FairGBM: Gradient Boosting with Fairness Constraints
Authors: André Cruz
Catarina G Belém
João Bravo
Pedro Saleiro
Pedro Bizarro
Venue: ICLR 2023 poster (2023)
Keywords: fairness
gradient boosting
constrained optimization
tabular data

Abstract: Tabular data is prevalent in many high-stakes domains, such as financial services or public policy. Gradient Boosted Decision Trees (GBDT) are popular in these settings due to their scalability, performance, and low training cost. While fairness in these domains is a foremost concern, existing in-processing Fair ML methods are either incompatible with GBDT, or incur in significant performance losses while taking considerably longer to train. We present FairGBM, a dual ascent learning framework for training GBDT under fairness constraints, with little to no impact on predictive performance when compared to unconstrained GBDT. Since observational fairness metrics are non-differentiable, we propose smooth convex error rate proxies for common fairness criteria, enabling gradient-based optimization using a ``proxy-Lagrangian'' formulation. Our implementation shows an order of magnitude speedup in training time relative to related work, a pivotal aspect to foster the widespread adoption of FairGBM by real-world practitioners.

Published as a conference paper at ICLR 2023
FAIRGBM:
GRADIENT BOOSTING WITH FAIRNESS CONSTRAINTS
André F. Cruz!. Catarina Belém João Bravo'
Pedro Saleiro'
Pedro Bizarro'
Feedzai MMPI for Intelligent Systems, Tübingen
UC Irvine
andre wru.gtuebingeenn........cc www.anngnn..ngg...mmmmm me
pedro. sectro.saleiroofeedaa...
ABSTRACT
Tabular data is prevalent in many high-stakes domains, such as financial services public policy. Gradient Boosted Decision Trees (GBDT) are popular in these settings due to their scalability, performance, and low training cost. While fairness in these domains is foremost concern, existing in-processing Fair ML methods are either incompatible with GBDT, or incur in significant performance losses while taking considerably longer to train. We present FairGBM, a dual ascent learning framework for training GBDT under fairness constraints, with little to no impact on predictive performance when compared to unconstrained GBDT. Since observational fairness metrics are non-differentiable, we propose smooth convex error rate proxies for common fairness criteria, enabling gradient- optimization using "proxy-Lagrangia"" formulation. Our implementation shows an order of magnitude speedup in training time relative to related work, a pivotal aspect to foster the widespread adoption of FairGBM by real-world practitioners.
INTRODUCTION
The use of Machine Learning (ML) algorithms to inform consequential decision-making has become ubiquitous in multitude of high-stakes mission critical applications, from financial services to criminal justice justice or healtheare (Bartlett et 2019 Brennan al.) | Tomar & Agarwal (013). At the same time, this widespread adoption of ML was followed by reports surfacing the risk of bias and discriminatory decision decision-making affecting people based on ethnicity, gender, age, and other sensitive attributes (Angwin et al. [016 Bolukbasi et al. 2016 Buollamini & Gebrul (018). This awareness led to the rise of Fair ML, research area focused on discussing, measuring and mitigating the risk of bias and unfairness in ML systems. Despite the rapid pace of research in Fair ML (Hardt et al. 2016 Zafar et al. 2017 Agarwal et al. 2018:; Narasimhan et al. 2019 Celis et al., 2021 and the release of several opwn- spen-source software packages (Saleiro et al. 2018 Bellamy et al. (218 Agarwal et al., 2018 Cotter et al. 2019b), there is still no clear winning method that "just works" regardless of data format and bias conditions.
Fair ML methods are usually divided into three families: pre-processing, in-processing and post- processing. Pre-processing methods aim learn an unbiased representation of the training data but may not guarantee fairness in the end classifier (Zemel et al., 2013 Edwards & Storkey 2016); while post-processing methods inevitably require test-time access to sensitive attributes and can be sub- optimal depending on the structure of the data (Hardt et al. 2016 Woodworth et al. 2017). Most in- processing Fair ML methods rely on fairness constraints to prevent the model from disproportionately hurting protected groups (Zafar et al. 2017 Agarwal et al. 2018 Cotter et al., (019b). Using constrained optimization, we can optimize for the predictive performance of fair models.
In principle, in in-processing methods have the potential to introduce faimess with no training- time overhead and minimal predictive performance cost - an ideal outcome for most mission critical applications, such as financial fraud detection or medical diagnosis. Sacrificing a few percentage points of predictive performance in such settings may result in catastrophic outcomes, from safety hazards to substantial monetary losses. Therefore, the use of Fair ML in mission critical systems is particularly challenging, as fairness must be achieved with minimal performance drops.
https://github. feedzai /

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Published as a conference paper at ICLR 2023
Tabular data is common data format in variety of mission critical ML applications (e.g., financial services). While deep learning is the dominant paradigm for unstructured data, gradient boosted decision trees (GBDT) algorithms
pervasive in tabular data due their state-of-the art performance and the availability of fast, scalable, ready-to-use implementations, e.g. LightGBM (Ke et al. 2017) or XGBoost (Chen & Guestrin 2016). Unfortunately, Fair MIL research still lacks suitable fairesss- constrained frameworks for GBDT, making it challenging to satisfy stringent fairness requirements.
As case in point, Google's TensorFlow Constrained Optimization (TFCO) (Cotter al. 2019b), well-known in-processing bias mitigation technique, is only compatible with neural network models. Conversely, Microsoft's 's ready-to-use fairleam EG framework (Agarwal al. 2018 supports GBDT models, but carries substantial training overhead, and can only output binary scores instead of a continuous scoring function, making it inapplicable to a variety of use cases. Particularly, the production of binary scores is incompatible with deployment settings with a fixed budget for positive predictions (e.g., resource constraint problems (Ackermann et al.) 2018)) or settings targeting a specific point in the ROC curve (e.g., fixed false positive rate), such in fraud detection.
To address this gap in Fair ML, we present FairGBM, a framework for fairness constrained opti- mization tailored for GBDT. Our method incorporates the classical method of Lagrange multipliers within gradient- boosting. requiring only the gradient of the constraint w.r.t. (with relation to) the model's output Y. Lagrange duality enables us to perform this optimization process efficiently as a two-player game: one player minimizes the loss w.r.t. Y, while the other player maximizes the loss non-differentiable, we employ differentiable
w.r.t. the Lagrange multipliers. As fairness metrics proxy constraints. Our method is inspired by the theoretical ground-work of Cotter et al. (2019b). which introduces new "proxy-Lagrange" solution does exist even when employing proxy constraints. Contrary to related work, our approach does not require training extra models, nor keeping the training iterates in memory.
formulation and proves that a stochastic equilibrium
We apply our method to real-world account opening fraud case study, as well as to five public benchmark datasets from the fairness literature (Ding et al., 202T). Moreover, we enable fairness constraint fulfillment at a specific ROC point, finding fair models that fulfill business restrictions on the number of allowed false positives or false negatives. This feature a must for problems with high class imbalance. the prevailing approach of using a decision threshold of 0.5 is only optimal when maximizing accuracy. When compared with state-of-the-ar in- prppoccssingg fairness interventions, our method consistently achieves improved predictive performance for the same value of fairness.
In summary, this work's 's main contributions are:
A novel constrained optimization framework for boossint, dubbed FairGBM. Differentiable proxy functions for popular faimess metrics based on the cross-entropy loss.
A nigh-performance implementation of our algorithm.
Validation on a real-world case-study and five public benchmark datasets (folktables).
2 FAIRGBM FRAMEWORK
We propose a fairness-aware variant of the gradient-boosting training framework, dubbed FairGBM. Our method minimizes predictive loss while enforcing group-wise parity on one more error rates. We focus on the GBDT algorithm, which uses regression trees as the base weak learners (Breiman 1984). Moreover, the current widespread use of GBDT is arguably due to two highly scalable variants of this algorithm: XGBoost (Chen & Guestrin 2016) and LightGBM (Ke et al. (017). In this work we provide an open- source fatrness-awart implementation of LightGBM. Our work is, however, generalizable to any gradient-boosting boosting algorithm, and to any set of differentiable constraints (not limited to fairness constraints). We refer the reader to Appendix for notation disambiguation.
2.1 OPTIMIZATION UNDER FAIRNESS CONSTRAINTS
Constrained optimization (CO) approaches aim to find the set of parameters 0 E θ that minimize the standard predictive loss L of a model fe given set of m fairness constraints G, E {1...., m]:
gr arg min L(l)
S. t. iE (E(1...m)
(0) < 0.
