Paper: Federated Recommendation with Additive Personalization (ICLR-2024)

Reviewer comment (Writing):
The manuscript requires clarity and consistency checks. For example, in Figure 1's title, "five dataset" is mentioned, whereas at the end of Section 1, it states “four dataset”.

Author response:
## W1 (Clarity and Consistency in Writing)
We reported experimental results on six datasets in the paper and we will make the text consistent. We will move the results to Section 4.4 on Page 7.

Reviewer comment (Writing):
The distinction between heterogeneity and personalization needs to be clearer. The manuscript suggests two challenges: heterogeneity, which seems to pertain to varying client interests, and personalization. Given their similarities in this context, why are they presented as two separate challenges?

Author response:
## W3 & Q2 (Differentiating Heterogeneity from Personalization)

Heterogeneity of users in federated recommendation syetems is the challenge we aim to address and the additive personalization is our proposed approach to address the challenge. So they are not seperated. FedRAP learns a user-specific item embedding and a globally shared item embedding jointly to enhance the performance in federated recommendation.

Reviewer comment (Presentation):
There is a need for reorganizing the content, especially in Section 3.1 (Problem Formulation). Here, the authors discuss the loss function and the proposed method's entire framework. A more suitable structure might involve mathematically introducing the problem in the Problem Formulation and discussing the method's framework in a separate section.

Author response:
## W4 (Organizational Refinements)

We will improve the organization and logical flow of the paper as you suggested in the updated draft.

Reviewer comment (Writing):
In Figure 2, the term "reconstruction error" is used. As per my understanding, it seems to measure the discrepancy between actual user ratings and predicted ones. The term "reconstruction error" suggests that something undergoes reconstruction. Can the authors clarify this?

Author response:
## W5 & Q1 (Clarification on ‘Reconstruction Error’)

In our paper, the term "reconstruction" refers to predicting the user ratings given in the training data. The reconstruction or prediction of ratings is achieved by the inner product between each user embedding $\mathbf{u}_i$ and each item embedding, which adds the global item embedding $\mathbf{C}$ and local item embedding $\mathbf{D}^{(i)}$ together. The reconstruction error compares the prediction with the ground truth ratings by Eq. (1).

Reviewer comment (Novelty):
The paper's primary innovation appears to be the maintenance of a user-specific item embedding matrix, D(i), for every user, i. Given that local interactions are usually sparse, which motivates federated training, the uniqueness of this approach is incremental. The two regularizers are essentially the normalization of two embedding tables. While differential privacy is prevalent in federated learning, its application here does not seem groundbreaking.

Author response:
## W6 (Questioning Novelty)

FedRAP addressed a key challenge in federated recommendation and achieved significant improvement compared to existing methods on standard benchmarks. Its performance is unprecedently on par with the centralized recommendation system performance. This is due to the following technical novelties:
(1) Additive modeling combining a local item embedding with a sparse global item embedding, which has not been studied for the problem; 
(2) A curriculum learning approach with two regularizations, which is critical to achieve the proposed additive modeling.

Reviewer comment (Experiments):
The manuscript cites PerFedRec [1] in the related works but does not present a comparative analysis in the experiments. It would be insightful for the authors to contrast their work with PerFedRec. Moreover, considering the work on PerFedRec++ [2] could be beneficial, even if it is a recent arXiv publication.

Author response:
## W7&Q4 (Comparative Analysis)

We will cite both PerFedRec and PerFedRec++ and discuss them in our uploaded draft. We are still tuning the hyperparameters for PerFedRec and aiming to include it in our experimental comparisons. Since PerFedRec++ has not released its code and it is a very recent preprint (published later than our preprint), we will try our best to include it in the future version of our paper.

Reviewer comment (Presentation):
Why is the term "Reconstruction error" used in Figure 2? What exactly is being 'reconstructed' in the given context?

Author response:
## W5 & Q1 (Clarification on ‘Reconstruction Error’)

In our paper, the term "reconstruction" refers to predicting the user ratings given in the training data. The reconstruction or prediction of ratings is achieved by the inner product between each user embedding $\mathbf{u}_i$ and each item embedding, which adds the global item embedding $\mathbf{C}$ and local item embedding $\mathbf{D}^{(i)}$ together. The reconstruction error compares the prediction with the ground truth ratings by Eq. (1).

