Towards Harmless Rawlsian Fairness Regardless of Demographic Prior

Summary

Although importance of group fairness appreciated, most existing works have required demographic information for debiasing. The paper introduces a novel method, VFair, to achieve fairness with minimum sacrifice of the utility under no prior demographic information scenario. VFair aims to achieve harmless Rawlsian fairness via minimizing variance of losses, which is pertinent to disparity of utility across subgroups.

Strengths

1. The paper is easy to read. 2. Considering important topic.

Weaknesses

1. Comparison in the experimental results is not comprehensive. 2. Motivation is less highlighted. It is unclear why the proposed method is unique and how it addresses limitations of previous methods. Also, please see the question section below.

Questions

- Why does the paper referring to Dirac delta distribution instead of uniform distribution when demonstrating Figure 1? If the indices (x-axis) are sorted by loss value, wouldn’t a uniform distribution be more appropriate for an optimal scenario? - The paper suggests that MUD (Maximum Utility Disparity) or accuracy parity across groups are implicitly connected to a uniform or Dirac delta distribution of instance-wise losses. Could the authors clarify this connection? Intuitively, these concepts do not seem necessarily interchangeable. - (line:137-141) The paper mentions overfitting and low variance at the same time, which seems counter-intuitive. Could the authors clarify how they propose to mitigate this apparent conflict? - How is the proposed method of “harmless fairness” differentiated from the previous work by Zhang et al. (2018)[1] on mitigating unwanted biases with adversarial learning? - The empirical results do not perfectly align with the TUD (Total Utility Disparity) and variance metrics presented. Could the authors explain these discrepancies? - There should be a comparison with more state-of-the-art methods to provide a comprehensive evaluation. Could the authors include or discuss more recent and relevant methods in their comparison? [1] B. H. Zhang, B. Lemoine, and M. Mitchell, “Mitigating Unwanted Biases with Adversarial Learning,” AAAI/ACM Conference on Artificial Intelligence, Ethics, and Society, 2018.

Rating

4

Confidence

4

Soundness

1

Presentation

2

Contribution

2

Limitations

Please see questions and weakness parts.

Summary

The authors propose VFair: an approach to Rawlsian, demographics-agnostic fairness where the variance over each data point's loss term is minimized together with the mean loss during training. These objectives are clearly often at odds with eachother, so they include a principled dynamic weighting scheme for the multi-objective optimization, making use of the mathematical relationship between the sample mean and variance. In experiments, this appears to outperform other baselines that are agnostic to demographics information.

Strengths

The authors effectively propose an incredibly simple idea: instead of only minimizing the mean loss, we also minimize the sample variance over all individual loss terms. It strikes me as an idea that must have been investigated before, but besides one weakly related references that were missed (Spady and Stouli, 2018), I was unable to find occurrences of this idea in prior work. The dynamic weighting for the objectives is intriguing, as it combines a lower bound based on black-box optimization (apparently not original), with a second, more stable lower bound that is well-motivated by exploiting the relation between the sample variance and mean. Spady, Richard, and Sami Stouli. "Simultaneous mean-variance regression." arXiv preprint arXiv:1804.01631 (2018).

Weaknesses

W1. The motivation for using the variance of as a second objective is found in Prop. 1, which reads "For any s that splits data into a number of groups, u ⊥ s holds if and only if the loss ℓ is (approximately) independent of the training example z, i.e., ℓ ⊥ z.". The first condition is either very unclearly phrased or simply incorrect. It seems to say that *for any split*: it holds that u ⊥ s iff ℓ ⊥ z. This clearly cannot be true: the mean accuracies of all groups can be equal while the individual losses within the groups can vary. Instead, Prop. 1 should read "u ⊥ s holds for any s that splits data into a number of groups, if and only if the loss ℓ is (approximately) independent of the training example z, i.e., ℓ ⊥ z.". Also, Prop. 1 only holds if $u$ is a fully decomposable sum over all individual data samples (just like ℓ is). W2. The extra motivation for minimizing the variance given in L169-L180 lacks rigour. First, Bennett's inequality uses the actual variance and not the sample variance (which VFair is optimizing), and it is unclear how they are related in the bound. Second, why care about this bound? We care about the actual mean, but not about so much about the gap between the actual and the empirical mean. W3. Related to W1, I more broadly wonder whether this approach even fits in the popular ML fairness literature. The idea of formalizing discrimination as a problematic bias in ML is that there is some unethical pattern in whom is being disadvantaged by an algorithm. If we are looking at the utility for each data point individually, disregarding demographics, are we still talking about an approach that "does not require demographic information to be fair"? It seems like we are now just saying that we don't *care* about the demographics. This doesn't make the proposed definition of fairness uninteresting, but it does take away the societal motivation for this work (in relation to discrimination law).