(1)
dee
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This problem is often re-formulated using the Lagrangian function,
[(e, A) = L( + (O),
(2)
where À E RT is the vector of Lagrange multipliers. The problem stated Equation is then, under reasonable conditions, equivalent to:
0" arg min max C(A, A), AERT
(3)
EE
which can be viewed as zero-sum two-player game. where one player (the model player) minimizes the Lagrangian w.r.t. the model parameters 0, while the other player (the constraint player) maximizes w.r.t. the Lagrange multipliers X (Neumann 1928). A pure equilibrium this game will exist in general for a given CO problem. Sufficient conditions for there to be one are, for example, that the original problem is convex optimization problem satisfying an appropriate constraint qualification condition (Boyd al., 2004). Consequently, two main issues arise when using classic CO methods with fairness metrics: the loss functions of state-of-the-arr ML algorithms are non-convex (as case of neural networks). and standard faimess metrics non-convex and non non-differentiable.
2.2 DIFFERENTIABLE PROXIES FOR FAIRNESS METRICS
As a fundamentally subjective concept, there is no "one-size-fits-lll" definition of fairness. Nonethe- less, popular faimess notions can be defined equalizing rate metrics across sensitive at- tributes (Saleiro et al.) 2018 Barocas et al., 2019). For example, equality of opportunity (Hardt et al.) 2016) is defined as equalizing expected recall across members of specific protected groups (e.g.. different genders or ethnicities). We will focus on fairness metrics for classification tasks, as the discontinuities between class membership pose a distinet challenge moon-differentibbiiiyy of the step- wise function). Extension to the regression setting is fairly straightforward, as these discontinuities are no longer present and common fairness metrics are already differentiable (Agarwal et al. 2019).
In the general case, model f is deemed fair w.r.t. the sensitive attribute S and some rate metric L if the expected value L independent the value of s E S:
E [((()]= = EE ((())S s), Vs S.
(4)
Equation 4 can be naturally viewed an equality constraint in the model's training process after replacing expectations under the data distribution by their sample averages. However, as discussed in Section 2.1 common fairness notions (i.e., common choices of L)) are non-convex and non- differentiable. Therefore, in order to find a solution to this CO problem, we must use some proxy metric that is indeed differentiable (or at least sub-differentiable) (Cotter et al. 2019b).
Proxy FPR, for
4
stop-wise
cross-entropy
hinge
2
positive
0
true negative
fix),, predicted log-odde
Figure 1: Convex proxies for instance-wise FPR metric, for data sample (#t, y:) with negative label.
Figure M shows examples of convex and sub-differentiable surrogates for the False Positive Rate
(FPR). Equalizing FPR among sensitive attributes is also known as predictive equality (Corbett-Davve Davies
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Name
Proxy metric, i
Proxy derivative, Øπ(2)
oi
Fairness metric
False positive False negative Predicted pos. Predicted neg.
My 0] log(1 + el(a)) Hy 1] log(1 e )(o)) log(1 + efl) log(1 + e- f(m))
My = 0f - olf(x))
predictive equality
1ly 11 (o((2)))))
equal opportunity
of(()) off()))
demographic parity
demographic parity
Table Instance-wise metrics used to compose common error rates and corresponding cross-entropy- based proxy metrics. a is the sigmoid function, ((x) is the predicted log-odds of instance and y E {0, 1 the binary label.
et al. 2017). As any function of the confusion matrix, the FPR takes in predictions binarized using step-wise wise function. As no useful gradient signal can be extracted from the step-wise function, we instead use a cross-entropy based proxy metric that upper-bounds the step-wise function. Ideally, for some fairness constraint c, we can guarantee its fulfillment by solving the CO problem using proxy upper-bound č such that c(0) I a() < O. Note that, while Cotter et al. (2019b) use a hinge-based proxy, which has discontinuous derivative, we opt for a cross-entropy- -nasep proxy, which has continuous derivative, leading to smoother optimization process. Table I shows instance- wiie rate metries commonly used to compose faimess metrics and the proposed proxy counterparts.
In practice, the fairness constraint in Equation 4 implemented using the set of S] inequalities in Equation 5 ie., we have, for every b E S:
(f) max (()=a)()) - L(s= se aES
(5)
where
RR, U (0) is the allowed constraint violation, and
(()=
Σ
f());
(6)
D(s=a)) (x.9)E
the proxy loss measured over the dataset D(s=a) C. of samples with sensitive attribute s. Original (non-prot (non-proxy) counterpart functions, G and ((--))- obtained by substituting the proxy instance-wise metric with its original (potentially non-differentiable) counterpart L.
2.3 FAIRNESS- GBDT
If our objective function and constraints convex, we could find the pure Nash equilibrium of the zero sum, two-player game corresponding to the saddle point of the Lagrangian, L. This equilibrium could be found by iterative and interleaved steps of gradient descent over our model function, and ascent over the Lagrange multipliers, X. Importantly, this setting is relevant for GBDT models but for Neural Networks, as the first have convex objective and the latter do not. See Appendix C for discussion on the limitations of our method.
However, discussed in Section 2.2] fairness constraints are not differentiable, and we must employ differentiable proxies to use gradient-based optimization. Instead of using the Lagrangian L, we instead use Lroxy-Lagrangian É.
=(f) Σ xa((),
where is predictive loss function, and é; is proxy inequality constraint given by Equation 5 On the other hand, simply using L for both descent and ascent optimization steps would now be enforcing our proxy-constraints and not necessarily the original ones. Thus, following Cotter et al. (2019h), adopt non-zero sum two-player game formulation where the descent step for the model player uses the Lroxy-Lagrangian É. and the ascent step for the X-player uses the Lagrangian L with the original constraints. The FairGBM training process (Algorithm is as follows:
Descent step. The FairGBM descent step consists in minimizing the loss i over the function space H (Equation 7). That is, fitting regression tree on the pseudo-residuals ft,i - where g the
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Algorithm FairGBM training pseudocode
Input: 7 E N, number of boosting rounds
C, L F x _ + R, Lagrangian and proxy Lagrangaga
My n E R. learning rates
1: Let hg arg min ((7,0)
Initial constant "guess"
2: Initialize f + ho
3: Initialize
4: for t E {1...., T do
5: Let 9: Bf(a;)
(C(f(x)).A)
D Gradient of proxy-Lagrangian w.r.t model
6: Let A = A
Gradient of Lagrangian w.r.t. multipliers
02
7:
Let h4 = arg min
E N
(-9: h,(x))))
b base learner D Gradient descent
8:
Update f + 1
9:
Update - (A + TT A)
A Projected gradient ascent
return 0o: fo....., bT
gradient of the proxy-Lagrangian, Ir,i 3f(x,)
0CISA)
AL (m (((s-s) Of(x))
ExE(mINt d if = if = k #
91.s
af(x))
(8)
9L [f(..)
A of(a.)
where (xx)) St-1 (2:4, and j arg max (S)= is the group with maximal proxy loss.
Ascent step. The FairGBM ascent step consists in maximizing the (original) Lagrangian L over the multipliers À E A (Equation 2 Thus, each multiplier is updated by simple gradient ascent step:
OC
de, = A + 11x OA;
- + mxG(f)
where E (1..... m). , m is the total number of inequality constraints, and 1ι R2 is the Lagrange multipliers' learning rate.
2.3.1 RANDOMIZED CLASSIFIER
The aforementioned FairGBM training process (Algorithm D converges to an approximately feasible and approximately optimal solution with known bounds the original CO problem, dubbed a "coarse- correlated equilibrium" " (Cotter et al.] (019b).. This solution corresponds to mixed strategy for the model player, defined distribution over all iterates, t [1, That is, for each input x, first randomly sample t [1, 7'. and then use ft to make the prediction for x, where fc E'mo
In practice, using solely the last iterate fr will result in a deterministic classifier that often achieves similar metries as the randomized classifier (Narasimhan al.) (201)), although it does benefit goes from the same theoretical guarantees (Appendix goes into further detail on this comparison). There are also several methods the literature for reducing randomized classifier an approximate deterministic one (Cotter et al. 2019a).
In the general case, using this randomized classifier implies sequentially training T separate models (as performed by the EG method (Agarwal et al. 2018),, severely increasing training time (by factor of at least T". When using an iterative training process (such as gradient descent), it only implies training single model, but maintaining all T iterates (as performed by the TFCO method (Cotter et al. 2019b)), severely increasing memory consumption. Crucially, when using gradient boosting. each iterate contains all previous iterates. Therefore, a GBDT randomized classifier can be fully defined by maintaining solely the last iterate, carrying no extra memory consumption nor significant extra training time when compared with vanilla GBDT classifier.