Reviewer comment (Writing):
Could the authors delineate the difference between 'heterogeneity' and 'personalization'? As of now, the distinction is not abundantly clear, and the terms seem somewhat interchangeable.

Author response:
## W3 & Q2 (Differentiating Heterogeneity from Personalization)

Heterogeneity of users in federated recommendation syetems is the challenge we aim to address and the additive personalization is our proposed approach to address the challenge. So they are not seperated. FedRAP learns a user-specific item embedding and a globally shared item embedding jointly to enhance the performance in federated recommendation.

Reviewer comment (Experiments):
The paper emphasizes the sparse embedding's ability to reduce communication costs, a known limitation of current methods. Why is this specific aspect not experimentally validated or discussed in the results section? Can the authors provide insights or potential experimental outcomes supporting this claim?

Author response:
## Q3 (Sparse Embedding)

Table R2. Sparsity of the global embedding matrix $\mathbf{C}$ learned by FedRAP-L2 and FedRAP on the ML-100K dataset. **Difference** represents the percentage of different elements (whose differences are above a threshold) between $\mathbf{C}$ learned by FedRAP and FedRAP-L2.

|             |  >1e-2 |  >1e-3 |  >1e-4 |  >1e-5 |  >1e-6  |
|-------------|:------:|:------:|:------:|:-------:|
| FedRAP-L2   | 79.39% | 98.05% | 99.83% | 99.99% | 100.00% |
| FedRAP      | 52.68% | 74.55% | 93.46% | 98.65% |  99.84% |
| Difference  | 26.71% | 23.50% |  6.37% |  1.34% |  0.16%  |

We explored the impact of the sparsity regularization on $\mathbf{C}$ in FedRAP by ablation study in Section 4.5, where we set the feature dimension of the item embedding to 16. We first evaluate the sparsity by calculating the percentage of elements in $\mathbf{C}$ exceeding a specified threshold for both FedRAP-L2 and FedRAP after the 100-th training iteration, as presented in Table R2. It shows that as the threshold increases, the difference between the two methods on sparsity gradually grows. Specifically, when the threshold is set to 1e-2, FedRAP, compared to FedRAP-L2, achieves a 33% reduction in communication overhead.

Furthermore, we randomly selected 16 items from the item set and visualized the corresponding distribution of entries in $\mathbf{C}$ after the 100th training iteration. As shown in the first column of Figure 7, $\mathbf{C}$ learned by FedRAP is sparser than $\mathbf{C}$ learned by FedRAP-L2.

These findings support our hypothesis that the user preferences affects item ratings and personalized item embedding can better capture the data heterogeneity. Moreover, they validate FedRAP's capability to learn better personalized models for each user.

Reviewer comment (Experiments):
Given that "PerFedRec" is cited in the related work and seems to be a relevant approach in this domain, why is it omitted from the experimental comparisons? A comparative analysis could provide a clearer perspective on the proposed method's advantages or potential differences.

Author response:
## W7&Q4 (Comparative Analysis)

We will cite both PerFedRec and PerFedRec++ and discuss them in our uploaded draft. We are still tuning the hyperparameters for PerFedRec and aiming to include it in our experimental comparisons. Since PerFedRec++ has not released its code and it is a very recent preprint (published later than our preprint), we will try our best to include it in the future version of our paper.

Reviewer comment (Experiments):
The variants in the ablation study introduced in Section 4.5 do not come with intuitive explanations of the motivations for comparisons with them. They are unclear to readers if they do not carefully read the following analysis.

Author response:
## W1 (Unclear Motivations)
In Section 4.5, we introduced eight variants of FedRAP based on three ablation study tasks. Specifically:
1. To investigate the roles of global item embedding and local item embedding in FedRAP and validate the basic assumption of user preference influencing ratings, we designed FedRAP-C using only global item embedding and FedRAP-D using only local item embedding.
2. To explore the impact of different constraints on C, we introduced FedRAP-No, which imposes no constraints on C, and FedRAP-L2, which uses the Frobenius norm on C.
3. To examine the influence of different weight curricula on FedRAP's performance, we introduced FedRAP-fixed using two constants $v_1$ or $v_2$ in hyperparameters, FedRAP-sin using a sine function for hyperparameter variation, and FedRAP-frac using fractional changes in hyperparameters. Additionally, we presented FedRAP-square with a hyperparameter periodically transitioning between zero and constants $v_1$ or $v_2$.

