Towards Harmless Rawlsian Fairness Regardless of Demographic Prior
Authors: Xuanqian Wang
Jing Li
Ivor Tsang
Yew-Soon Ong
Venue: NeurIPS 2024 poster (2024)
Keywords: Harmless fairness
demographics-free
reducing variance of losses
Primary area: fairness
TL;DR: Harmless Rawlsian Fairness Regardless of Demographics via decreasing Variance of Losses

Abstract: Due to privacy and security concerns, recent advancements in group fairness advocate for model training regardless of demographic information. However, most methods still require prior knowledge of demographics. In this study, we explore the potential for achieving fairness without compromising its utility when no prior demographics are provided to the training set, namely _harmless Rawlsian fairness_. We ascertain that such a fairness requirement with no prior demographic information essential promotes training losses to exhibit a Dirac delta distribution. To this end, we propose a simple but effective method named VFair to minimize the variance of training losses inside the optimal set of empirical losses. This problem is then optimized by a tailored dynamic update approach that operates in both loss and gradient dimensions, directing the model towards relatively fairer solutions while preserving its intact utility. Our experimental findings indicate that regression tasks, which are relatively unexplored from literature, can achieve significant fairness improvement through VFair regardless of any prior, whereas classification tasks usually do not because of their quantized utility measurements. The implementation of our method is publicly available at https://github.com/wxqpxw/VFair.

Towards Harmless Rawlsian Fairness Regardless of Demographic Prior
Xuanqian Wang!* Jing Li Ivor W. T.ang233,4 Yew-Soon Ong
School of Computer Science and Engineering, Beihang University, China 2 Institute of High-Performance Computing, Agency for Science, Technology and Research, Singapore Centre for Frontier Al Research, Agency for Science, Technology and Research, Singapore College of Computing and Data Science, Nanyang Technological University, Singapore wwxxqq@buaa edu. cn {kyle. Skyle.jingli. jingli, ivor. tsann) coo asysongentu. edu.
Abstract
Due to privacy and security concerns, recent advancements in group fairness advocate for model training regardless of demographie information. However, most methods still require prior knowledge of demographics. In this study, we explore the potential for achieving fairness without compromising its utility when no prior demographics are provided to the training set, namely harmless Rawlsian fairness. We ascertain that such a fairness requirement with no prior demographic information essential promotes training losses to exhibit Dirac delta distribution. To this end, we propose a simple but effective method named VFair minimize the variance of training losses inside the optimal set of empirical losses. This problem is then optimized by a tailored dynamic update approach that operates both loss and gradient dimensions, directing the model towards relatively fairer solutions while preserving intact utility. Our experimental findings indicate that regression tasks, which are relatively unexplored from literature, can achieve significant fairness improvement through VFair regardless of any prior, whereas classification tasks usually do not because of their quantized utility measurements, The implementation our method is publicly available at hittts://// //tps:///gtthbb com/xxqpxs/VPaiz
Introduction
Fairness in machine learning has gained significant attention owing to its multifaceted ethical implications and its far-reaching potential to shape and influence various aspects of society 2 K In high-stakes decision-makee domains, algorithms that merely prioritize model utility may yield biased models, resulting in unintentional discriminatory outcomes concerning factors such gender and race. Group fairness, a.k.a. statistical fairness [4, addresses this issue by explicitly encouraging the model behavior to be independent of group indicators, such disparate impact (5), or equalized odds [6. However, with increasing privacy concerns applied in practical situations, sensitive attributes challenge for faimess learning.
not accessible which raises
According to literature, numerous efforts have been directed towards achieving fairness regardless of demographic information, which can be mainly categorized into two branches. One branch is to employ proxy-sensitive attributes g I0] These works assume that estimated or selected attributes are correlated with the actual sensitive attributes and thus serve as proxy of potential biases. The other branch follows Rawlsian fairness (II), which focuses on reducing the disparity in group utility. Unlike the former branch, the group utility here is predefined and centered, and thus it is
Work done during an intersship at STTRRR Corresponning author.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Probability density
Loss value
ERM
Dirac detaa distribution Lees distribution VFair
Worst-case Uniform
Viair
0.25
Wonst group
Loss value
Sorted exampic index
(a) Probability density of losses.
(b) Per-cxample loss sorted in ascending order.
Figure I: Illustration of our idea through different forms of loss curves.
typically not meaningful to test learned models on other group fairness metrics. Worst-case fairness methods 12 [3], belonging to Rawlsian fairness, commonly leverage prior about the worst-off' group's size to identify under-represented members and prioritize the utility of the approximate worst- off group. Such taxonomy overlooks the differences in tasks, as the majority of aforementioned fairness approaches are designed for classification tasks, In applications where discrete outcomes (c.g. binary decisions) provide insufficient information, there a crucial need for fair regressors. As relatively few discussions [4, [5]
exist for fair regression tasks, our work bridges the gap by incorporating regression tasks into general predictive loss under Rawlsian fairness.
The trade-off nature between model utility and fairness has emerged as a subject of dynamic dis- course [16 (88. Worst-case fairness methods which inherently prioritize the worst-off group's utility often come at the expense of the overall utility [13 19). In this work, we focus on scenarios where no prior demographic information is provided, aligning the ingredients with the standard training setup, and then advocate for a primary problem (harmless Rawlsian fairness):
Regardless of demographic prior, what extent the model's overall utility?
improve Rawlsian faireesssairness without hurting
This problem is particularly important in utility-intensive scenarios 20 and we investigate it in both classification and regression tasks to answer the question.
Our idea. We approach the problem from a novel perspective. The crux of the desired fairness lies in pursuing minimum group utility disparity across all groups. Since during the training phase, we not aware of what the actual sensitive attributes are used for test data, the safest way is to ensure every possible disjoint group of training data has the same utility. To this end, we expect the training loss for each individual example to be very close, meaning that the loss variable approaches a Dirac delta distribution. As shown Fig. [ (a). The Dirac delta distribution essentially represents an Oracle model, where all the loss values are concentrated at zero, resulting in both a mean and variance of O. In the distribution view, the motivation of our method which is dubbed as VFair, is to approximate this ideal by minimizing both the mean and variance of the training losses. Fig. (b) also shows the comparison between VFair and other methods, using a regression task as an example. Oracle denotes models with unlimited capability that make predictions with zero error. Empirical Risk Minimization (ERM) refers to models without any fairness design. Worst-case represents fairness methods that require the prior of the worst-off group (e.g., lower bound of partition ratios). Uniform model, initially introduced by [12]. represents a model that performs equally poorly across all groups on classification tasks, Here, extend it to regression. In simplified logistic regression task that applics Mean Squared Error (MSE) loss with targets of or 1, "uniform regressor" predicts values close to 0.5 for each example, resulting in losses close to 0.25, indicated by the yellow dashed line. As depicted by Fig. (b), we expect VFair to exhibit the following two properties.
(1) VFair achieves more flattened loss curve compared to ERM and Worst-case. A flattened curve indicates similar losses for each example, indicating fairer solution for unknown group partitions. (2) VFair maintains an area under the curve comparable to that of ERM, reflecting the overall model utility. Since flattened curve may deteriorate into uniform model that significantly sacrifices overall utility, VFair prioritizes keeping the overall average loss at a low value.