Questions

Q1. Could you explain why the 'training losses exhibit a Dirac delta distribution'? Because you are stripping the variance? Q2. The derivation of Eq. 8 can be more intuitively explained: the Z-score of a random variable $\geq 0$ is always lower-bounded by $-\frac{\mu}{\sigma}$, so $\lambda$ must be lower-bounded by $\frac{\mu}{\sigma}$ for $w_i$ to be positive.

Rating

7

Confidence

4

Soundness

2

Presentation

3

Contribution

3

Limitations

No, for societal impact, please refer to papers that more broadly discuss the problems with a technical approach to algorithmic fairness and the problematic assumptions we need to make (e.g. relating to the measurability of the utility). The limitations were not discussed in detail.

Summary

The authors suggest a framework aimed at enhancing the fairness guarantees of classifiers in scenarios where sensitive information is unavailable. Their approach seeks to identify a classification rule that minimizes the variance in losses from the training sample, while ensuring that the overall average utility does not significantly decline from the maximum possible utility.

Strengths

S1 - The paper successfully validates all the claims outlined in the abstract and introduction. Each assertion is supported with empirical evidence and detailed analysis. The authors have meticulously followed through on their initial promises, providing a cohesive and comprehensive study that aligns well with the stated objectives. S2 - The problem addressed in this paper is of high relevance in reality. Ensuring the fairness of classifiers, especially in the absence of sensitive information, is a crucial issue with significant practical implications. S3 - The authors effectively address the issues and challenges posed by the general methodology when applied in practical scenarios. For instance, the insightful analysis on gradient alignment enhances the practical applicability of their approach. S4 - This analysis offers valuable insight into an important finding in the field of algorithmic fairness: the distinctions between achieving fairness in classification and regression tasks. S5 - The abstract and the introduction effectively substantiate all the claims made, including the contributions put forth by the authors. These assertions find validation through the description of the methodology employed and the experiments conducted. The method section elaborates on the techniques and approaches considered, demonstrating how they align with the stated objectives. Furthermore, the experimental results provide empirical evidence that supports the claims made in the introduction.

