Summary
This paper presents a new ADMM algorithm that focuses on three specific cases of rank-based losses. The algorithm's convergence is theoretically analyzed in the paper. Additionally, the authors conducted comprehensive experiments to compare the new algorithm with traditional approaches. The results indicate that the proposed algorithm outperforms traditional methods in terms of both efficiency and effectiveness.
Strengths
1. The authors proposed a new algorithm that can address three specific cases of rank-based losses, whereas traditional algorithms like SGD, DCA, and LSVRG can only handle one. Additionally, the new algorithm permits the regularization term to be a weakly convex function.
2. The authors' theoretical analysis of the new algorithm's convergence is a significant contribution that has not been achieved in previous work.
3. To demonstrate the advantages of the new algorithm, the authors conducted comprehensive experiments. The results show that the new algorithm generally outperforms existing methods in terms of both efficiency and effectiveness. Overall, this study provides valuable insights into the development of more efficient and effective algorithms for rank-based losses.
Weaknesses
Significant Issues (Detailed Explanation Required)
1.The representation of the loss vector function in line 23 is unclear. If function l maps an n-dimensional column vector to a real number, how a comparison of magnitude can be made later on?
2.As is widely known, due to the unknown underlying distribution of the data, we can only optimize the discrete form of risk expectation, which is the arithmetic mean of n observations. The theoretical basis for doing so is that the arithmetic mean converges in probability to the expectation. Therefore, could you please explain the theoretical basis for the discrete form of spectral risk that you employed in lines 78-79.
3.Could you please clarify how the conclusion stated in line 116 was derived? If it is a result obtained from citing other papers, please provide the source. If it is a result you have proven yourself, please provide a detailed proof.
4.In line 159, definitions for two consecutive blocks disorder are provided, but definitions for three or more consecutive block disorder are missing.
5.In line 6 of Algorithm 2, it is not possible to select the disordered blocks because definitions for three or more consecutive blocks disorder have not been provided.
6.In line 6 of Algorithm 2, you assume that the optimal solutions for are equal to each other. Could you please a more detailed proof or a citation if the conclusion is derived from another paper?
7.In line 225, you stated that Assumptions 4 and 5 are weaker than Assumption 2. Please provide a detailed explanation for this claim.
8.Could you please provide specific information on the loss functions and regularizers used in the experiments in Sections 5.2 and 5.3?
Minor issue (needs improvement).
1.The "l" in line 23 and the "l" in line 71 have different meanings. It’s suggested to use distinct notations to indicate this difference.
2.In Equation (1), the independent variable of is , where is a d-dimensional column vector. However, the independent variable of is written as an n-dimensional column vector in line 24.
3.Line 71 should use lowercase "d" instead of uppercase.
4.In line 85, please provide a brief explanation of the term "fairness".
5.There is a missing negative sign in line 127.
6.In line 154, "" should be in lowercase.
7.The explanations in lines 169-170 appear to contradict the explanations in lines 187-188.
8.To avoid confusion among readers, please use a consistent notation for the loss function "" in lines 71, 125, and 194.
9.Please provide an explanation for "dist" as used in line 249 at its initial occurrence in line 212.
10.The placement of "Dataset" in Tables 1 and 2 is inconsistent.
11.Please use the notation "new-ADMM" to distinguish the modified version of the traditional ADMM algorithm.
Questions
Please see the above comments about the Weakness.
Rating
5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
Confidence
2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.