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Statisticallyy, our main idea can be understood minimizing the loss distribution's 's second moment (e.g.. loss variance) while not increasing its first moment. By developing dynamic approach operated at both the loss and gradient levels, our idea is proven feasible and effective.
Contributions. The key contributions of this research can be outlined follows.
We introduce the setting of harmless Rawlsian fairness regardless of demographic prior in both classification and regression tasks. To well position this setting, we also discuss its connections with Worst-case fairness and harmless fairness from the view of variance reduction and re-weighting.
We advocate that minimizing the variance of prediction losses is straightforward yet effective fairmess proxy. By incorporating it as secondary objective, the overall model performance can remain uncompromised.
We develop dynamic approach for conducting harmless updates, which is operated at both the loss and gradient levels, guiding the model towards a fair solution without compromising utility.
We analyze the difference between fair regression and classification tasks, and experimentally demonstrate that, regardless of any prior, harmless Rawlsian fairness is achievable in regression tasks but unfortunately not in classification tasks.
2 Related work
Worst-case fairness without demographics. In alignment with the Rawlsian faimess principle, sequence of studies has followed the Worst-case scheme, which focuses on improving the performance of the worst-off group without full demographics. DRO [13] identified the worst-off group members by a lower bound for the minimal group ratio. The behind insight is that examples yielding larger losses are more likely sampled from an underprivileged group and thus should be up-weighted, which inherits the fairness strategy for handling group imbalance [21] 22) Similarly, [12] also considered
training a fair model with given ratio of the protected group and connected such a fairness learning setting with the subgroup robustness problem [23] In contrast to these studies, ARL (24) introduced the concept of Computational Identifiability to enhance the Worst-case scheme. ARL presented an pnppuuaaiional-denffaalllllii
adversarial re-weighting method to identify the worst-off group in the computational identifiable region without relying on any demographic prior. This embodies the genuine essence of achieving fairness without demographics and is closest to our setting.
Harmless fairness. In utility-intensive scenarios, fair model is meaningful only when it preserves good utility. Basically, these works engaged in discussing the extent to which fairness can be achieved without compromising model utility. Some (25) 26) searched for the so-called minimax Pareto fair optimality for off-the-shelf binary attributes and then upgraded their method to the multi- value attribute cases with only side information about group size [2]. pre-processing method [0] accomplished cost-free fairness through re- weighting training examples based on both fairness- measures and predictive utility on a validation set. Based on the concept of Rashomon Effect, [27] achieved fairness from good-utility models under selective labels through constrained optimization perspective, needing a proper upper bound for the average loss. The same fairness notation also applies to regression task 15). where the prediction error of protected groups remains below some predefined threshold, and the aacuuray frontier is experimentally achieved. Notably, these works more or less require direct or implicit demographic information and cannot adapt to problem setting. A dynamic barrier gradient descent algorithm (28) was recently introduced which allows models to prioritize must-satisfactory constraints. Inspired by this, we conceptualize harmless fairness within a similar framework, enabling us to move beyond a utility-only solution and obtain a fairer model that can narrow the utility gaps among possible data partitions.
3
Vaiir methodology
3.1 Problem setup
Consider a supervised learning problem from input space X' to a label space V, with training set { where 2, (z,, w) E X y. For a model parameterized by θ and training point =
"Throughout this paper, random variables are represented with lowercase letters unless otherwise specified.
3

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let (2;; 8) be the associated loss. Suppose for each 2,, there exists sensitive attribute E S. Thus K-value sensitive attribute will naturally partition data into disjoint groups. Such sensitive attributes are not observed during model training but can be accessible for fairness testing. Following the principle of Rawlsian fairness, the utility disparity over groups used as faimnsss evaluation metric. For example, in classification tasks, denoting dg as the classification accuracy of the k-th group, we can define the maximum utility disparity, i.c., MUD = maxi,je (w, - uy), as a proper fairness metric. More metrics will be introduced in Section 4.1 and the same applies to regression tasks. The fundamental objective of this work is to develop a model that minimizes group utility disparity 24 [22 [5] to the greatest extent possible while maintaining the overall predictive utility (compared to ERM) regardless of demographic prior.
3.2 Fairness via minimizing variance of losses
An ERM model may exhibit variable predictive utility across different groups. Conventionally, fair counterpart is achievable by properly incorporating the objective of minimizing group utility disparity (c.g., MUD), which is however not applicable when demographics are not accessible at training stages. Intuitively, predictive model that can be fair for any arbitrary partitions on the test set implies that the loss of each training example should be close to each other, exhibiting Dirac delta distribution. A compelling piece of evidence is that an Oracle model, as depicted in Fig. | (b), ensures that each individual loss f(z; 0) is sufficiently small, resulting in no disparity, i... MUD 0. This case suggests that group fairness can be instance-wise characterized and hence bypasses the unobserved sensitive attributes. We present this insight by the following proposition.
Proposition 1. u 1 s holds for any s that splits data into a number of groups, if and only if the loss É is (approximately) independent of the training example 2, i.e., {L 2.
The proof of Proposition is left to Appendix A and the approximation arises from the quantization of utility metries, e.g., classification accuracy.
To achieve such a Dirac delta distribution, several fairness objectives can be adopted. We defer the discussion to Appendix B and conclude that applying the variance of losses as a fairness objective is simple yet efficient. Intuitively, the small variance does encourage the loss to be invariant of input. Suppose that we intend achieve small MUD through minimizing the maximum group utility disparity, denoted by ÍMUD The following proposition shows that standard deviation of training losses essentially serves as useful proxy.
Theorem 1. Vs E S, 44 E O MUD
C V=(=0) where C is a constant.
Appendix B. gives the proof of Theorem I Although fMUD is upper-bounded in the form of standard deviation as stated in Theorem[[] []] not introduce ambiguity. So far, we connect Rawlsian fairness with the variance of training losses, without using any prior of demographics.
we term it "variance" for convenience in statements where it does
3.3 Objective formulation
Notably, solely penalizing the variance of losses will not necessarily decrease the expectation of losses, leading to the emergence of uniform model [12]. Thus, to improve fairness without compromising the overall model utility, our full objective is formulated as follows:
min lEB
V. (=(;(2;))) 0)] s.l. [=((((; 66
where 5 controls how much we can tolerate the harm on the overall predictive utility, and the sense that 8 = inface E=[((=;0)) suggests vero-tolerance. In particular, we fold in any regularizers into f(() to make our method easily adapt to specific scenarios. The empirical risk of Eq. is written as
min PEB
(L(z;)) 2()))
s.t.
E(2:: 0) 55
N 1=1
N
E=1
(
A(0)
We use (a(0) and (0) to denote the primary and secondary objectives, respectively. Since we minimize (0) inside the optimal set of minimizing (0), the eventually learned model is viewed to be harmlessly fair with regard to the overall performance.

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Note that the objective of Eq. looks similar to variance-bias research 22 inequality, the expected risk can be upper bounded by the empirical risk plus a variance-related term with high probability:
30 Following Bennett's s
1 N
V V=(e(=;0) ((2 + C1V
C2 N
E. [((=;))
N
where C1 and C2 are some constants which reflect the confidence guarantee. We emphasize Eq. is apparently distinct from our fairness motivation. As derivated (30), the right-hand side of Eq can be well approximately by robust regularized risk, a.k.a. DRO's objective [31]
F(0:n) = = C C(E, (((()))-n - m + +
min inf AEB yER
where C' = (2(1/amii 1)2 1) and ammn is bound of the worst-off group's ratio. Given an 't' which is the optimal solution of the f-th inner optimization but also happens to be close to the mean loss, ie., nf = ja(0),, ) Eq. can be viewed penalizing the upper semi- variane of training loss. This observation connects Worst-case fairness with variance penalization from a new aspect. Although focusing the variance of training losses in method as well, penalize it inside the optimal set of empirical losses. Our method is eventually capable of achieving harmless fairness.
3.4 Harmless fairness update
Directly calculating the optimal set of fi()) < 5 in Eq. can be very expensive. A common approach is to consider an unconstrained form of Eq. 2 i.c., Lagrangian function, which however needs to not only specify proper 8 beforehand but also optimize the Lagrange multiplier to satisfy the constraint best. Besides, the constrained form of Eq.22 makes our task different from traditional objei-obeective optimization tasks. Recognizing that such re-balancing between two loss terms essentially operates on gradients, in a manner analogous to the approach outlined by 28 gradient update scheme,
we consider the following
0++ <- 0² 0- (> Vā(0)),
where yf is step size and X 2 0) is the dynamic coefficient we aim to get. For simplicity, we omit the time stamp t and model variable 0 when it is not necessary to emphasize them. Now we provide how do we dynamically adjust
Gradient view, The idea of designing to keep decreasing j when the constraint is not met, meaning that the combined gradient should never hurt the descent of f. As depicted in Fig. (a),
V
(a), if the gradients Vā and V forms an obtuse angle, detrimental component emerges in the direction of Vp (indicated by the red dashed arrow). Otherwise, the gradient conflict does not happen, shown as Fig. 2 (b). Conse- quently, should be sufficiently large to ensure that the combined force's 's component in the pri- mary direction remains non-negative, that is
4
V
(4)
(b)
Figure 2: Two situations when updating primary and secondary gradient simultaneously.
λV + Projup (V6) 2 eVP A Vā
V
= A
(6)
Here, e represents the extent which we wish update Vp when two gradients are orthogonal. We choose = in Eq. 6 because it keeps an intact update for the primary gradient V fa in any cases. The
harmless component of optimizing o, illustrated as the dotted yellow arrow Fig. 2 (a), undergoes with equal strength. The derivation of X₁ essentially assumes that the constraint of Eq. 2 is satisfied if
Vp = 0, which avoids an elaborately specified When V * O but ||V small, indicating that the primary objective is nearly minimized, set À max A1, 0} prevent negative values.
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Loss view. Recall that ā takes ji as input according to Eq which inspires us to further inspect the combined gradient, denoted by V, beyond treating them separately as we do in the gradient view. Theorem 2. Given the objective of Eq. the combined gradient derived by the update scheme of Eq. 5 can be expressed with an caaampl--rweighttigg form.
0c,
Vō
11)
00
The proof of Theorem can be referred to Appendix [ Eq. 7 shows that our faimess formulation with dynamic gradient update implicitly reweights each training example via an unnormalized weight w, i.e. the Z-score of loss plus a coefficient X. This finding connects our work with recent Worst-case which up- weight the training examples whose losses are relatively larger, and also a harmless fairness method [20] which directly applies the re-weighting scheme.
fairness studies [33 [2 22
As we can see ui < 0 for all examples whose Z-scores below -X, raising a concern of unstable optimization [32 To guarantee that the weight of each training example is non-negative, we require
1 0
E [N]
X+
(1i
(1)
20
(8)
(
max E[
min E sE[N]
: X2
where the last inequality holds because predictive losses typically designed to be non-negative, facilitating the climination of the sorting procedure.
Remark 2. According to Eq. 8 X is positive. Notably, A2 can approach 0 á < 8, where we may obtain a model with good utility but poor fairness. Since Z-scores fall within the range of -3 to +-3 capturing a significant portion (99.7%) of the data in normal distribution, X2 is often capped by 3.
In summary, combining Eq. and Eq. we compute the adaptive each step that ensures harmless fairness update:
A max (A1, A2) max 11
V Vā
7 3
Note that Eq. rrequirss the computation of gradients and values for both j and ô which is time- intensive and memory-intensive if executed on the entire dataset. To scale up to large datasets, we provide an efficient mini-batch update strategy. Detailed implementation and algorithm can be referred to Appendix
Experiments
4.1 Experimental setup
Datasets. Six datasets encompassing binary classification, multi-class classification, and regression are employed. (i) UCI Adult 333 (ii) Law School 34 (iii) COMPAS [35], (iv) CelebA (36), (v)
Communities & Crime (C & C) [37, (vi) AgeDB
38 Note that datasets (i-iii) can transformed
into a logistic regression task by applying MSE loss with the category label the target. Following the convention established by [5), we select sex (or gender) and race (or Young on CelebA) as
sensitive attributes for datasets (i-iv), four attributes for C & C, and one for AgeDB datasets.
Metrics. During the evaluation phase, we gain access to the sensitive attributes that partition the dataset into K disjoint groups. As discussed in Section 3.1 our training objective is to uphold high overall predictive utility level while minimizing group utility disparities the greatest extent feasible. Henceforth, we assess the performance of our method across five distinct metrics: (i) Utility: Overall accuracy for classification (also specified by other metrics like F1-score and prediction error when necessary) and MSE for regression tasks. (ii) WU: The worst group utility among all K groups. (iii) MUD: Maximum utility disparity, as described in Section 3.1 (iv) TUD: Total utility disparity.
TUD = Eke(ro (ux ú) where ū is the global average utility. (v) VAR: The variance of prediction
error.
Since we not able to exhaustively enumerate all possible sensitive attributes and test faimess