Weaknesses

W1 - Reproducibility issues. The experimental setting lacks detail regarding critical aspects such as the employed learning rate, the number of epochs, and the hyperparameters or tuning procedures for different methods. Additionally, the authors do not report how the dataset is split. Providing this information is essential for enabling others to replicate the study and verify its findings. W2 - The paper overlooks an important body of work from the field of algorithmic fairness that operates without knowledge of demographic information: [1]. This work constitutes a significant contribution to the field and could provide valuable context and support for the current study. Besides, including and considering such an approach in the experimental section would enhance the quality and informativeness of the provided results and derived conclusions. W3 - The proposed fairness criteria operate at the instance level, thus can be viewed as an individual fairness strategy. However, the authors do not highlight this similarity or discuss their approach in relation to other existing works based on individual fairness. It would be beneficial to include this information, reference these works, and incorporate some comparisons in the experimental section. W4 - The discussion of the results includes several overstatements. For example, on lines 307-310, the authors claim that VFair yields superior performance. However, this is an exaggeration. While VFair may exhibit higher utility in some cases, it comes with a substantial cost to fairness. Moreover, even when VFair demonstrates higher overall utility, the improvement is marginal, less than 1%, which does not substantiate the claim of superiority. W5 - The paper lacks insight into the computational cost of the proposed method. There is no empirical validation to determine whether it is more costly than existing methods and, if so, to what extent. Providing this information would be valuable, as it would illuminate whether a trade-off exists between computational cost and the results obtained without demographic information. Understanding this balance is crucial for assessing the practical applicability and efficiency of the proposed approach. W6 - The authors claim in line 256 that DRO needs the identification of the worst-off group through a bound of group ratio, but as far as I am aware the latter is not true. The method only requires defining the value of $\eta$ but has nothing to do with the demographic information. W (minor) - The section titles should only contain upper case letters at the start of the first word, and not at the beginning of every word in the title. W (minor) - In equation 5 you employ the parameter $\eta$, which is also used in equation 4 but to refer to a completely different parameter. I would recommend using different letters for each of the parameters to avoid confusion. [1] Martinez, N. L., Bertran, M. A., Papadaki, A., Rodrigues, M., & Sapiro, G. (2021, July). Blind pareto fairness and subgroup robustness. In International Conference on Machine Learning (pp. 7492-7501). PMLR.

Questions

Q1 - Why don't you bold the DRO results in Table 1 when they outperform the results of your proposed method? Q2 - What are the Z-scores? Q3 - How well does it scale with the increasing number of instances? Q4 - In line 141 the authors talk about the risk of overfitting, however they do not provide a deep insight into the issue. How likely is it that it happens? Under which circumstances? Q5 - What happens to the method when outlier instances are present? These outliers could significantly complicate the optimization of the classification rule or even result in a trivial classification rule.

Rating

5

Confidence

3

Soundness

2

Presentation

2

Contribution

3

Limitations

The authors do not clearly state the limitations of their proposed method. As a suggestion, it would be interesting to address potential issues such as overfitting, scalability, and susceptibility to outliers.

Summary

The paper proposes a novel view of Rawlsian fairness for scenarios where no demographic information is provided. The core proposal of the paper is VFair, a method for reducing the variance of the predictive loss across a dataset, with the core tenet that a well-concentrated loss distribution would assign similarly-beneficial outcomes to all participants. They also discuss connections and differences with exisiting 'worst-case' approaches such as Distributionally Robust Optimization and Blind Pareto Fairness.

Strengths

The motivation behind the proposed VFair is easily understood as a constrainted optimization objective of minimizing predictive loss variance subject to a performance constraint. This is implemented via a simple Lagrange multiplier approach which essentially weights the standard loss minimization objective with an additional (empirical) loss variance objective . The multiplier itself is actually not optimized for exactly, rather its lower bounded to ensure two reasonable conditions on the update: A) The overall loss gradient points towards (mean) loss reduction (i.e., the variance reduction component does not overpower the mean loss reduction component) B) The per-sample effective loss is positively weighted (i.e., no sample is encouraged to increase its loss value) The resulting method relies on a simple exponential moving average of the overall predictive loss of the dataset and a few simple computations.

Weaknesses

my main concerns with this paper are the following: A) Computational costs. Steps 8/9 in Algorithm 1 require the independent computation of the gradient wrt the mean objective and the gradient wrt the std objective. While not egregious, this would require two backwards passes through the network so the method is computationally more intensive than some of the discussed alternatives like DRO-BPF B) Although the motivation of VFair is shown in Eq 1, the loss constraint $E_z[\ell(z,\theta)]\le \delta$ (in particular the delta parameter) does not end up playing a role in the final method. It is not immediately apparent what the equivalent delta value would be for the proposed method

Questions

See point B in weaknesses

Rating

8

Confidence

5

Soundness

3

Presentation

4

Contribution

3

Limitations

Yes

Encouraging discussion

Dear reviewers, The authors have responded to your questions. Can you please check them and update your evaluation of this work as needed? Many thanks! -AC