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To summarize, FairGBM is the result of employing the proxy Lagrangian CO method with cross- entropy-based proxies of faimess constraints, resulting in an efficient randomized classifier with known optimality and feasibility bounds.
3 EXPERIMENTS
We implemented FairGBM as fork from the open-source Microsoft LightGBM implementation. The LightGBM algorithm (Ke et al. 2017) is a widely popular high performance GBDT implementa- tion in C++, with high-level Python interface for ease-of-use. This algorithm in particular builds on top of the standard GBDT framework by introducing gradient-base based one-side sampling (GOSS) and exclusive feature bundling, both aimed at decreasing training and inference time. Although the FairGBM framework ( (Algorithm I1 could be applied to any gradient boosting algorithm, we choose to implement it on top of LightGBM due to its excellent scalability. Additionally, although our experiments focus on binary sensitive attributes, MairGBM can handle multiple sub-gron sub-groups.
We validate our method on five large-scale public benchmark datasets, popularly known as folktables datasets, as well as real-world financial services case-study. While the folktables datasets provide an easily reproducible setting under common literature objectives and constraints, the real-world scenario poses a distinct set of challenges that are seldom discussed in the faimess literature, from highly imbalanced data to tight constraints on the maximum number of positive predictions.
We compare FairGBM with a set of constrained optimization baselines from the Fair ML literature. Fairlearn EG (Agarwal et al., (0188) is a state-of-the art method based on the reduction of CO to a cost-sensitive learning problem. It produces randomized binary classifier composed of several base classifiers. Fairlearn GS (Agarwal et al.] 2018) is a similar method that instead uses a grid search over the constraint multipliers X, and outputs single (deterministic) classifier that achieves the best trade-off. RS Reweighing is a variation of GS that instead casts the choice of multipliers as another model hyperparameter, which will be selected via Random Search (RS) this should increase variability of trade-offs. Both EG, GS and RS are trained using LightGBM as the base algorithm, and both are implemented in the popular open spen-source fairlear package (Bird et al.) 2020). Finally, we also show results for the standard unconstrained LightGBM algorithm.
is well-known that the choice of hyperparameters affects both performance and fairness of trained models (Cruz et al. 202T). To control for the variability of results when selecting different hyper- parameters, we randomly sample 100 hyperparameter configurations of each algorithm. In the case of EG and GS, both algorithms already fit n base estimators part of single training procedure. Hence, we run 10 trials of EG and GS, each with a budget of n = 10 iterations, for a total budget of 100 models trained (leading mean and variance of each algorithm, we perform bootstrapping over the trained models (Efron & Tibshirani 1994). Each bootstrap trial consists of k 20 random draws from the pool of n = 100 trained models (randomly select 20%). The best performing model (the maximizer of [a performance + (1-a)- - fairness)) of each trial on validation data then separately selected. This process was repeated for 1000 trials to obtain both variance (Tables 2and (66 and confidence
equal budget for all algorithms). To calculate the statistical
intervals (Figures 2bb A2b and A All experiments (both FairGBM and baselines) can be easily reproduced with the code provided in the supplementary m
3.1 DATASETS
The folktables datasets were put forth by Ding et al. (2021) and are derived from the American Community Survey (ACS) public use microdata sample from 2018. Each of the five datasets poses a distinct prediction task, and contains a different set of demographic features (e.g., age, marital status, education, occupation, race, gender). Notably, the ACSIncome dataset (1.6M rows) is a recreated modern-day version of the popular 1994 UCI-Adult dataset (Dua & Graff] 2017) (50K rows), which has been widely used in ML research papers over the years. On this task, the goal (label) is to predict whether US working adults' yearly income is above $50K. Due to space constraints, we focus on empirical results the ACSIncome dataset, while the remaining four folktables datasets are analyzed in [ppendix[A] We use the same performance and faimess metrics for all folktables datasets: maximizing global accuracy, while equalizing group false negative rate (FNR) over different binary

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ACSIncome (validation)
ACSIncome (test)
1,0
fairness
1.0
0.8
Faimess (FNR ratio)
0.6
0.6
performance
0.4
FairGBM
FairGBM
LightGBM
LightGBM
Fairleam (LGBM)
0.2
Fairleam GS (LGBM)
RS Reweighing (LGBM)
RS Reweighting (LGBM)
Fairleam EG (LGBM)
Fairleam EG (LGBM)
0.74
0.76
0.78
0.80
0.82
0.0
0.2
0.4
0.6
1.0
Performance (Accuracy)
(a) Scatter plot.
(b) Best attainable trade-off's per algorithm.
Figure 2: [ACSIncome] Left: scatter plot showing fairness and performance of 100 trained models of each algorithm, evaluated on validation data. EG and GS show only 10 markers, as each run already trains 10 models itself. Right: plot of best test-set fairness-accuracy trade-off's per algorithm (models selected on validation data). Lines show the mean value, and shades show 95% confidence intervals. FairGBM (blue) achieves statistically significant superior rrfde-off for all a E [0.00, 0.99).
gender groups, also known equality of opportunity (Hardt al. 2016). Each task is randomly split in training (60%), validation (20%), and test (20%) data.
The Account Opening Fraud (AOF) dataset, our real-world case-study, spans an 8-month period of (anonymized) data collection, containing over 500K instances. Specifically, pertaining to an online bank account application form, which also grants access to a credit line. As fraudsters are in the minority relative to legitimate applicants, our data is highly imbalanced, with only 1% fraud prevalence. This poses a distinct set of challenges and requirements for model evaluation. For example, as 99% accuracy can be trivially achieved by constant classifier that predicts the negative class, the target performance metric not accuracy but true positive rate (TPR) at given false positive rate (FPR). In the AOF case, business requirement dictates that the model must not wrongly block more than 5% of legitimate customers, i.e., maximum 5% FPR. This type of requirement is arguably commonplace in production ML systems (Ackermann et al.) 2018 Jesus al. 2022). See Appendix for for details on how we operate FairGBM at arbitrary ROC points. Moreover, for the AOF case target FPR equality among individuals of different age-groups (preventing ageism). As this task is punitive (a positive prediction leads to a negative outcome - denied account opening), model is considered unfair if disproportionately blocks legitimate eustomers of specific protected group (given by that group's FPR). Further details on the AOF dataset are provided in Appendix
3.2 RESULTS THE folktables DATASETS
Figure 2a shows seatter plot of the fairness-an accuress- results in the validation set for models trained on the ACSIncome dataset. Note that the axis spans small accuracy range, as all models consistently achieve high performance on this task. Figure 2b)ure/ssswwss shows a plot of the best attainable trade- off for each model type (results obtained with bootstrapping previously described). Importantly, for all trade-off choices a E [0.00, 0.99), the FairGBM algorithm dominates all other methods on the scalarized metric. Only when disregarding fairness completely (a = 1.0), do LightGBM, EG, and GS achieve similar results to FairGBM (differences within statistical insignificance). The RS algorithm suffers from severe lack of consistency, with most models being extremely unfair.
Table 2 shows another view over the same underlying results, but with specific fairness-ad carness-accuracyy trade-off chosen (a 0.75 used for model selection), and displaying performance and fairness
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Trade-off a 0.75
Run-time
Algorithm
Validation
Test
Total (h)
Relative
Fair. (%)
Perf. (%)
Fair. (%)
Perf. (%)
ACSIncome dataset
FairGBM
99.5
81.7 11.700.0 0.06
99.3 + 0.89
81.7 0.08
9.9
x2.1
LightGBM
75.0 3.41
8
74.6 3.57
81.1 0.88
4.6
baseline
GS
66.4 1.53
0.14
65.8 + 1.39
81.8
43.8
x9.6
RS
41.4 + 26.6
3.004
41.5 + 26.5
+
37.1
x8.1
EG
94.4 + 0.33
93.8 + 0.13
81.6 0.17
99.4
x21.7
AOF dataset
FairGBM
89.3 + 4.62
65.9 + 1.33
87.5 3.36
65.9+1.66
3.5
x2.4
LightGBM
5
61.7 2.68
66.6 + 14.9
61.1
1.4
GS
98.5 + 1.00
23.6
3.45
98.4 1.67
23.7 3.64
21.4
x14.7
RS
84.0 + 19.3
36.9
8.43
84.6 20.9
37.4 8.89
10.3
x7.1
Table 2: Mean and standard deviation of results on the ACSIncome (top rows) and AOF (bottom rows) datasets, with the model-selection trade-off set as a = 0.75. For each row, we select the model that maximizes [ar performance + (1 aa) fairness] measured in validation, and report results on both validation and test data. See related Tables A2 and Al for results with other trade-off choices.
results instead of the scalarized objective. Table A2 shows ACSIncome results for two other trade-off choices: E {0.50, 0.95). Among all tested algorithms, FairGBM has the lowest average constraint violation for all three studied values of a on the ACSIncome dataset (p < 0.01 for all pair-wise comparisons), while achieving better performance than RS, and similar performance (differences not statistically significant) to LightGBM, GS, and EG - i.e., FairGBM models are Pareto dominant over the baselines. The EG algorithm follows, also achieving high performance and high fairness, although significantly behind FairGBM on the latter (p < 0.01). At the same time, the GS and RS Reweighing algorithms achieve a surprisingly low fairness on this dataset, signalling that their ensembled counterpart (the EG algorithm) seems better fitted for this setting. As expected, fairness for the unconstrained LightGBM algorithm is considerably lower than that of FairGBM or EG.