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via the metrics (ii-v),, VAR necessarily serves as fairness proxy for any other possible selected sensitive attributes during the test phase. To ensure the reliability of the results, we repeat all the experiments 10 times and average the outcomes.
Baselines. We compare VFair against seven baselines including ERM, DRO 13 ARL 24 FaiRRF [91. MPFR (15). BPF [2], and FKL (39. Note that DRO, BPF, FairRF, MPFR, and FKL all require some prior demographic information; DRO and BPF necessitate the identification of the worst-off group through a bound of group ratio, while FairRF selects some observed features as pseudo-sensitive attributes, which consequently constrain its application to image datasets (i.e., CelebA); MPFR and FKL which are particularly designed for fair regression tasks also incorporate sensitive attributes. Methods take general loss functions like VFair which apply to both classification tasks and regression tasks, i.e., DRO and ARL are implemented for regression tasks by using the MSE loss. Note that BPF, MPFR, and FKI. are not designed with stochastic updates and they suffer from out-of-memory issues under our experimental setup on the UCI Adult and AgeDB datasets. Therefore, the experimental results of this part are not included. Please find more experimental setup details in Appendix
Table 1: Comparison of regression results (x (x10²) on five benchmark datasets with the best rank in bold. Here, J. is for Utility and WU because MSE is used, and smaller values indicate better utility.
Utility
WU
MUD
TUD J
VAR
ERM
12.88
19.75m20
7,33am4
13.45m20
4.89mam
DRO
24.85
24.98ku
0.14om0
0.23mu1
0
ARL
12.86
19.72mmm
7,33
13.54
4.86mz7
BPF
18.75aa0
43.25
26.33
47.33:s.0
3,98azs
Law School
MPFR
13.88
29.39
16.68
32.07
7.15
FKL.
13.10
19.37
6.77
13.42
5.01
VFair(Ours)
12.95aa
19,08
6.63amm
12,53
3.66u1z)
Improved
-0.07
+0.67
+0.7
+0,92
+1,23
ERM
23.08
24.49am0
2.500
3.45
3.23asi
DRO
24.97/am0
25.05mm.0
0.12amm
0.17au
0
ARL.
22.73m.
24.26 pan
2.922 (e)
3.78I m
3.19mm
BPF
50.80
63.460..
22.87am
37.77
11.18am0
COMPAS
MPTR
36.26
38.36
6.23
9.13
17.33
FKI.
28.56
30.49
3.69
6.47
7.58
VFuir(Ours)
23.15pus
23.83a20
0.93a20
1.17a25
0.47mam
Improved
-0.07
+0.66
+1.57
+2.28
+2.76
ERM
41.15a29
109.72isa
106.56
337.26
87.52Pa4
DRO
99.34aa8)
2:7.51:4229
248.56usaa
115.62
284.49.220
ARL
40.43a19
109.00keas
106. 88
331.38
83.98
BPF
71.05
127.28:672)
110. 1G
320.65
96.76
C C
MPFR
93.57
296.36
295.59 59
843.47
375.79
FKL
83.73
278.30
275.29
794.59
321.42
VFain(OUus) 41.17am
106.40:..0
104_54..
318.33x sey
67.44.1
Improved
-0.02
+3.32
+2.02
+18,93
+20.08
ERM
4.25mm4
4.32mam
0.
0.
0.57mm:
DRO
17.72ma5
17.980249
0.5mmm
0.5
5.767
AgeDB
ARL
5.11
5.29
0,36o4D
0.36m49
2.51
VFuii((Urs)) Improved
3,57mm
3.63am
0.12m
0.12m
0.23mon
+0.68
+0.69
+0.03
+0.03
+0.34
4.2 Examine harmless fairness in regression tasks
Table showcases the comparison results of different methods regression tasks. The standard deviation calculated from every 10 repeated experiments is presented in the bracket. In the "Improved" row, we computed the improvement of VFair compared to ERM, where "+" denotes improvement rather than a numerical increase. Results with significant changes at the 0.05 significance level are highlighted in green, while others are in yellow. Note that our objective is to gain improvement in faimess metrics while maintaining utility, signsignnf changes in utility are desired. However, significant drops in utility violate the harmless setting.
According to Table L we have the following findings.
(1) VFair significantly improves most fairness metrics with non-significant changes in Utility. Exceptions on C & C and AgeDB are due to their
7