These three ablation study aim to validate the contributions of three key innovations in FedRAP: two-way personalization, encouraging the sparsity of C, and a curriculum transitioning from full to additive personalization.

Reviewer comment (Writing):
There are some typos and grammar errors which should be corrected.

Author response:
## W2 (Improve Writing)
Thank you for bringing this to our attention! We will thoroughly review the paper and address any typos and grammar errors to ensure its clarity and quality. Your feedback is valuable in enhancing the overall presentation of the work.

Reviewer comment (Experiments):
Can you provide an ablation study of the regularization in Eq2?

Author response:
## Q1 (Ablation Study)

We introduce a new variant of FedRAP called FedRAP-S, where we remove the regularization $- \lambda_{(a, v_1)} ||\mathbf{D}^{(i)} -  \mathbf{C}||^2_F$ encouraging the difference between the global item embedding $\mathbf{C}$ and local item embedding $\mathbf{D}^{(i)}$ from Eq. (3). We trained FedRAP-S five times on the ML-100K dataset and report the results in Table R1, where FedRAP-S shows a significant performance degradation compared to FedRAP. This degradation could be attributed to the absence of constraints between user-specific item information and globally shared item information in FedRAP-S. Without such constraints, the personalized model becomes overly individualized, leading to overfitting on user data and a decrease in generalization ability. Therefore, enforcing differentiation serves as a bridge between personalized and shared models and controls the complexity of the personalized component and preventing overfitting. This ensures a balance between personalization and generalization in the model.

Table R1. Experimental results of FedRAP and FedRAP-S shown in percentages on the ML-100K dataset.
|          |      HR@10     |     NDCG@10    |
|----------|:--------------:|:--------------:|
| FedRAP   | 97.09$\pm$0.56 | 87.81$\pm$2.00 |
| FedRAP-S | 65.86$\pm$1.34 | 39.99$\pm$0.46 |

Reviewer comment (Writing):
"FedRAP-No: Removes item diversity constraint on C" — should "diversity" be "sparsity"? Is this a typo?

Author response:
## Q2 (Typo)

It should be "FedRAP-No: Removes item sparsity constraint on C" instead of "diversity." This is indeed a typo. We appreciate your keen observation, and assure you that this error will be corrected in the future version of the paper.

Reviewer comment (Evaluation):
In Figure 7, it seems that each user-personalized matrix is row-sparse with most rows to be all-zeros. How do we understand this row-sparsity? Can you (or did you) take advantage of this row-sparsity to further reduce the communication cost (e.g., by only sending the non-allzero rows)?

Author response:
## Q3 (Explanation of Fig. 7)

In Fig. 7, the row-sparsity pattern in each user-personalized matrix, denoted as local item embedding  $\mathbf{D}^{(i)}$, indicates non-zero elements corresponding to items the i-th user has interacted with. Conversely, all-zero rows signify items that the user has not accessed. To address this, global item embedding $\mathbf{C}$ is introduced to incorporate global item information, allowing FedRAP to predict whether a user will interact with items they have not engaged with before. It's noted that optimizing the storage of $\mathbf{D}^{(i)}$ can reduce client-side space cost. However, since FedRAP transmits only $\mathbf{C}$ between the client and server, optimizing the storage of $\mathbf{D}^{(i)}$ does not lead to a reduction in communication costs.

Reviewer comment (Evaluation):
How do we justify whether the degradation numbers in Table 1 are large or small? Are there any baselines' degradation results to be compared with?

Author response:
## Q4 (Baseline Comparison)

We have evaluated the performances on the Movielens-100K (ML-100K) dataset, comparing FedMF, FedNCF, PFedRec, and FedRAP with and without Differential Privacy (DP). Due to space constraints in the main text, the detailed results of our experiments are provided in Appendix Sec. B.4, as illustrated in Tables 5 and 6. The results demonstrate that FedRAP maintains a performance advantage, even in the presence of privacy-preserving measures. These findings showcase the robustness and efficacy of FedRAP in privacy-preserving federated recommendation scenarios.