A similar trend is visible on the other four folktables datasets (see Figure A1 and Tables A3 A6) FairGBM consistently achieves the best ciiness-accuuaae trade-offs among models, either isolated (ACSIncome and ACSEmployment), tied with EG (ACSTravelTimee) or tied with both EG and GS (ACSMobility and ACSPublicCoverage) Collectively, EG is arguably the strongest CO baseline, followed by GS, and then RS. However, the total time taken to train all FairGBM models is under tenth of the time taken to train all EG models (see rightmost columns Table and EG also requires keeping tens of models in memory (n 10 in experiments), straining possible scalability.
3.3 RESULTS ON THE ACCOUNT OPENING FRAUD DATASET
While most models achieve high performance on the ACSIncome dataset, on AOF we see signifi- cantly wider range of performance values (compare AOF plot in Figure A2a with ACSIncome plot Figure Zah. Moreover, the unconstrained LightGBM algorithm this setting shows significant average unfairness, achieving its peak performance at approximately 33% fairness.
On the AOF test set, FairGBM dominates LightGBM on both faimness and performance for the == 0.5 and a = 0.75 trade-offs, while achieving superior fairness with statistically insignificant performance differences on the a = 0.95 trade-off (results for all three trade-offs Table [T]) Remaining baselines achieve high fairness FairGBM. For example, on a 0.75 (Table 2) GS achieves near perfect fairness (98.4 + 1.67) but catches only 36% of the fraud instances that FairGBM catches (23.7 /23.7/65.9 = 0.36), while taking 6 times longer to train (14.7/24 7/.4 = 6.1). In fact, FairGBM significantly extends the Pareto frontier of attainable trade-offs when compared any other model in the comparison (see Figure A2b).
extreme performance cost when compared to
Note that the EG method was excluded from the comparison on the AOF dataset as it has critical incompatibilities with this real-world setting. Importantly, it produces randomized binary classifier
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that implicitly uses a 0.50 decision threshold. This is optimal to maximize accuracy which is trivial on AOF due to its extreme class imbalance - but severely sub-optimal to maximize TPR. Due to lack of real-valued score predictions, neither can compute score threshold after training to maximize TPR on the model's predictions, nor can we fulfill the 5% FPR business constraint. Nonetheless, EG is still part of the comparison the five folktables datasets.
RELATED WORK
Prior work algorithmic fairness can be broadly divided into three categories: pre-processing. in-processing, and post-processing; depending on whether it acts on the training data, the training process, or the model's predictions, respectively.
Pre-processing methods aim to modify the input data such that any model trained on it would no longer exhibit biases. This is typically achieved either by (1) creating new representation U of the features X that does not exhibit correlations with the protected attribute S (Zemel et al. 2013) Edwards & Storkey| 2016). or (2) by altering the label distribution Y according to some heuristic (Fish et al. [016;; Kamiran & Calders 2009) (e.g., equalizing prevalence across sub-groups of the population). Although compatible with any downstream task, by acting on the beginning of the ML pipeline these methods may not be able to guarantee faimess on the end model. Moreover, recent empirical comparisons have shown that pre-processing methods often lag behind in-processing and post-processing methods (Ding et al. 2021).
In-processing methods alter the learning process itself in order to train models that make fairer predictions. There are a wide variety of approaches under this class of methods: training under fairness constraints (Zafar et al. 2017; Agarwal et al. 2018 Cotter et al. 2019b), using a loss function that penalizes unfairness (Fish et al.] 2016 losifidis & Ntoutsi 2019 Ravichandran et al. 2020), or training with an adversary that tries to predict protected- ggoup membership (Grari et al. 2019). The main shortcoming of in-processing methods lies in their selective compatibility with particular algorithms or families of algorithms. As a case in point, there is currently no constrained optimization method tailored for the GBDT algorithm, besides the one present in this work. However, the state-of- the-art results for numerous tabular data tasks are currently held by boosting- models (Shwartz-Ziv & Armon 202T). AdaFair (losifidis & Ntoutsi 2019) is a bias mitigation method for the AdaBoost algorithm (Freund & Schapire 1996), similar method to GBDT. However, we did not consider it as a direct baseline in this work as it is only compatible with the equal odds fairness metric (Hardt et al., 2016), and not with equal opportunity predictive equality (used in our experiments). Moreover, this method lacks any theoretical guarantees, employing a series of heuristics used change the weights of samples from underprivileged groups
Post-processing methods alter the model's predictions to fulfill some statistical measure of fairness. In practice. this is done by (1) shifting the decision boundary for specific sub-groupt (Hardt et al.) 2016 Fish et al. 2016). or by (2) randomly classifying a portion of individuals of the underprivileged group (Kamiran al. 2012 Pleiss et al.) 2017). Methods based shifting the decision-boundary have the clear advantage of achieving 100% fairness in the data where they are calibrated (training or validation data), while also being compatible with any score-based classifier. However, post- processing methods can be highly sub-optimal (Woodworth et al., 2017). as they act on the model after was learned. Moreover, they can lead to higher performance degradation when compared to in en-processing methods (Ding et al. 2021).
5 CONCLUSION
We presented FairGBM, a dual ascent learning framework under fairness constraints specifically tailored for gradient boosting- To enable gradient-based optimization we propose differentiable proxies for popular faimess metrics that are able to attain state-of-the-a trade-offs on tabular data. When compared with general-purpose purpose constrained optimization methods, FairGBM is more consistent across datasets, and typically achieves higher fairness for the same level of performance. Crucially, FairGBM does not require significant extra computational resources, while related CO algorithms considerably increase training time and/or memory consumption. Finally, enable fairness constraint fulfillment at a specified ROC point or with a fixed budget for positive predictions, a common requirement in real-world high-stakes settings.
ddinesss-performann

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Published as a conference paper at ICLR 2023
ACKNOWLEDGMENTS
The authors thank Sérgio Jesus (Feedzai) for invaluable feedback and help in the paper review rebuttal process. The authors thank the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting André F. Cruz during part of this research.
The project CAMELOT (reference
--EB--04 leading to this work is co- financed by the ERDF European Regional Development Fund through the Operational Program for Competitiveness and Internationalisation COMPETE 2020, the North Portugal Regional Operational Program NORTE 2020 and by the Portuguese Foundation for Science and Technology FCT under the CMU Portugal international partnership.
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A ADDITIONAL RESULTS
This section displays results the four folktables datasets that omitted from the main body: ACSEmployment, ACSMobility, ACSTravelTime, and ACSPublicCoverage (Ding et al. (021). Each dataset poses distinct prediction task: ACSEmployment (2.3M rows) relates to employment status prediction, ACSMobility (0.6M rows) relates to prediction of address changes, ACSTravelTime (1.4M rows) relates prediction of the length of daily work commute, and ACSPublicCoverage (1.IM rows) relates to prediction of public health insurance coverage. Additionally, we display extra plots and results for other trade-off choices on the ACSIncome and AOF datasets.
ACSEmployment
ACSMobility
1.0
a- performance +[1 at) fairness
performance +(1 at) fairness
0.8
0.6
0.4
FairGBM
LightGBM
0.2
Fairleam GS (LGBM)
RS Reweighting (LGBM)
Fairleam EG (LGBM)
0.0
ACSPublicCoverage
ACSTravelTime
1.0
a. performance +(1 at) fairness
a' performance +[1 at) fairness
0.8
0.6
0.4
0.0
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
1.0
Figure Al: Plot of best test-set fairness-accuracy trade-off's per algorithm (models selected on validation data), on four folktables datasets. Lines show the mean value, and shades show 95% confidence intervals.