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specific group partition. C & C is split into 16 groups with some extremely small groups, limiting the improvement on WU and MAD while VFair still outperforms others on TAD and VAR. AgeDB is split by gender with ratio of 4:6, where ERM can also be relatively fair. (2) VFair gains significant VAR improvement on all datasets, guaranteeing that the group utility disparity remains low for any downstream sensitive attributes. (3) The utility of the test set turns out clear distinctions among compared methods because prediction error (MSE) is sensitive to both the possible distribution shift of test data and model parameters. In this sense, only VFair and ARL can still approach the utility of ERM while the rest usually cannot. (4) DRO gains utility close to 0.25 on each group (i.e. uniform regressor shown in Fig. (b)) on Law School and COMPAS while using the real prior, shadowed in gray.
4.3 Examine harmless fairness in classification tasks
In the context of classification, fairness metrics provide limited improvements without compromising utility (see Appendix [F. for detailed results). To further investigate the performance gap between regression and classification tasks, we depict classification losses in Fig. following the same scheme in Fig. (b) on real dataset COMPAS. Curves on other datasets are left in Appendix F.2
Our observation. (1) Regardless of the uniform classifier DRO, method VFair exhibits more flattened loss curve compared to others while maintaining compara- ble area under the curve (filled with pink), signifying harmless fairness solution. Such results align with our initial idea, as presented in Fig. (b). (2) Our method VFair implies the Worst-case faimess, the average loss of the worst-off group for VFair will be consistently lower than any other method. Our claim is obviously true if the group size small. Regarding a larger group size, thanks to the fact the total area under each curve is nearly equal and the curve of VFair is always above others at left, we conclude that the worst-off group's 's losses for VFair are also the lowest. (3) The vertical dotted blue line represents the threshold, where the intersection with the loss curve of VFair values -0.5)..)). Divided by it, the samples on the left are correctly classified, and conversely on the right. As evidenced by the figure, this threshold close to each method's intersection. Imagine situation where the loss curve rotates around the decision point with smaller angle to the x-axis, obtaining smaller sample disparity. However, due to the discrete metric and unchanged group partition, the accuracy-base metrics' values for this method remain unchanged after rotation. Therefore, despite our method approaching horizontal loss curve, thus providing a smaller disparity for any potential group split, the fairness improvement is still bounded by the overall utility.
2.5
DRO
2.0
ARI.
VFai
Conrect Whong
1.5
FaidRE
Arg. loss
1.0
0.5
5kc
5k
Socted ovample index
Figure 3: Per-example losses for all com- pared methods sorted in ascending order on train set.
Beyond accuracy utility. Classifying imbalanced data often applies Fl-score as a metric, which is free of the effect on true negative samples which can dominate the accuracy result. We test F1 F1-score performance on UCI Adult and CelebA because they have a remarkable imbalance ratio. The results are summarized in T
Table 2: Classification results (x (x100) comparison on two imbalanced datasets with Fl Fl-score as the utility metric. The best rank is highlighted in bold.
UCI Adult
CelebA
Utilityt
WU
MUD
TUD |
Utility
WU
MUD
TUD J
ERM
75.02
72.17
6.87
8.88
91.40
70.17
19.39
22.82
DRO
36.27
16.06
23.59
41.17
77.52
74.29
3.9
4.78
ARL
74.90
71.85
7.32
9.49
91.60
70.39
20.14
24.33
VFair
75.98
72.74
5.82
7.40
91.91
75.70
14.39
18.50
We observe that on UCI Adult, the earned fairness for each fairness method is still limited while on CelebA, VFair yields superior performance. A reasonable explanation is that VFair has the opportunity to discover better solutions in a relatively larger solution space, where more diverse
8

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minima can be examined through fairness criteria. And though Fi-score removes the influence of true negative samples, takes the quantified property and hence may only help amply the gains.
From quantized to continuous. For scenarios where prediction error (the difference between prediction and true label) is desired in classification, e.g-, assessing whether model overestimates or underestimates, VFair should be more applicable. To justify this insight, we compare fairness methods (except for FairRF and DRO as they often fall short on utility) the three datasets reused for regression tasks. Instead of evaluating specific attributes as we do in Section 4.2 we test VFair on all possible divisions of the test set by randomly splitting them into groups. The three methods are ranked based their performance under each metric. From the best to the worst, the rank score is 1, and 3. The average rank over 100 times is reported.
Table 3: Average rank of four compared methods. All methods are trained only once.
K
K WU
10
K
20
Utility
MUD
Utility
MUD
TUD
Utility
MUD
TUD
ERM
2.5
2.31
2.36
2.51
2.4
2.46
2.5
2.27
2.44
2.39
UCT Adult
ARL
2.5
2.48
2.51
2.35
2.6
2.54
2.5
2.23
2.56
2.61
VFair
1
1.09
1.21
1.13
1.14
1
1
1
1,5
1
ERM
2.7
2.66
2.37
2.36
2.7
2.61
2.52
2.54
2.7
2.52
2.5
2.53
ARL.
2.3
2.34
2.36
2.37
2,3
2.39
2.48
2.46
2.3
2.31
2.5
2.47
Law School
VFair
2.7
1.27
1.27
1
1.17
ERM
2.5
2.21
2.56
2.57
2.5
1.89
2.57
2.56
2.5
1.53
2.58
2.62
COMPAS
ARL
2.5
2.44
2.43
1.98
2.43
2.44
2.5
2.42
2,38
VFair
1.35
1.01
2.13
2.91
Results in Table 3 show that our method VFair has a better rank than other methods regardless of the choice of K, demonstrating that VFair prefers the utility metrics that are loss/error-related. As mentioned in Section[4]] VAR serves as approximation for an extreme group split, where each group consists of only one member. Thus, the significantly low VAR in Table and Table good results in random partitions on the test set, evidencing that variance can serve as an effective optimized term in Rawlsian fairness tasks without prior demographic information.
4.4 A closer look at VFair
We examine VFair through extensive experiments. Here present the partial results and main conclusions. One can refer to Appendix F22
F3 and F.4 or more details.
And
B033
Adal
COMPOS
esc
Apdro
103
384
Low
1.50
2000
35.3
42.6
(a) Training results on COMPAS
MSE on five regression datascts.
(c) The curves of a and xe during training on C & C.
the classification task.
Lower is better.
Figure Experimental verification of the harmless update strategy.
Method efficacy. We monitor the performance of VFair during the training phase by evaluating it with four utility-related metrics on the test set of COMPAS. Fig. 4 (a) indicates these curves naturally improve in the desired direction under the variance penalty, verifying the effectiveness of our method.
= 1, max(A1, 0), = A2 and X max(X 'r X2). As depicted in Fig. 4 (b), we present the per-dataset utility five regression datasets (results are proportionally scaled on each dataset for a clearer presentation). The full version, considering both \₁ and dg exhibits the most stability in preserving low MSE, enabling harmless
Ablation study. We train our model under four settings:

---

solution. In Fig. 4 (c), we demonstrate an example of Y and X2 on C & C dataset during training, where both serve distinct and complementary roles in preventing the model from sacrificing utility.
Model examination. We scrutinize the fair models by studying their parameters and prediction similarity with ERM. Our experiments found that the model learned by VFair is more dissimilar from ERM than other methods. For example, on Law School, the cosine similarity of model parameters in ARL and VFair with ERM is 0.6106 and 0.5839, respectively. This indicates that VFair may explore a larger model space to achieve better performance.
Conclusion
Towards harmless Rawlsian fairnsss regardless of demographics, we have introduced straightforward yet effective variance-based method VFair. VFair harnesses the principle of decreasing the variance of losses to steer the model's learning trajectory, thereby bridging the utility gaps appearing potential group partitions. The optimization with a devised dynamic weight parameter operated at both the loss and gradient levels, ensuring the model converges at the fairest point within the optimal solution set. By capping the Z-score, our dynamic weight parameter can also prevent the model from overfocusing on outliers with larger losses. The experiments affirm that regression can be prior-free task to Rawlsian harmless fairness because error-based metrics are more consistent with loss. Strong prior for demographies may be needed for quantized metrics like accuracy in classification tasks. As discussed in Appendix G] limitations may arise from computational costs, where VFair takes twice the time of ERM to uncover more information without access demographic prior. Future work will involve identifying and addressing further challenges that may arise when applying VFair for the prediction of non- data.
Acknowledgement
This research is supported by the National Research Foundation, Singapore and Infocomm Media Development Authority under its Trust Tech Funding Initiative (No. DTC-RGG-04). Any opinions, findings and conclusions or recommendations expressed this material are those of the author(s) and do not reflect the views of National Research Foundation, Singapore and Infocomm Media Development Authority.
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Jordi Muñoz-Mari, Luis Gómez-
12

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A Proof of Proposition
Proposition 1. u 1 holds for any that splits data into number of groups, if and only if the loss E (approximately) independent of the training example 2, i.e., 1 2.
Proof. Suppose that splits data into K disjoint groups. Let the random variable & represent the group index. We can rephrase the statement as Vs, - k|s f 2, which is established through the following two steps.
=" difficult, we consider its contrapositive, i.e., "f y 2 = 7s, a y k". If the value of l spreads across a large range, indicating some examples are well-fitted (small loss) while others are not (large losses), we can simply split them according to if well-fitted. Since u1 o u2, u & k follows.
Step 1. Since proving "Vs,u k|s =
Step 2. The assertion," "f T Vs. L k", is true when the condition & is strictly satisfied. Particularly, a quantized utility is applied, e.g.. accuracy, the assertion holds even if we relax the condition- exhibits approximate dependence are concentrated in proximity to the decision boundary, resembling the characteristics classifier. In the context of finite partition by the accuracy of each subgroup within uniform classifier statistically converges towards 0.5 for binary classification. (ii) All losses are conspicu- ously distanced from the decision boundary, akin ideal classifier. In this case, ideal classifier consistently achieves subgroup accuracy of 1, irrespective of the chosen split. In both situations, we can indeed conclude that Vs, 1 k)s.
Two distinct scenarios arise. (i) All losses uniform
B Fairness objective
B.1 Proof of Theorem 1
To prove Theorem 1 we need the following lemma.
Lemma 1. Given N non-negative numbers {v: LN the following inequality holds
max U3
min U. AE[N]
1z-1/
(10)
sE[N]
Proof. Let a = min the triangle inequality, we have
arg min U/ arg max :E[N]
max
arg min 8, arg max vú iE(N]
According to
sE[N]
aE[N]
max ie
min 0 TE[N]
max (E(N]
min 0y <
l1s
Ui+1
iE[N]
Particularly, the equality holds if N arranged in monotonic order.
Theorem 1. Vs E S, 1O E O, LMOD & C. CVV where C a constant.
Proof. Let rk denote the expected loss of k-th group. We have
13

