Research on recommendation fairness has risen up in recent years. As recommender systems are typically customer-centric design, customer-side fairness is extensively studied. However, some less obvious fairness issues hidden on the provider side have not received comparable attention. One remaining question is whether product competitiveness in recommender systems (e.g., recommendation scores) exhibits monotonic variation with respect to protected sensitive attributes on the provider side, such as item prices in E-commerce or ad bids in sponsored search. It is inherently unfair for sellers if the recommendation score of their listed products decreases as they lower their prices. Our investigation reveals that such instances of unfairness are not uncommon in recommender systems. In this paper, we define this phenomenon as an individual monotonic fairness issue, and propose a novel, fairness-aware framework to address it. Our approach leverages monotonic neural additive models, theoretically ensuring monotonicity, and incorporates contrastive learning to enhance fairness through augmented samples. Additionally, we introduce specific evaluation metrics to quantify fairness. Extensive experiments on real-world datasets demonstrate that our method significantly improves monotonic fairness while still maintaining a high level of personalization compared to state-of-the-art recommendation algorithms. The source codes are available at https://github.com/yuchguo1007/MNAM-CL.
Over recent decades, recommender systems have rapidly evolved and become integral to modern web
and mobile applications like eBay, Netflix, and Spotify. These online platforms serve as intermediaries
between content providers (e.g., eBay sellers, Netflix filmmakers, Spotify artists) and customers by
ofering recommendation services. Traditional personalized recommendations strive to enhance customer
satisfaction by suggesting products to best match customers’ interest, relying on historical user
interactions. However, such data-driven design inevitably introduces unfairness, either on the customer side
or the provider side. With the awakening of the unfairness in recommender systems, which is broadly
defined as harmful disparity in user experience [
CEUR Workshop
ISSN1613-0073 )80 % ( ion60 t ro40 p o rP20 0
Provider fairness, or supplier fairness, refers to not discriminating against individual provider or groups
on sensitive attributes [
Neural Additive Models (NAMs) make restrictions on the structure of neural networks, which yields a
family of models that are inherently interpretable while sufering little loss in prediction accuracy when
applied to tabular data. Methodologically, NAMs belong to a larger model family called Generalized
Additive Models (GAMs) [
NAMs learn a linear combination of networks that each attend to a single input feature: each in the
traditional GAM formulationis parametrized by a neural network [
Contrastive learning has emerged as a powerful paradigm in unsupervised and self-supervised learning
techniques [
In this section, we introduce the definition of monotonic fairness and its measurement methodology. DEFINITION 1 (MONOTONIC FAIRNESS). Generally, assume we can partition a multi-dimensional vector ∈ ℝ into = (, ) ∈ ℝ − × ℝ , such that a function () for = (, ) is monotonic on if this inequality holds1: (, ) < (, ′), ∀, ∀ < ′, where < ′ denotes the inequality for all the elements (i.e., ≤ ′ for all 1 ≤ ≤ , where denotes the -th element of ). The formula above shows that is monotonic on . For a diferentiable function , Equation (1) is equivalent to: min ∈[1,] Assume that and refer to the unprotected and protected attributes in recommender systems, Equation (2) indicates the individual monotonic fairness of each protected attribute. 1Assume that all monotonic constraints are increasing; the monotonically non-increasing case can be considered analogously.
According to Definition 1, the best match metric to measure monotonic fairness is pairwise ranking accuracy [22, 23, 24, 25], where the idea is to calculate the accuracy of a system ranking a pair of items correctly conditioned on the true outcome. Formally, the metric is defined as:
PairAcc = ( () < ( ′)| ∈ ,
′ ∈ ) = ( (, ) < (, ′)|∀, ∀ < ′) Intuitively, this metric means that given an item from dataset , the probability of model score keeps monotonic compared with itself when the protected feature varies. When referring to cases not meeting the criteria (i.e., unfair cases), they can be divided into two types:
( (, ) > (, Unfairness = { ( (, ) = (, ′)|∀, ∀ < ′)|∀, ∀ < ′), ′),
As shown in Equation (4), reverse and irrelevant represent diferent levels of unfairness, both of which are the targets to be eliminated. For irrlevant cases, the tolerable precision of the equal sign is set to 1e-6.