Figure Al shows plots of the test-set a- a-weighted metric attainable by each algorithm as a function of E [0, 1}. on each folktables dataset (model-selection based on validation results). Results follow similar trend to those seen on the ACSIncome dataset (Figure 26): FairGBM consistently achieves the top spot, either isolated (ACSEmployment and ACSIncome) or tied with other methods on part of the trade-off spectrum (ACSMobility, ACSPublicCoverage and ACSTravelTime). EG achieves competitive trade-offs as well, although not as consistently across datasets, and at a high CPU training cost. GS ties with EG and FairGBM for the best trade-offs on the ACSMobility and ACSPublicCoverage datasets. Detailed fairness and performance results for all folktables datasets (for E {0.50, 0.75, 0.95)) are shown in Tables A2 A6
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Account Opening Fraud (val.)
Account Opening Fraud (test)
1.0
a performance +(1 a) fairesss
1.0
0.8
Faimess (FPR ratio)
0.6
0.4
0.4
FairGBM
FairGBM
LightGBM
0.2
LightGBM
0.2
Fairleam GS (L GBM)
Fairleam (LGBM)
RS Reweighing (L GBM)
RS Reweighting (LGBM)
0.0
0.0
0.4 Performance (TPR)
0.2
0.6
0.0
0.2
0.8
a
(a) Scatter plot.
(b) Best attainable trade-off's per algorithm.
Figure A2: [AOF dataset] Left: scatter plot showing fairness and performance of 100 trained models of cach algorithm, evaluated validation data. GS shows only 10 markers, each run already trains 10 models itself. Right: plot of best test-set fairness-accuracy trade-offs per algorithm (models selected validation data). Lines show the mean value, and shades show 95% confidence intervals. FairGBM (blue) achieves a statistically significant superior trade-off for all a E [0.05, 0.98).
Account Opening Fraud (AOF)
Validation
Test
Algorithm
Fair. (%)
Perf. (%)
Fair. (%)
Perf. (%)
Trade-off 0.50
FairGBM LightGBM
9
64.8 2.54
90.1 + 4.51
64.7 2.59
70.2
1..833.9
78.4 + 9.89
55.8 - 3.36
GS
98.9
98.7 2.74
23.4 3.87
RS
95.3 + 3.55
31.2
96.1 3.47
31.3 + 4.53
Trade-off 0.75
FairGBM
89.3 4.62
65.9 1.33
87.5 3.36
65.9 1.64
LightGBM
58.0
2.67
66.6
61.1 + 2.86
GS
9
2.45
1.67
23.7 3.64
RS
84.0 19.3
84.6
37.4 8.89
Trade-off a 0.95
FairGBM
9.70
66.6 0.88
80.2 + 9.13
66.6 1.06
LightGBM
33.7 1.770
0.46
36.0 1.29
67.3 - 1.01
GS
98.5 1 0.99
23.6
08.3 1.74
23.8 3.51
RS
81.5 21.2
37.6
82.2 23.2
38.2 - 9.64
Table Al: Mean and standard deviation of results on the AOF dataset, for three different
choices of model-selection trade-off: E {0.50, 0.75, 0.95). Model selection metric was [a performance + (1 - a) fairness). The best model is selected on validation data, and results are reported both validation and test data.
Figure A2 shows a scatter plot and a plot of best attainable trade-offs on the AOF dataset. When compared to the ACSIncome results (Figure 2), performance and fairness values, arguably making it more challenging but more interesting task. These differences further motivate focus real-world setting.
a significantly wider range of attainable
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ACSIncome
Validation
Test
Algorithm
Fair. (%)
Perf. (%)
Fair. (%)
Perf. ( (%
Trade-off a = 0.50
Fai
99.6 0.73
81.6 + 0.08
99.4 + 0.74
81.7 + 0.09
LightGBM
75.6 3.28
80.8
75.5 + 3.32
80.8 0.80
GS
66.4
8.17
6 1.36
81.8 0.20
RS
42.3 25.8
3.70
42.4 + 25.8
77.0 + 3.73
EG
94.4 0.32
81.6
93.8 + 0.11
81.6 + 0.18
Trade-off a 0.75
FairGBM
99.5 0.83
81.7+
99.3 + 0.89
81.7 0.08
LightGBM
3.40
81.1
7.57
81.1 + 0.88
GS
1.54
0.14
65.8 1.39
81.8 0.14
RS
41.4 26.6
4 3.05
77.5 + 3.06
EG
94.4 0.33
8.16
98.8 0.13
81.6 - 0.17
Trade-off 0.95
FairGBM
1.07
81.8 + 0.06
98.5 + 1.22
81.8 0.06
LightGBM
71.2
81.9
70.8 0.34
8.00
GS
6
81.8
81.8 1.48
RS
38.3 + 25.6
7.98
77.8 2.97 25.6
EG
94.4 0.36
0.16
93.9
81.6 + 0.16
Table A2: Mean and standard deviation of results on the ACSIncome dataset.
ACSEmployment
Validation
Test
Algorithm
Fair. (%)
Perf. (%)
Fair. (%)
Perf. (%)
Trade-off 0.50
FairGBM
99.6 0.26
83.1 + 0.07
99.4 + 0.30
83.0 + 0.08
LightGBM
91.8 + 0.58
82.1 + 0.22
91.4 + 0.50
82.0 + 0.25
GS
73.9 0.85
83.1 + 0.13
74.7 + 0.84
83.1 + 0.14
RS
65.2 25.6
81.6
65.3 + 25.5
81.5 - 2.95
EG
87.6 1.11
83.0
88.4 + 1.12
83.0 + 0.17
Trade-off a 0.75
FairGBM
99.6
83.1 0.03
99.4 + 0.31
83.1 3.11
LightGBM
0.54
82.3+0.17
9..1
0.19
GS
7
83.2
7.99
83.1
RS
65.1
8.96
25.5
81.5 2.93
EG
8
83.1 0.15
88.4 + 1.12
83.0 + 0.16
Trade-off 0.95
FairGBM
99.5
83.1 0.02
09.4 0.40
83.1
LightGBM
91.0
82.4
0.11
8.01
GS
73.7
83.2
83.1 7.97
RS
65.0 25.5
81.6
65.1
81.6 6 2.94
EG
86.8 1.65
83.2 + 0.06
$7.71..67
83.1 0.06
Table A3: Mean and standard deviation of results on the ACSEmployment dataset.
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ACSMobility
Validation
Test
Algorithm
Fair. (%)
Perf. (%)
Fair. (%)
Perf. ( (%
Tradc-off a 0.50
Fai
95.0 1.36
75.8 + 0.74
96.2 + 2.44
75.7 + 0.74
LightGBM
81.1 1.44
76.1 0.31 0.31
82.3 1.03
76.1 0.30
GS
92.4 2.46
76.0
2.92
75.8 0.94
RS
60.0 + 25.3
+
60.8 + 26.5
75.8 + 2.26
EG
96.3 + 2.50
76.5 0.13
94.6 + 2.11
76.4 + 0.12
Trade-off 0.75
FairGBM
93.9 1.59
76.4 0.28
94.4 + 1.85
76.3 0.28
LightGBM
8.50
76.1 0.09
8.03
76.1 + 0.08
GS
2.18
0.66
2.66
76.0 0.72
RS
60.0 25.3
60.8 2.25
75.8 2.24
EG
96.3 + 2.52
76.5
9 2.09
76.4 0.11
Trade-off a 0.95
FairGBM
92.1 1.42
+ 0.09
1.17
16.5
LightGBM
79.9 1.40
76.2
1.07
7.02
GS
90.8
7.14
7 93.7
RS
59.8 + 25.4
7.20
60.5 26.6
75.9 +: 2.20
EG
96.0 2.90
7.16
94.6 2.02
76.4 + 0.09
Table A4: Mean and standard deviation of results on the ACSMobility dataset.