---

MUD
max Fk kc[K]
min
Th
max & kE(N]
-minn &
kk(
N-1
Σ
14 1+11
(11)
i=1
N
2
14 Lgl
C
14: E
KJ
NV
CRV=1((=;00)
(12)
N2 v=(((z;0)
(13)
where 1 follows inequality given by Lemma 1, 2 uses the norm inequality of |
S
v di 2. 3 is derived from the fact that V=(((z;0)) Nラ. (he E2) and is similar
2 and further uses Σ |4, e,l L.
Note that Theorem adopts the result of Eq. [2 which scales one side by factor N, making not a very tight bound. However, we justify that this option is more efficient than others the next subsection. Additionally, although we start with (MUD. is easy to verify that the derived bound also serves as proxy for other utility disparity metrics, e.g., TUD.
B.2 Option of loss for Rawlsian fairness
To compare the efficacy of three forms of faimess loss, i.e., Eqs. 6², and ā respectively:
and 13 we denote each as ît
न -= =NN-1
Di=i
N-1
14, l+tal (Pairwise)
Σi=l (l+ - 12)2 (Standard deviation)
0² M (4+ a)) (Variance)
Here, analyze the choice of the objective from both theoretical and experimental levels. The experiment results are shown in Table
Table 4: Comparison of three faimess objectives four benchmark datasets, where the tulityybbsed results are with %, and the results of VAR are x 102 for a neat presentation. Best results are in bold.
Objective
Utility 1
WUt
MUDJ
TUD4
VAR.
82.98
78.35
16.19
21.10
UCI Adult
6²
84.70
80.34
15.72
20.79
7.18
84.74
80.36
15.71
20.71
8.17
84.05
72.96
11.92
22.51
0.03
Law School
2
85.33
74.60
11.67
20.91
6.91
85.40
74.81
11.24
20.31
19.35
55,78
51.60
8.70
12.24
COMPAS
2
63.45
59.14
8.71
11.36
0.04
66.80
63.86
6.25
8.47
1.86
A 44.88
20.16
49,16
53.85
CelebA
0
92.45
89.53
3,44
4.63
14.4
93.43
91.09
2.73
3.85
11.7
14

---

Pairwise difference objective. Eq. 1 computes the consecutive pairwise difference of all training losses. Putting it under the proposed harmless update, we need particularly get the dynamic value for X2.
Similar to Eq. 8 the X2 is set to guarantee samples will not be assigned negative weights.
ae:
V
4
4+1
V
(14)
00
By inspecting the possible combination of the absolute equation, it is obvious that Φ1 ON E (-1,1}, and Φ; E (-2, 2], vi N1, Consequently, Aa can be calculated as:
Vie [N] x+ Φ5 20=122:>>
(15)
When operated on mini-batch, unlike ē and 62, the pairwise difference objective does not consider global information, losing the relative relationships when attempting to identify the Worst-case group (also discussed Appendix D). The instability arising from the difference of pairwise sample losses might mislead the upgrading process, as evidenced in our experiments. On challenging datasets such as COMPAS and CelebA, the model tends to converge towards a uniform classifier, even constrained by dynamic parameters.
Variance objective. By dropping constant factor of Eq. 13 we employ 8² = Ei=1( (fe f2)² as secondary objective. Similar the proof of Theorem 2, we have
V = XV jt + VO²
N
0e,
(16)
(A+2 2 -()--)))
ii))
N
00
Consequently, we get A2 = ( min 4x).
can be observed from Eq. 13 that 6² serves as a broader constraint for ÉMUD- As a result, it a less restrictive objective for group disparity compared to ô. However, the square- version term penalizes more on both smaller and larger losses, resulting in an unavoidable decrease in overall utility (e.g.. unreliable data with spurious correlation) and hence all utility- based faireess metrics. Please the evidential experiments Table that using 8² as objective results in lower variance but higher group disparity.
C Proof of Theorem 2
Theorem 2. Given the objective of Eq. 2 the combined gradient derived by the update scheme of Eq. 5 can be expressed with an example-reweighiing form,
N
02,
XV V0
A +
(f:
N
00
iml
Proof. Based on the form of (i()) and ((0) in Eq.
we have
0e
(17)
20
15

---

Vō
1
Σ
N
2(1; - (1)
Ole; (t)
2v
N
Σ Li=1(e (1e 1i)2
N
1=1
30
1
Eg f 06;
1
Σ
(Lg (3) 1
Σ
dek
N
No
N
00
1
Eg 3 0g
(18)
Σ
N
δ 00
A=1
N flx
Σ 4
Np
No
N
08
j=1
The example-reweighting form of gradients follows by unifying Eq. 17 and 18
D Implementation and algorithm
To enable the application on large datasets, we provide mini-batch update strategy. worth noting that the mean loss encompasses global information that could guide the update direction for each sample. The variance on mini-batch computed on local mean loss may cause unstable optimization, especially when the batch size is small. As such, we consider maintaining global mean which assists with the mini-batch update. To this end, we employ Exponential Moving Average (EMA) as an approximation for the global mean loss:
p Bp
4
(19)
1=1
where the decay parameter 3 is set 0.99 for all datasets in our experiments, and denotes batch size. The comprehensive implementation of our VFair is elucidated in the following algorithm.
Algorithm 1 Harmless Rawlsian Fairness without Demographics via VFair.
Input: Training set D = {= J where = (I,, v1) E X x y
Output: Learned model parameterized by 0 E θ
1: Initialize parameters 0
2: Initialize A <
3: for epoch + 1 to Nepochs do
4: for mini-batch B C do
5: Compute the losses {E, 1==1
6: Update ji' as in Eq. 19
7:
Update + / Σd (e,
)2
8:
Compute primary gradient V ft
9:
Compute secondary gradient Va Compute X in Eq. 6
10:
11:
Compute 22 as in Eq.
12:
Compute dynamic X as in Eq. Update parameters 0 as in Eq.
13:
14:
end for
15:
end for
E Experimental setup details
All the deep-learning-basee models, excluding FairRF, which operates within a distinct problem setting, conform to shared neural network framework. Specifically, for binary elassification tasks, the core neural network architecture consists of an embedding layer followed by two hidden layers,
16

---

with 64 and 32 neurons, respectively. In the ARL model. an additional adversarial component is integrated, detailed in its respective paper, featuring one hidden layer with 32 neurons. For multi- classification tasks, the primary neural network transforms into Resnet18, and the embedding layer transitions a Conv2d-based frontend. Throughout these experiments, the Adagrad optimizer was employed. FairRF, utilizing its officially published code implementation, maintains the same backbone network with nuanced variations in specific details. Particularly, fair regression methods MPFR and FKL are implemented adapted from [15].
As For the loss function, we implemented Binary Cross-Entropy, Cross-Entropy and Mean Square Error for binary classification, multi-class classification, and regression tasks, respectively. Note that our method is general and can be compatible with any other forms of loss.
All experiments were conducted on Ubuntu 20.04 with one NVIDIA GeForce RTX 3090 graphics processing unit (GPU), which has memory capacity of 24 GB.
To compare all baselines under the harmless fairness setting, we implement them into the same scheme and select the epoch with the nearest loss compared to converged ERM. Detailedly, each method has an empirical loss, which in our method denoted as á and in ARL is denoted as learner loss (compared to adversarial loss). Based on this loss, we select the harmless epoch which has the nearest loss value compared to well-traines ERM model.
F More experimental results
F1
Experimental results on classification tasks
Table 5: Comparison of classification results on four benchmark datasets, where the results of utility
(i.e., accuracy) based metries are with % and the results of VAR are 102 for neat presentation.
Utility f
WU f
MUD 1
TUD
VAR 4
ERM
84.67
80.20
16. 16.13
20.78(a99)
33.89(4.7)
DRO
74.39
69.82(a36)
16.89aas)
27.26(224)
UCI Adult
ARL
84.60
80.1 (091)
16.17
20.9 (0.95)
36. 18
FairRF
84.27
80.01 (0.1))
15.73
20.26x0.50
25.83
VFair
84.74
80.36
15.71
20.7
08. 07.17)9
p-value
0.08
0.54
0.24
0.86
ERM
85.59(0.7)
74.49
12.08(274)
21.50
36.95
DRO
59.7619.99 52.28(s.00)
10.49
16.561187
244.81
Law School
ARL
85.27 74.78(212)
11.52(220
21.52
37.95
FairRF
81.91 68.75(161)
14.48(165)
26.84(2.00
30.80(199)
VFair 85.40ros9)
75.25
11.00.1.2)
19.91
06.29ko24)
p-value
0.62
0.33
0.32
0.24
ERM
66.70
63.20(1.4))
07.15
09.12
15.63(3.88)
DRO
24.97
25.05(1.7)
0.12(.08)
0.17a.m
0
COMPAS
ARL
66.651a.s)
63.27
06.93(18))
09.09
14.42(s.64)
FairRF
62.90lu.m) 61.55
02.64
03.69121
06.93
VFair 66.80mm
63.86(a.7))
06.25
08.47a
1.86
p-value
0.66
0.24
0.1
0.36
ERM
92.80
89.77
03.64
04.77
40.08
DRO
83.97
82.19
2.37
2.7
21.48
CelebA
ARL 93.26
89.84
04.02
05.41
37.38
FairRF
VFair
93.43
91.09
02.74
03.85
11.70
From the experimental results in Table 5 we can observe that: (1) VFair, without any prior, consis- tently achieves top-2 performances classification tasks, competing with or outperforming baselines that use priors, e.g., DRO and FairRF. However, except for VAR, metrics carn limited improvements.
17

