy of FedAMP is better than the proposed method on some datasets. In particular, the accuracy of the MCLR of FedAMP on different datasets is close to or even outperforms mh. The reason should be provided. Q3. How to determine the number of global/local epochs in your experiment setting?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

2 fair

Contribution

3 good

Limitations

The authors adequately pointed out the limitations of this work.

Summary

In this paper, the authors propose pFedBreD to decouple prior knowledge from each client. pFedBreD extracts the personalized prior with Bregman Divergence for better performing personalized tasks. The authors provide convergence analysis and experiments evaluated on 5 datasets.

Strengths

1.    The authors give a detailed convergence analysis for the proposed method. 2.    The theoretical derivation of the paper is comprehensive in the Appendix. 3.    The authors provided extensive experiments for different tasks and models and the results show the effectiveness of improving the local models' performance.

Weaknesses

1.    The motivation of the work is not clearly presented. It is hard to understand why the authors use Bregman Divergence and Relaxing Mirror Descent.  2.    It is confusing that the authors use the average results and the standard deviation of them on all tasks to represent the overall performance of methods. Could the authors give some intuition or explain the purpose of this? 3.    More related works need to be introduced. And we'd like to see experimental results compared to more related works, such as [1], [2], [3], and [4]. 4.    This paper focuses on the specific label distribution problem. It would be better if the authors could discuss the performance of other heterogeneous data distribution problems (e.g., different number of classes is different). [1] Personalized Federated Learning with Feature Alignment and Classifier Collaboration. ICLR 2023. [2] Ditto: Fair and robust federated learning through personalization. ICML 2021. [3] Personalized Federated Learning with First Order Model Optimization. ICLR 2021. [4] Personalized federated learning using hypernetworks. ICML 2021.

Questions

1.    The intuition of the work is not clear. Could the authors explain the motivation for using Bregman Divergence and Relaxing Mirror Descent in detail? 2.    In Table 1, why the second-best performance is 79.44 (mh) rather than 79.68 (Per-FedAvg+FT)?

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

2 fair

Presentation

3 good

Contribution

2 fair

Limitations

The authors have discussed the potential limitations.

Summary

The paper introduces a novel scheme, pFedBreD, which addresses the incomplete information challenge in personalized federated learning by incorporating personalized prior knowledge into the global model of each client. This is achieved by decoupling the personalized prior from the local objective function and applying Bregman divergence regularization. The proposed approach leverages the Expectation-Maximization (EM) algorithm to approximate complete information from both global and local clients. Extensive empirical evaluations on multiple benchmarks demonstrate the effectiveness of the proposed method, and a theoretical analysis is provided to support its theoretical foundations.

Strengths

1. The paper is well-written and easy to read. 2. This paper introduces a novel approach that incorporates Bregman divergence and leverages the Expectation-Maximization (EM) algorithm to approximate complete information from both global and local clients. It effectively enhance personalized federated learning. 3. The effectiveness of the proposed method is validated through extensive empirical evaluations and thorough theoretical analysis in the paper. 4. This work showcases superior performance across multiple benchmarks when compared to various baseline methods.

Weaknesses

1. The authors discuss the concepts of prior knowledge injection and extraction in Figure 1, as well as analyze the process of information injection and extraction. To enhance clarity, it would be helpful if the authors explicitly indicate in the framework design section which step corresponds to these specific actions. 2. Certain aspects of the paper would benefit from additional clarifications to enhance understanding. See below.

Questions

1. Is the method of calculating GCE mentioned in the paper? Does it depend on model parameters or extracted feature maps? 2. Some abbreviation is not clearly explained in the paper. For example, what is MCLR, FT, AM, etc.? 3. How does the computation cost of the proposed method compare to other approaches? Is the local training phase highly time-consuming? For example, what computational resources were utilized in the experiment, and what was the duration required to complete the experiment? 4. Does the scalability of the proposed method remain unaffected? For instance, can the proposed method handle a scenario with more than 100 clients?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

2 fair

Contribution

2 fair

Limitations

The authors have adequately addressed the limitations in the paper.