ACSTravelTime
Validation
Test
Algorithm
Fair. (%)
Perf. (%)
Fair. (%)
Perf. (%)
Trade-off 0.50
FairGBM
98.2 1.28
66.7 + 0.99
98.3 + 1.39
66.6 + 0.98
LightGBM
93.6 + 0.68
65.8 + 0.59
93.1 + 0.59
65.8 + 0.64
GS
72.8 +
66.6 + 0.52
73.0 + 0.98
66.5 + 0.52
RS
52.5 + 20.6
64.3 2.19
52.5 + 20.6
64.3 2.18
EG
96.1 2.96
66.0
96.1 + 2.96
66.0 + 0.78
Trade-off a = 0.75
FairGBM
9
67.0
97.6 + 1.96
66.9 - 0.71
LightGBM
9.45
66.5
0.28
66.6
GS
7.26
6.47
7.08
06.6
RS
52.1
64.6
52.1
64.5 1.84
EG
95.7 + 3.06
66.2
95.7 + 3.05
66.2 0.79
Trade-off 0.95
FairGBM
95.6
67.2 0.50
95.5 + 4.64
6..2
LightGBM
92.3 -
$6.6
92.3 0.27
66.6
GS
72.3 1.33
72.6 6.47++0.45
66.7 0.46
RS
49.6 20.9
6.88
10.62210
64.7 1.82
EG
94.3 4.12
6.77
94.2 + 4.18
66.4 0.74
Table A5: Mean and standard deviation of results on the ACSTrave/Time dataset.
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ACSPublicCoverage
Validation
Test
Algorithm
Fair. (%)
Perf. (%)
Fair. (%)
Perf. ( (%
Tradc-off a 0.50
FairGBM
79.9 + 0.23
98.0 + 0.65
80.0 = 0.26
LightGBM
89.1
78.4 0.58
90.0 2.05
78.5 0.63
GS
79.9
97.6
80.1 0.15
RS
66.6 24.8
78.4
67.1 + 25.7
78.5 + 2.25
EG
79.9
98.9 + 0.88
80.0 + 0.23
Trade-off a 0.75
FairGBM
99.5 0.56
80.0
97.9 + 0.74
LightGBM
8.62
78.6 0.41
78.7 8.64
GS
80.0 0.41
0.27
80.1 0.15
RS
66.5 24.9
67.1 2.14
78.5 2.21
EG
98.6 + 1.30
79.9
98.9 + 0.93
80.0 + 0.19
Trade-off o 0.95
FairGBM
99.0
80.1 0.10
97.7 1.24
80.2 2.1
LightGBM
85.5
79.1
86.4 1.23
79.3
GS
80.0 9.40
80.1 9.26
RS
66.5 + 24.9
67.0 25.7 2.17
78.5 2.20
EG
98.4
7.15
98.8 + 1.06
80.0 + 0.16
Table A6: Mean and standard deviation of results on the ACSPublicCoverage dataset.
B DESCRIPTION OF ACCOUNT OPENING FRAUD DATASET
15
Age Distributian
0.030
Fraud Rate (96)
Fraud Rate (%6
1.3
Age Distribution
0.025
-30
Fraud Rate (%6)
12
20
0.015
1.0
0.010
0.005
0.8
0.7
50
Month
Age
(a) Fraud Rate by Month.
(b) Fraud Rate by Age.
Figure A3: Plot of the variation of Fraud Rate depending on the month of the application and applicant's age. The plot also contains distribution of Age over all the applications in the dataset.
The Account Opening Fraud (AOF) dataset is in-house dataset that comprises 8 months of data from real-world fraud detection task. Specifically, on the detection of fraudulent online bank account opening applications in large European consumer bank. In this setting, fraudsters attempt to either impersonate someone via identity theft, or create a fictional individual in order to be approved for new bank account. After being granted access to new bank account, the fraudster quickly maxes out the line of credit, or uses the account to receive illicit payments. All costs are sustained by the bank.
The temporal aspect of the dataset plays an important role, as oftentimes fraudsters adapt their strategies time try improve their success rate. This translates into considerable concept
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drift throughout the year (e.g., a model trained on 1-year-old data will perform poorly on recent data). With this in mind, we split the AOF dataset temporally, using 6 months for training. month for validation, and I month for test, such that train the oldest data and test on the most recent. The simpler strategy of randomly splitting in train/tesd/allidation in this setting would not properly mimic real-world environment, and would lead to over-optimistic results.
Each instance (row) of the dataset represents an individual application. All of the applications were made on an online platform, where explicit consent to store and process the gathered data was granted by the applicant. Each instance is labeled after a few months of activity, as by then it is apparent whether the account owner is fraudulent (positive label) or legitimate (negative label). A total of 67 features are stored for each applicant, 6 being categorical, 19 binary, and 42 numerical. Most features represent aggregations over the original information and context of the application (e.g., count of the number of applications in the last hour).
The prevalence of fraud varies between 0.85% and 1.5% during the eight month period (see Fig- ure A3a). We observe that these values are higher for the later months, which were used as validation (the 7th or second-to-last month) and test (the 8th, or last month) data. Additionally, the distribution of applications also changes from month to month, ranging from 9.5% on the lower end to 15% on the higher end. The extremely high class imbalance (approximately 1 positive label for each 99 negative labels), the gradual change in fraud prevalence, together with naturally shifting consumer patterns along 8 months of real-world data are examples of common real-world challenges that are not often present in datasets from the faimess literature.
Due to the low fraud rate in the data, measuring accuracy of the models would lead to misleading results. A trivial classifier that constantly outputs legitimate predictions would achieve an accuracy close to 99%. To address this, a commonly used performance metric in the fraud detection industry is the true positive rate (TPR, or Recall), as reflects the percentage of fraud that was caught by the ML model. Moreover, in order to keep attrition on legitimate customers low, requirement of at most 5% false positive rate (FPR) is used, i.e., at most 5% of legitimate (label negative) customers are wrongly blocked from opening a bank account. Additionally, due to the punitive nature of the classification setting (a false positive negates financial services to legitimate applicant), we aim to balance false positive rates between the different groups in the dataset.
As a protected attribute for this dataset, we selected the applicant's age. Specifically, we divide applicants into two groups: under 50 years old, and at or above 50 years old. There is surprising but clear relation between fraudulent applications and reported age, so we expect that fairness w.r.t. the age group will make for challenging setting. Figure A3b shows plot of the age distribution, as well as the variation of fraud rate over age values.
C DISCUSSION ON THE LIMITATIONS OF FAIRGBM
In this section, we discuss expected limitations of the proposed approach.
When compared with vanilla LightGBM, FairGBM requires approximately double the training time (see Table 2). This compute overhead of FairGBM can be attributed to (1) the computation of the proxy gradients relative to the constraint loss, and (2) the addition of an extra optimization step per iteration the ascent step.
From an application standpoint, FairGBM specifically tailored for gradient boosting methods. This contrasts with other bias mitigation methods in the literature such as EG (Agarwal et al.] (018).. which, despite having considerably slower runtime, are applicable to a wider range classifier types (all binary classifiers in the case of EG).
Despite discussing several choices for differentiable proxies for the Type and Type errors in Section 2.2 our experiments only concern one of these proxies. As future work, would like to perform a more thorough study on the impact of different choices of differentiable proxies for the step-wise function (e.g., sigmoid, hinge, or squared loss).
Moreover, FairGBM as it is devised in this work is limited to group-wise wise fairness metrics, and incompatible with metrics from the individual faimness literature. In fact, individual faimess algorithms tailored for GBM have been developed in related work VVrgo et al. (202T). The BuDRO method proposed by Vargo et al. is based optimal transport optimization with Wasserstein distances, while
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proposal fully relies gradient-based optimization with the dual ascent method. A possible extension of our method to a wider range of constraints that enables individual fairness is a topic we aim to explore in future work.
D OPERATING FAIRGBM AT A SPECIFIC ROC POINT
Without fairness constraints, meeting specific ROC operating point can be achieved by appropriately thresholding the output of classifier that learns to approximate the class probabilities: p(y = 1[x) (Tong) 2013). That the case of classifier that is trained to minimize proper scoring rule such as binary cross-entropy.
However, when optimizing for the Lagrangian (Equation 7). we are no longer optimizing for classifier that upproximates the true class probabilities. This key point that is often overlooked in the constrained optimization literature. Namely, both L and É have implicit threshold when evaluating constraint fulfillment: the 0.5 decision threshold, or 0.0 when considering the log-odds (see Figure T In practice, FairGBM will be optimized fulfill the constraints at this pre-defined threshold, but constraint fulfillment may not (and likely will not) generalize to all thresholds. Indeed, could any decision threshold during training, but it is impossible to know which threshold would meet our ROC requirements beforehand.