---

We calculated the p-value for each metric between ERM and VFair to quantify the limitation. The results show that the p-value of metrics, except VAR, remains high. Generally, p-value less than 0.05 is considered indicative of significant difference between the two groups. Even with the same datasets, especially on COMPAS, it found that harmless Rawlsian fairness is difficult to earn for classification while comparatively easier for regression tasks. (2) From the Utility dimension, FairRF and DRO sometimes fail to guarantee a comparable utility, because constraining group fairness on their proxy attributes unavoidably hurts the overall model performance. With this cost, they sometimes achieve a noteworthy fairness improvement. Note that DRO turns into a uniform classifier COMPAS, shadowed in gray. (3) CelebA seems exception where VFair attains meaningful fairness improvement while others do not. A reasonable explanation that VFair has the opportunity to discover better solutions in relatively larger solution space, where more diverse minima be examined through fairness criteria. (4) We also notice that hecause we explicitly optimize variance, VAR has been remarkably decreased in VFair across all datasets, showing flattened prediction erros on all test sets.
F.2
VFair training curves
EBM
3M
66
Schocoungh Ido
(a) UCI Adult
(b) Law School
COMPAS
(d) CelebA
Figure 5: Full version of per-example losses for all compared methods sorted in ascending order on the training set of four benchmark classification datasets. Dash lines represent their average losses.
TLB
3am
SI
(a) UCI Adult
(b) Law School
(c) COMPAS
(d) CelebA
Figure 6: Full version of test performance curves of four utility-base' fairness metrics during the training process (Step/5) on four benchmark datasets with Accuracy served as the utility.
(a) UCI Adult
(b) Law School
(c) COMPAS
(d) CelebA
Figure 7: The loss curve of primary objective during the training process four benchmark datasets.
depict full version of the per-sample losses for compared methods sorted in ascending order on the training set in Fig. 5 From Fig. 5 we surprisingly see that across different datasets our VFair is the unique one that has the flattened curve while DRO, ARL,, and FairRF are essentially close to ERM.
18

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The full version of test performance curves of four utility-related metrics during the training process on four benchmark datasets are present Fig. Our VFair effectively improves all utility-related metrics.
Fig. 7 illustrates the convergence of training loss four benchmark datasets. As the final combined objective is updated directly at the gradient level, which does not have unified loss form, we display the curve of losses of the primary objective, representing the model's utility. We observe that our upgrading method in Eq. efffectively steers the model towards convergence. Note that our dynamic updating strategy similar 28 which is theoretically proven to converge.
F.3 Detailed ablation results
According to the ablation setting in Section 4.4 we conducted throughout experiments on the classification task and the regression task, respectively.
As shown in Table 6 method already achieves competitive results by solely employing A2. The full version which integrates both λ and X2 demonstrates more stable results. Notably, on the Law School and COMPAS datasets, there exist situations when the model converges towards uniform classifier, as indicated by the gray region. These uniform classifiers predict all the samples near the decision boundary, causing their losses share very similar values and form variances at a scale of around le 7. This phenomenon underscores the effectiveness of X2 in preventing the model from collapsing low-utility model. Moreover, by adding Å₁, our method consistently improved in four utility-reatted metrics. These results show that )1 effectively guides the model to converge to a better point at the gradient level.
Table Comparison of classification ablation results (%) on four benchmark datasets. All of the results are averaged over 10 repeated experiments to mitigate randomness, with the best results highlighted in red and the second-best blue (excluding the uniform situation).
\
X2
Utility
WU 1
MUD +
TUD
VAR +
84.71
80.36xa44)
15.85
20.94
3r0.32)
V
8..68
80.27
15.91
20.97
7.75ka.1)
UCI Adult
V
84.52(0.40
80.08..65)
15.99(..3)
20.92.0.50
6,58(.15))
V
V
84.74
80.36x049)
(..7
20.71
8. 8.17.09
==1
84.36
74.30
10. 10.88
20.73(163)
0.05xmm
V
85.40b.30
75.09(..8)
11. 11.200.82)
20.43
6.3
Law School
45.39
32.03
30.3
$3.12.5.088
O
V
v
85.40
75.25
11.00.1.2)
19.91
6. 6.29/a20
A=
A
55.2
49.90s.44
10.5 (4.30)
13.28(5.51)
Oko
V
64.29(0.9)
60.44..63)
7.34
9.67(487)
0.03g.00
COMPAS
66.45
63.49(..9m
6.60k240
8.40k3.2)
1.9
V
66.80
63. 63.866.57)
6.25
8.47(.225)
1.86m.1
A
92.04
89.22
3.66
4.65
0.1269
V
93.46
90.62
3.49
4.67
0.1161
CelebA
93.23
90.08
3.70
5.14
0,0753
93.43
91.09
2.73
3.85
0.1170
As shown in Table 7 simply employing À = 1 or X can reach more significant fairness improvement, but at the cost of sacrificing utility. The full version considering both X and X is the only one containing harmless on all datasets, which was discussed in Section 4.4
F,4 Model similarity with ERM.
We examine the similarity between fair models and an ERM model. We conduct experiments comparing ERM, DRO, ARL (without adversary network), and VFair, as they share the same model structure. By calculating the Cosine similarity of model parameters and prediction similarity with ERM reference, get results shown in Table g
19

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Table 7: Comparison of regression ablation results (%) on four benchmark datasets. All of the results are averaged over 10 repeated experiments to mitigate randomness, with the best results highlighted in red and the recond-best in blue (excluding the uniform situation).
A1
2
Utiliyy +
WU +
MUD 4
TUD +
VAR +
X
15.53.oo
(7.47
6.940.71
11.270
0.89(a
12.62
15.26
9.55
15.50uas)
1.63
UCI Adult
11.43)225)
14. (4
9.78m.44
15.97
2.44.0.4)
11.49
(4.24
9.92(0.99
16.25
2.52.0.3)
A == 1
24.22
24.55
0.36xa.m7)
0.661a.13)
0.01
17.39(0.31)
(0.77
3.73
7.10ro20)
0,85
Law School
12.90
19.01 (0.1))
1.60
12.51
3.6 3.63
12.95
19.08
6.63
12.53
3.66(..12)
== A
24.92
25.03
0.24
0.34
0.02,0.1)
v
23.86 17.17)
(a
1.1 810288
0.45
COMPAS
24.79
24. (0
0.24(a.11)
0.3 (o.1)
0.02,0.0)
V
13.
23.83
0.93
1.17
0.47
A ==
106.52(1.2) 40.63.0.67)
105.582.06)
315.92(7
68. 68.69337
V
106.28 o1.32pm.5)
104.22
315. ((7.1))
66, 66.963a5
C&C C
/
44.92
106.2 (2665)
96.55
299.77(5.95)
60.54g237
(1.17
106.40
104.54
318.33(8.0)
67. (3)
Table 8: Similarity between fair models and an ERM model on three benchmark datasets.
Cosine Similarity
Prediction Similarity
DRO
ARL
VFair
DRO
ARL
VFair
UCI Adult
0.2956
0.9957
0.9955
32.75%
97.45%
96.55%
Law School
0.1693
0.6106
0.5839
37.19%
95.61% %
95.91%
CelebA
0.1663
0.1886
0.1474
66.47%
95.41%
94.62%
As evidenced by Law School and CelebA, similar predictions do not necessarily indicate similar model parameters. Note that VFair could be more distinct from ERM compared to other fair models, especially on complicated image dataset CelebA. The better fairness improvement in Table [5 also proves that VFair can explore different minima in broader model space, guiding the model to converge to fairer point.
F,5 Regression results on UCI Adult
Table 9: Comparison of regression results (x (x10²) on UCI Adult. Here, is for Utility and WU because MSE is used, and smaller values indicate better utility.
Utility 4
WU 4
MUD +
TUD L
VAR +
ERM
1 (1.37
14.34k.1
10.83
17.72c..0
4.94(..n
DRO
22.54
23. 130.57)
2.12.o
3.54
12
ARI.
11.700.39)
14.780.4)
11.23ta.54
18. 18.26xn82)
4.63vam
UCI Adult
MPFR
FKL
VFair Improved
11 11.49
14.24t..)
9.92
16.25.o.35)
2.52ma4
-0.12
+0.1
+0.91
+1.47
+2.42
Table shows the compared regression results the UCI Adult dataset. Note that MPFR and FKI are not designed with stochastic updates and they suffer from oft-of-memory issues under our experimental setup on the UCI Adult dataset.
20