We propose solve this by introducing ROC requirement another in-training constraint. In the AOF setting, this is achieved by introducing an additional constraint global FPR < 0.05. In practice, instead of shifting the threshold meet our target ROC operating point, shifting the score distribution such that the 0.5 decision threshold corresponds to our target ROC point, enabling constraint fulfillment& any attainable ROC point.
E RANDOMIZED CLASSIFIER VS LAST ITERATE
FairGBM on ACSIncome (val.)
FairGBM on Account Opening Fraud (val.)
1.00
1.0
0.98
0.9
(FNRratio) ratio)
Faimess (FPR ratio)
0.96
0.8
Fairness (FNR
0.94
0.7
0.92
0.90
0.6
0.88
randomized last iterate
0.5
randomized
0.86
last iterate
0.77
0.78
0.79
0.80
0.81
0.82
0.2
0.4 Performance (TPR)
0.6
Performance (Accuracy)
(a) ACSTncome results.
(b) AOF results.
Figure A4: Comparison between using the FairGBM randomized classifier (blue circles) or the predictions of the last FairGBM iterate (orange crosses).
Figure A4 shows a comparison between using the randomized classifier predictions or solely the last iterate predictions the ACSIncome dataset. As mentioned in Section the first approach benefits from theoretical convergence guarantees, while the latter benefits from being a deterministic classifier (which may be requirement in some woaldworld settings). In practice, using the last iterate version of FairGBM (which always uses all trees the GBM ensemble) achieves similar results to the randomized classifier version (which randomly picks the number of trees it will use for each
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prediction). The same trend is clear the AOF dataset, and concurs with related work randomized classifiers by Cotter et al. (2019b).
F BACKGROUND ON GRADIENT BOOSTED DECISION TREES
A gradient boosting algorithm estimates mapping f X + that minimizes a loss function,
1 N Σ Mvn, f (x:)), L(f)
(10)
where is constrained to be sum of base (weak) learners h2 H. In the case of GBDT, these can be shallow decision trees with fixed depth or fixed number of nodes:
T
Thhss
(II)
t=
where 7), step size parameter. Typically, he would be constant function that minimizes L and To = 1. Gradient boosting can then be understood as performing gradient descent on the space of functions/ f. Each subsequent step, he being essentially a projection onto of the negative gradient of the loss L w.r.t. f. In other words, the base learner whose predictions are close possible, in the 1a sense, to the negative gradien
h = arg min bEH
-r,s - h(xx)))²
(12)
where It.; are the gradients evaluated the current iterate fi Eimi Amhm:
9t.i ally, f(xx))
(13)
0f(x,)
f(o))=fe-1(a))
Note that Equation
2 is equivalent to:
N
h4 = arg min N.E
g.she(zi) + n (2x1)
(14)
XGBoost (Chen & Guestrin 2016 and LightGBM (Ke et al. 2017 replace the approximation above with local quadratic one thus implementing the following second order step:
Σ g..hh((ss) + (2.))((())) (.. + 2(he),
h, arg min b
(15)
where Hi, is the hessian of w.r.t. f computed at the current iterate and S2 is a regularization term penalizing complex base learners.
II practice, heuristic is used that builds the decision tree by greedily choosing sequence of splitting variables and splitting values that decrease the value of the function to minimize
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G NOTATION
the Lagrangian function, which uses the original constraints c; see Equation 2
the proxy- proxy-Lagrangian function, which uses the proxy constraints č; see Equation
an inequality constraint function; it is deemed fulfilled if c(0) < O; this function may be non con-differentiale;; examples include constraint on TPR parity or parity of any other metric of the confusion matrix.
proxy inequality constraint that serves as sub-differentiable proxy for the corresponding constraint <; Equation 5
I
an instance-wise loss function, i.c., / y x 4 where y is the set of possible labels and 5 the set of possible predictions; see green line in Figure
sub-differentiable proxy for an instance-wis loss function; see blue and purple lines in Figure [
D
dataset of samples (xr, y, s) D, where x E X S R" is the features, y E y C No is the label, and S Ng is the sensitive attribute.
L(sma)
a predictive loss function measured over data samples with sensitive attribute value $ = a, { (rr, y, 8) : a, (xr, y, 8) D): the subscript is omitted when measuring loss over the whole dataset D; examples include the false-negative rate or the squared error loss.
L(S=a)
sub-differentiable proxy for a predictive loss function measured over data samples with sensitive attribute value S a, {x, 8).
a, (I, y, D}; the subscript is omitted when measuring loss over the whole dataset D.
X
Lagrange multiplier associated with constraint c; and proxy constraint c the space of strong learners. the space of weak learners.
F
H
f
strong learner.
weak learner.
S
the range of random variable S; the letter S specifically is used for the sensitive attribute, and S for the different values the sensitive attribute can take.
H
REPRODUCIBILITT CHECKLIST
This section provides further details regarding implementation and hardware used for our experiments. We follow the reproducibility checklist put forth by Dodge et al. (Dodge et al. 2019).
Regarding reported experimental results:
V Description of computing infrastructure.
ACSIncome and AOF experiments: Intel i7-8650U CPU, 32GB RAM. ACSEmployment, ACSMobility, ACSTrave/Time, ACSPublicCoverage experiments: each model trained parallel on a cluster. Resources per training joh: vCPU core (Intel Xcon E5-2695), 8GB RAM
Average run-time for each approach.
Folder runt s of the supp. material
Details of train/ vaiiattaiittiionteestt splits.
See Section
3.1 and data notebooks in folder notebooks of the supp. material
Corresponding validation performance for each reported test result.
Folder results of the supp. materials
4 A link to implemented code
Regarding hyperparameter search:
"These experiments were added as part of the paper rebuttal process, and thus required faster infrastructure to meet the conference deadlines.
'https: /i thub. com feedzai rag wtwe:/treeeeeeeee http:////rreeeeeponaaaatraaalllr
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Bounds for each hyperparameter.
Folder
of the supp. material
Hyperparameter configurations for best-performing models.
Folder hyperparametees of the supp. materials
Number of hyperparameter search trials.
LightGBM, FairGBM, and RS: 100 trials.
EG and GS: 10 trials each trial trains 10 separate base models, for total budget of 100 models trained (equal budget for all algorithms).
The method of choosing hyperparameter values.
Random uniform sampling.
Expected validation performance.
Folder others of the supp. materials
23


Reviews:
[{"review_id": "uCVW-q0z0sp", "reviewer": "Reviewer_MVBV", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "", "main_review": "", "summary_of_the_paper": "This paper is focused on ensuring fairness on tabular data. Since Gradient boosted decision trees (GBDT) - based classifiers are found effective on tabular data, the authors propose FairGBM framework for training GBDT under fairness constraints. The experimental result shows improvement in the training time, predictive performance and fairness.", "summary_of_the_review": "Although the authors claimed to develop a learning framework for fair GBDT, the current approach is only applicable for classification task. Furthermore, constrained optimization is not new in fair ML research. Their formulation of constrained optimization is very similar with  (Agarwal et al., 2018)'s reduction approach. The only difference is using the differentiable proxy functions which was adapted from (Cotter et al. 2019). So, the main ideas of the paper have limited novelty. In addition, the paper lacks adequate experiments to establish author's claim. See above section. \n\n-------------------------------------------------\nI thank the authors for explaining some of my concerns. Although I am not completely convinced regarding the novelty of the paper, after reading other reviewer's comments, I have decided to increase my rating.  \n ", "strength_and_weaknesses": "Strength:\n- The paper is well written and well motivated. \n- There are not much existing work that focused on fairness for GBDT models. \n- In depth formalization of the proposed framework\n\nWeakness:\n- It is not clear how the proxy-Lagrangian can be designed/derived for any fairness metrics. Is the cross-entropy-based proxy only applicable for demographic parity, equal opportunity and predictive equality?\n- The proposed constrained optimization method works for GBDT-based classifier. Is it possible to address unfairness in regression task with the current approach? What would be the proxy function on that case? Note that Agarwal et al., 2019 extended their reduction-based approach for regression task as well. It would be great if the authors include discussion or additional experiments on this.  \n- Baseline models EG, GS and RS were trained with 10 iterations for an equal budget for all algorithms. But Agarwal et al., 2018 stated that 5 iterations were enough for their reduction approach in all cases. Additional experiments with varying number of iterations for all models would be helpful to understand if EG were not overfitted with additional iterations.\n- Instead of completely discarding EG from the experiment of real-world data, why not changing the decision threshold and n in EG for feasibility, in case of this dataset.\n- How trade-off \\alpha = 0.5, 0.75, and 0.95 selected? Fairness-accuracy trade-off plots for all models would be helpful to understand the impact of different constraint methods.\n- Fairlearn package is mainly implemented in Python, while FairGBM is implemented in C++. Does FairGBM get additional runtime benefit due to C++? \n ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "dG1zrLiwXVZ", "reviewer": "Reviewer_f61N", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "", "main_review": "", "summary_of_the_paper": "The paper proposed a new FairGBM method to train GBDT under fairness constraints that shows little impact to predictive performance but improved fairness metrics as compared to unconstrained GBDT. The major challenge in the Fairness constraint is from the non-differentiable property of fairness notion, which is resolved by the proxy Lagrangian in this paper. Afterwards, the problem is resolve under the two-player game formulation where a descent step optimizes the loss and a ascent step ensures the fairness. Numerical results on ACSIncome-Adult and AOF dataset show that FairGBM proposed from the paper have better trade-off among Fairness, Performance, and Efficiency. ", "summary_of_the_review": "Overall the paper proposed a fairGBM with a proxy Lagrangian formulation. The problem is well motivated and solution is reasonable sound. There are some doubts on the experimental results, while overall results demonstrate the efficiency of the new proposed algorithm. ", "strength_and_weaknesses": "Strength\n[+] The problem is well motivated. Fairness is an important topics and designing a optimization framework in GBDT to ensure fairness is an interesting and important area.\n\n\nWeakness\n[-] FairGBM is a modified version of LightGBM with fairness constraint. From the experimental results in Table 2, it shows FairGBM is better than lightGBM in both performance and fairness. Could the author helps to clarify the source of improvement of performance? It seems contra intuitive that a fairness constraint algorithm outperforms a unconstraint algorithm that purely optimize for performance.\n\n[-] Could the author helps to confirm fairness metrics used in evaluation and model training (\\tiltle(c)_i in equation 7)? In figure 2, the fairness metrics is different across dataset, FNR for ACSIncome-Adult and FRR for Account Opening Fraud. Is different fairness constraint selected when algorithm is applied on different datasets? ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "_FpMj24uS6", "reviewer": "Reviewer_WMdi", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "", "main_review": "", "summary_of_the_paper": "The paper proposes a first of its kind in-processing learning framework FairGBM for training GBDT, without affecting its performance, constrained by fairness. The paper tries to advanced the area of FairML, limiting risks of unfair or biased ML systems and aims to establish a gold standard method. The authors provide evidence that FairGBM is an order of magnitude faster compared to existing related work such as LightGBM, RS Reweighing, Fairlearn GS and Fairlearn EG when tested against benchmark datasets and is superior to them in both fairness, performance and runtime. The authors discuss background related work in detail by providing an in-depth analysis of pre-processing, in processing and post processing methods and argue why introducing fairness during the in processing is more beneficial vs the other two. ", "summary_of_the_review": "The authors provide sufficient ground of reasoning why FairML is necessary in terms on risks of biases and discrimination affecting various ML work and how tabular data, an important format of information, important across various applications could be a strong opportunity for evaluation of the method proposed. The authors provide sufficient background around relevant work and argue correctly why the choice of opportunity is in processing and why constrained optimization options with fairness metrics and their non-convex properties lead to the development of the mentioned proxy functions. Further the work put forward in terms of experimental setup and comparison to other methods is fairly strong to justify why this method could be considered as a gold standard method for tabular data and for gradient boosting models. Although the scope is limited, it is still strong and hence I propose that this work should be accepted. \n", "strength_and_weaknesses": "Strengths: \n1. Strong summarization of relevant work, including pre processing, in processing and post processing and gap analysis to find area of opportunity for method development that can lead to highest impact i.e. there is a strong lack of a gold standard method that just works across the board and key identification of in-processing step as area of development. \n2. The method proposed is efficient and does not require additional training or storage for keeping intermediate training states. \n3. Method is applied to two diverse datasets to cover a variety of issues, bias, class imbalance, budget constraints on positive predictions etc., one of these datasets is benchmarked\n4. The paper proposed mentions that the work is generalizable to any differentiable constraints, not just fairness constraints. \n5. Comparison to other methods is fairly strong towards assesment of performance and fairness. \n\n\nWeakness: \n1. While the authors explicitly focus their attention to tabular data for evaluation of FairGBM, it would have been thoughtful to discuss potential impact of these methods on other structured/unstructured datasets as well (such as images, natural language etc). Even though the authors discuss there is no gold standard method that works regardless of data format or bias, it is then counterintuitive to focus the attention to just tabular data, given there are several other formats of data available. \n2. Could be worth testing on more benchmark datasets to increase confidence coverage. \n3. While the work is supposedly generalizable to additional constraints, apart from fairness constraints, it is not tested or validated for any other type of constraint. \n4. While authors claim FairGMB can be applied to any GB algorithm, most comparisons to other constrained optimized methods are done by implementing FairGBM on LightGBM, while other methods also use LightGBM as base learners. \n5. The authors can perhaps provide some commentary of how this work can be extended to other ML models, including deep learning, beyond just gradient boosting methods. ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "Smnd1AxV4ub", "reviewer": "Reviewer_Cc3g", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "", "main_review": "", "summary_of_the_paper": "The paper presents a method for training gradient-boosted trees with fairness constraints via a (proxy) Lagrangian approach. They provide an algorithm, an open-source implementation, and empirical results on two datasets (only one appears to be open-source) showing that the proposed algorithm generally improves over existing methods.", "summary_of_the_review": "Overall, this paper pursues an important direction for machine learning research -- tree-based models are, as the authors note, SOTA for tabular data yet are incompatible with many gradient-based regularization approaches, so new methods are needed. In general, I think the paper is well-written, but the discussion of the experimental results could be improved. Given the clear differences between the two datasets, I also think that adding additional datasets (e.g. additional tasks from folktables) would considerably improve the paper. See detailed comments above/below.", "strength_and_weaknesses": "## Major Comments\n\n* The authors note that there are clear differences between the two datasets (e.g. differences in label imbalance, differences in spread over performance metrics). Given this, it is hard to make much sense of the results, since they seem to imply meaningfully different conclusions (i.e. Fairlearn EG achieves excellent tradeoffs on ACS Income and much lower variance than the proposed method; GS and RS achieve near-perfect fairness on AOF, but not on ACSIncome). Given that the authors are already (I assume) using the folktables package to generate ACS Income dataset, why not use additional tasks already available in that package (Public Coverage, etc.)? This would also provide more publicly verifiable results on open datasets.\n\n* The AOF dataset is not clearly described. Is it an open dataset (I do not see it in supplement)? What is the source? What features exist in the dataset, what are their data types, etc.? Particularly if the dataset is *not* open, much more detail would be useful.\n\n* Given the very strong performance of EG on ACSIncome, I wonder why more effort was not made to include it in AOF experiments. If EG gives a randomized binary classifier, why can't the average of many (randomized) predictions be used as a de facto continuous prediction?\n\n* The authors perform 10 experimental iterates, but do not use these iterates to provide measures of statistical variability in comparing their point estimates -- a missed opportunity, and also a critical one given that several similar algorithms are being compared. Please provide, if possible, estimates of variation (i.e. SD over trials, Clopper-Pearson confidence intervals, etc.) of the various metrics being compared e.g. in Table 2, Figure 2. This will help the authors eliminate subjective language in their analysis such as \"excellent trade-offs\", \"only slighting lagging behind\", etc.\n\n* The paper is missing a discussion of the limitations of the proposed approach. Please comment on this.\n\n* It's not clear why equalizing the group FNR make sense for any real-world task on ACS Income. Please comment on the motivation for this, or choose a constraint that actually has some grounding in the income task.\n\n* I think the paper should comment on, and ideally compare to, the approach described in \"Individually Fair Gradient Boosting\", Vargo et al., https://arxiv.org/pdf/2103.16785.pdf ).\n\n## Minor Comments\n\n* Please use some other form of marker to differentiate between models in Fig. 2; it is difficult to see the differenecs between colors.\n\n* Hwo is the alpha=0.75 in Table 2 chosen? If it is arbitrary, how do the comparisons change with \\alpha? Is it possible to instead plot curves over all values of alpha in [0,1]?\n\n## Typos etc\n\nP1 \"no clear winner method\" -> no clear winning method\n\nPlease spell out \"w.r.t\" in the paper\n\nEquation (5): If I understand correctly, the max can be over a,b \\in S (eliminating the need for \\forall b \\in S)\n\nI don't see S_s or L_S_s defined in the paper.\n\nP8: \"significative\"", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Accept: poster