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F.6 Comparison with Rawlsian fair classification methods with sensitive attributes
Table 10: Comparison with methods with access to attributes, where the utility-based results are with %, and the results of VAR x00 for neat presentation.
Utility
WU f
MUD 4
TUD 4
VAR
PMG
79.48
73.02
22.36
27.85
416.86
UCI Adult
MMPF
85.33
81.23
12.78
14.38
VFair
84.74
80.36
15.71
20.71
8.17
PMG
78.52
70.14
9.47
15.59
81.83
Law School
MMPF
82.72
74.70
9.92
18.57
VFair
85.40
75.25
11.00
19.91
6.29
PMG 53.52
49.14
9.97
10.58
13.21
COMPAS
MMPF
66.39
63.91
2.15
5.44
VFair
66.80
63.86
6.25
8.47
1.86
We have further supplemented control experiments, where the model has access to sensitive attributes and is optimized under constrained regularization. In detail, we reproduced the MMPF in [25] and further designed experiments that penalize the losses of the minority group, denoted as PMG. As MMPF is not applicable image datasets, the results conducted three benchmark datasets shown in Table TO By leveraging additional group information, MMPF achieves improved fairness results, showing that group priors indeed needed for significant fairnsss improvement in classifi- cation tasks. However, MMPF is not a harmless approach, particularly evident on Law School, where it sacrifices model utility for fairer point. PMG yields unsatisfactory performance consistently due to its excessive focus on the minority group, missing general information from other groups.
G Computational costs
Since the backward pass is the bottleneck of the total computation, we found that VFair requires approximately twice the computation time compared to the ERM method, shown in Table [1 with the Law School dataset as an example. Note that ARI., an adversarial method, requires a comparable wall-clock time to VFair due to its inner and outer optimization nature.
Table 11: Comparison of four methods' wall-clock time on Law School with the same experimental setup.
Method
ERM
DRO
ARL
VFair
Time
349.4s
243.5s
640.1s
677.6s
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Answer: [Yes]
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Reviews:
[{"review_id": "SSEIwbrQLl", "reviewer": "Reviewer_cPfu", "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.", "questions": "See point B in weaknesses", "limitations": "Yes", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 3, "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 . \n\nThe multiplier itself is actually not optimized for exactly, rather its lower bounded to ensure two reasonable conditions on the update: \nA) The overall loss gradient points towards (mean) loss reduction (i.e., the variance reduction component does not overpower the mean loss reduction component)\nB) The per-sample effective loss is positively weighted (i.e., no sample is encouraged to increase its loss value)\n\nThe 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:\n\nA) 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\n\nB) 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", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Reply to weaknesses\n\n1. Computational costs. Your comment on two backward passes is correct. We will include this extra computation cost as one of the limitations of our work. Since the backward pass is the bottleneck of the total computation, we found that VFair requires approximately twice the computation time compared to the ERM method, as shown in Table 1 with the Law School dataset as an example. Note that ARL, an adversarial method, requires a comparable wall-clock time to VFair due to its inner and outer optimization nature.\n\n   Table 1: Comparison of four methods' wall-clock time on Law School with the same experimental setup.\n\n   | Method | Time   |\n   | ------ | ------ |\n   | ERM    | 349.4s |\n   | DRO    | 243.5s |\n   | ARL    | 640.1s |\n   | VFair  | 677.6s |\n\n2. Delta value. Sorry for any confusion on this point. (1) When presenting the optimization steps in the paper, we considered VFair to be executed independently, so we might not know the appropriate delta value beforehand. In this sense, the final delta value a trained model can achieve will be mainly determined by the maximal number of epochs, assuming it is well-converged. (2) In the experiments, to ensure all baselines comply with the harmless fairness setting, we terminate each training process at the epoch with the nearest loss to the delta derived from a converged ERM (See lines 555-559).", "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": "", "extra_scores": {}}, {"review_id": "DfvP2y6jw1", "reviewer": "Reviewer_Xh7a", "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.", "questions": "Q1 - Why don't you bold the DRO results in Table 1 when they outperform the results of your proposed method?\n\nQ2 - What are the Z-scores?\n\nQ3 - How well does it scale with the increasing number of instances?\n\nQ4 - 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? \n\nQ5 - 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.", "limitations": "The authors do not clearly state the limitations of their proposed method. \n\nAs a suggestion, it would be interesting to address potential issues such as overfitting, scalability, and susceptibility to outliers.", "rating": 5, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 3, "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. \n\nS2 - 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.\n\nS3 - 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. \n\nS4 - 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.\n\nS5 - 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.\n\nW2 - 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.\n\nW3 - 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.\n\nW4 - 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.\n\nW5 - 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.\n\nW6 - 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. \n\n\nW (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. \n\nW (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.   \n\n\n\n[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.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Reply to weakness\n1. Reproducibility issues. We will provide more training details in the appendix. (1) Throughout experiments, all methods are set with a batch size of 32 and a learning rate of 0.01. As for the training epoch, as mentioned in lines 555-559, to ensure all baselines comply with the harmless fairness setting, we terminate each training process at the epoch with the nearest loss value to a well-converged ERM. (2) The datasets are randomly split in a 7:3 ratio following ARL's experimental implementation. \n2. Comparison with BPF. We have discussed the relationship between our method and BPF, referenced as [12] in our paper. BPF, as an improved version of DRO, also utilizes group ratio prior. Considering your comments, we added BPF as another baseline. However, as shown in Table 1 in the newly uploaded supplementary PDF, VFair still outperforms BPF on all metrics. \n3. Connection with Individual Fairness. Although VFair operates at the instance level, it differs from Individual Fairness. (1) Individual Fairness requires that if two individuals are close on the similarity metric, they should be close on the treatment metric, resulting in a continuous treatment metric outcome. (2) VFair falls in (Rawlsian) group fairness, which does not consider the similarity between individuals but focuses on performance disparities between different groups, pursuing close treatment (utility in this paper) metric outcomes. (3) As mentioned in line 145, group fairness pursues $\\ell\\perp z$, while Individual Fairness pursues $\\ell\\sim f(z)$, where $f()$ represents a similarity metric. (4) The similarity metric $f()$ also serve as a form of prior. In contrast, VFair does not call for any form of prior.\n4. Analysis of results. We have strived to present our findings accurately and objectively and we believe there is no exaggeration of effects. Note that we study harmless fairness; therefore, only methods that do not compromise much on overall utility will be finally ranked. (1) Regarding Table 2, DRO turns out a uniform regressor with low utility. In this context, our method outperforms other methods on all metrics except for DRO. (2) Note that lines 307-310 mention that Table 2 aims to show the limited improvement on UCI but significant improvement on CelebA (except for DRO). We acknowledged the limited improvement on UCI and analyzed the reason.\n5. Computational costs. Thank you for this suggestion. (1) Our proposed method requires two rounds of back-propagation, which thus leads to more computation cost compared to ERM or DRO. (2) Since the backward pass is the bottleneck of the total computation, we found that VFair requires approximately twice the computation time compared to the ERM method, as shown in Table 1 with the Law School dataset as an example. (3) Note that ARL, an adversarial method, requires a comparable wall-clock time to VFair due to its inner and outer optimization nature.\n \n   Table 1: Comparison of four methods' wall-clock time on Law School with the same experimental setup.\n   |Method|Time|\n   |-|-|\n   |ERM|349.4s|\n   |DRO|243.5s|\n   |ARL|640.1s|\n   |VFair|677.6s|\n6. Eta in DRO. When applying DRO, using a defined eta can be interpreted as using some group ratio. As evidenced in the official code of DRO in dual_robust_opt.py, the calculation of eta is achieved by bi-search with group ratio eps as input of the get_rho() function.\n7. Minor weakness. Thank you for this suggestion. We will edit the section title and the symbol expressions according to your advice.\n# Reply to questions\n1. Presentation of DRO results. Similar to W4, we study harmless fairness. As mentioned in lines 270-273 and lines 65-68, DRO turns out a uniform regressor with low utility.\n2. Explanation of Z-Score. We use Z-score as it is a fundamental statistical measure. It is calculated by subtracting the mean from the individual value and then dividing it by the standard deviation. In our context, the Z-score of each example's loss is calculated as  $\\frac{\\ell - \\hat{\\mu}}{\\hat{\\sigma}}$.\n3. Adaptation on larger datasets. As shown in Appendix D, our method adopts a stochastic optimization strategy, from which one can see the complexity will be linear to the number of training samples. Note that baseline methods MPFR and FKL are not designed with stochastic updates and suffer from out-of-memory issues, as shown in Table 6.\n4. Confusion caused by the term 'overfit'. Sorry for any confusion on this point. This section was intended to introduce the derivation of the instance-level loss, which bypasses the unobserved sensitive attributes, rather than implying that our model would overfit. The logic is as follows: (1) We aim for MUD=0 for fairness. (2) Oracle model achieves zero loss for each sample, and thus MUD=0. (3) A loss of 0 on the training set indicates overfitting in practice.\n\n   Aiming for MUD=0 does not necessarily lead to overfitting.\n5. Discussion about outliers. (1) We agree that the outlier problem has been studied in Fairness problem. We have also investigated some works in this direction, such as DORO[1], ARL, and GRASP[2]. However, these methods have different strategies to solve the outlier problem, and there is no general, representative method. (2) According to our analysis in the Loss view on page 5, we can simply cap the value of Z-score, preventing the model from excessively concentrating on outliers that produce large losses. As shown in Table 5, on the COMPAS dataset whose labels are found to be noisy [3], VFair achieves the best performance (except for FairRF which leverages feature correlations prior). We will leave a thorough comparison with other existing strategies in future work.\n# Reply to limitations\nRefer to the above answers.\n\n[1] Zhai R, et al. Doro: Distributional and outlier robust optimization.\n\n[2] Y. Zeng, et al. Outlier-robust group inference via gradient space clustering.\n\n[3] Preethi L, et al. Fairness without demographics through adversarially reweighted learning.", "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": "", "extra_scores": {}}, {"review_id": "UMybgpZFdG", "reviewer": "Reviewer_kaxC", "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.", "questions": "Q1. Could you explain why the 'training losses exhibit a Dirac delta distribution'? Because you are stripping the variance?\n\nQ2. 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.", "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). \n\nThe limitations were not discussed in detail.", "rating": 7, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "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.\n\nThe 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. \n\n\nSpady, 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.\".\n\nAlso, Prop. 1 only holds if $u$ is a fully decomposable sum over all individual data samples (just like ℓ is).\n\nW2. 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. \n\nW3. 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).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Reply to weakness\n\n1. Rigor of expression. Thank you for your careful reading and rigorous derivation. We will update Proposition 1 and the assumptions regarding u as you suggested.\n\n2. Confusion caused by lines 169-180. Sorry for any confusion on this point. Lines 169-180 offer a deeper reflection on our method and do not serve as extra motivation. After deriving Equation (2), we further considered the commonalities and differences between our method and existing works. Equation (3) illustrates the fundamental difference between our method and bias-variance research, while Equation (4) demonstrates the essential similarity between our method and DRO.\n\n3. About demographic prior. We believe that demographic prior is meaningful, for demographic prior is still used during the evaluation stage. Table 7 shows a comparison between VFair and methods using demographic prior during the training stage. Results indicate that demographic prior does indeed provide some improvement. \n\n# Reply to questions\n\n1. Explanation for Dirac delta distribution. Please refer to Figure 1 in the newly uploaded supplementary PDF, where we provide a more detailed description of the Dirac delta distribution.\n\n2. More concise explanation. Thank you for your suggestion. We will improve the clarity and logic of Remark 2 following your comments.\n\n# Reply to limitations\n\nWe will add a Limitations section to discuss the additional computational costs of the proposed method. Briefly, our method, VFair, requires two backward propagations, resulting in approximately double the computation time compared to ERM. Please also refer to our detailed responses to reviewer cPfu.", "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": "", "extra_scores": {}}, {"review_id": "uTkpHTor7w", "reviewer": "Reviewer_UBKm", "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.", "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?\n- 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.\n- (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?\n- 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?\n- The empirical results do not perfectly align with the TUD (Total Utility Disparity) and variance metrics presented. Could the authors explain these discrepancies?\n- 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?\n\n\n[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.", "limitations": "Please see questions and weakness parts.", "rating": 4, "confidence": 4, "soundness": 1, "presentation": 2, "contribution": 2, "strengths": "1. The paper is easy to read.\n2. Considering important topic.", "weaknesses": "1. Comparison in the experimental results is not comprehensive.\n2. Motivation is less highlighted. It is unclear why the proposed method is unique and how it addresses limitations of previous methods.\n\nAlso, please see the question section below.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Reply to weakness\n1. Experimental results. We compared the regression and classification performance among six benchmark methods across six datasets. Additionally, we discussed the results of using F1-score as utility metric, randomly splitting groups, methods using demographic prior during the training phase, and different $lambda$ settings. By thoroughly examining various scenarios and conditions, we have ensured that our analysis and conclusions are well-founded and credible.\n\n2. Novelty and effectiveness. We studied Rawlsian harmless fairness without demographic information in both classification and regression tasks, which has not been studied before. Moreover, as supported by reviewer kaxC in the 'Strengths' section, our idea is incredibly novel and impressive. Besides one weakly related reference, they were unable to find occurrences of this idea in prior work.\n\n# Reply to questions\n\n1. Explanation for Dirac delta distribution. Please refer to Figure 1 in the newly uploaded supplementary PDF, where we provide a more detailed description of the Dirac delta distribution. We speculate that your misunderstanding may stem from confusion regarding the meaning of the x-axis of Figure 1 in our paper. The x-axis represents the index of sorted losses, rather than the actual loss values, which is different from Figure 1 in the supplementary PDF.\n\n2. From MUD to loss distribution. (1) MUD is a group-level metric. When demographic information is inaccessible, we strive to minimize MUD across all possible group divisions. (2) From the perspective of individual instances, when the loss for each example is as similar as possible, MUD will approximate zero regardless of the group division. (3) If the loss for each example approximates zero, the loss distribution will resemble a Dirac delta distribution. If the loss for each example approximates $\\mu$ (e.g. $\\mu$=0.25 in a 0-1 regression task), the model will behave like a uniform regressor or classifier. Note that this does not imply that the loss distribution itself is uniform; rather, the model's performance is uniformly poor across instances.\n\n3. Confusion caused by the term 'overfit'. Sorry for any confusion on this point. This section was intended to introduce the derivation of the instance-level loss, which bypasses the unobserved sensitive attributes, rather than implying that our model would overfit. The logic is as follows: (1) We aim for MUD=0 for fairness. (2) Oracle model achieves zero loss for each sample, and thus MUD=0. (3) A loss of 0 on the training set indicates overfitting risks in practice. \n\n   And aiming for MUD=0 does not necessarily lead to overfitting in our method.\n\n4. Difference with [1]. We study different problems. They focus on achieving fairness with access to demographic information. However, our task is more challenging as we aim to achieve fairness without demographic information.\n\n5. Consistency of TUD and VAR in experimental results. In our experimental results, TUD and VAR consistently outperform other methods in most cases, except for some classification cases. As discussed in lines 298-301, under discrete utility metrics, even if our method has smaller loss disparities at the instance level, fairness metrics may still not improve.\n\n6. Comparison with SOTA. Our method uniquely addresses Rawlsian harmless fairness without requiring demographic information in both classification and regression tasks, a topic that has not been extensively studied before. Existing works not included in this comparison generally struggle to adapt to this specific setting. Besides the employed baselines (which were carefully modified for harmless fairness), to the best of our knowledge, no other recent work targets this same research problem.\n\n[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.", "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": "", "extra_scores": {}}]

Author rebuttal:
We appreciate the valuable comments from the reviewers. In response to some issues that required additional experiments and illustrations, we added new experiments and figures in the supplementary PDF.

Meta-review: This paper proposes an interesting approach to achieving Rawlsian fairness in scenarios where no demographic information is provided. The paper's novel approach was appreciated, and the reviewers and the AC also welcomed its theoretical rigor.  My recommendation is to accept it. Should the paper make the cut, however, the final version should include a more detailed discussion of related work, explicit information on the experimental setup, and a clearer explanation of the computational costs.
Decision: Accept (poster)