In this section we describe the proposed framework in details. The architecture of MNAM-CL, as illustrated in Figure 2, is based on the classic two-tower model. It addresses reverse unfairness instances by isolating protected attributes from the population and constructing a certified monotonic neural additive model. Furthermore, to tackle the more challenging irrelevant instances, where subtle changes in protected attributes fail to influence final outcomes, we employ an additional approach. Augmented samples are generated through a self-supervised manner by simulating real changes to protected attributes, serving as extra data for fairness tasks to assist model training.
Neural additive models (NAMs) [
Input: A training dataset = { , } Output: Augmented dataset ′ = {( , ← lower boundary of ; upper boundary of ; ∈ ′ = (, ) do
; ′ = 1( < ′); ′ = (, 1, ⋯ , ′, ⋯ , ) ; end end
Generate an augmented sample (( , ′), ′); their input feature and the output. Drawing inspiration from NAMs, we develop a Monotonic Neural Additive Model (MNAM), as illustrated in Figure 2. Each of the protected attributes gets an expert network as the weight, the input of which are unprotected features. Thus MNAM is mathematically formulated as follows: () = () + ∑ ℎ () ⋅ Θ ( ), =1 where (⋅) is the score function for unprotected features, Θ (⋅) is the normalization function for -th protected feature, and ℎ (⋅) is the weight function, respectively. The partial derivative of (⋅) with respect to is given by the following formula: min ∈[1,] Under the condition that ℎ (⋅) > 0 and Θ (⋅) is diferentiable, the above derivation theoretically guarantees ′ monotonicity between and as long as Θ ( ) ≥ 0. In our work, ℎ (⋅) is a multi-layer fully connected network with sigmoid as the final activation function, which satisfies the monotonic constraint while introducing nonlinearity.
Contrastive learning aims to learn generalizable and transferable representations from unlabeled data using contrastive pairs [20]. In our study, we focus on protected attributes, augmenting original training data in a self-supervised manner.
The augmentation module plays a crucial role in contrastive learning, as indicated by previous
research[
With the above data augmentation manner, the choice of loss function is significant. As shown in Figure 2, MNAM-CL consists of two kinds of losses: primary loss and fairness loss. For the primary task we use pointwise cross entropy as the loss function: =1
= − ∑ log( ̂ ) + (1 − ) log(1 − ̂ ), where and ̂ are the true label and the sigmoid probability of -th sample, respectively. As for the fairness task, we use BPR loss [26] to measure the mutual information between the original samples and augmented samples.
Let Δ ̂ = ̂ ′ − ̂ , then we have =1 =1 = ∑
∑ ′ log (Δ ̂ ) + (1 − ′) log (1 − Δ ̂ ), where ̂ ′ is the predicted score of augmented sample ′, and is sigmoid function. Finally the total loss function becomes a linear combination of Equation (7) and Equation (8). We also add 2 -regularization terms to avoid overfitting: (7) (8) (9) = + ∗ + , where is a temperature hyperparameter. MNAM-CL basically follows the conventional stochastic gradient descent (SGD) training routine.
Questions (RQs): In this section, we conduct experiments on three public datasets and answer the following Research • RQ1: How to define sensitive attributes for monotonic fairness? • RQ2: Is monotonic unfairness prevalent in standard models in recommendation? • RQ3: Could MNAM completely eliminate monotonic unfairness?
5.1.1. Dataset We evaluate fairness and recommendation performance on three datasets: MovieLens2, Steam3 and Beauty4. Table 1 provides a summary of the dataset statistics. Note the original ratings of some datasets are explicit integer ratings range from 1 to 5, and we transform them into binary labels by threshold 3 to construct a binary classification model. Additionally, we mark protected attributes for each dataset, selecting one attribute for both MovieLens (i.e., ratings) and Steam (i.e., price), and multiple attributes for Beauty (i.e., ratings and price). It is worth mentioning that after splitting the validation set from raw dataset at a ratio of 20%, we follow the same procedures as Algorithm 1 to generate a monotonic fairness validation set. 4http://snap.stanford.edu/data/amazon/productGraph/categoryFiles/
We compare MNAM-CL with several baselines: (1) Wide&Deep [27]. This model combines both linear
models and deep models to improve memorization and generalization capabilities. (2) NeuMF [28]. A
neural network-based collaborative filtering method utilizing binary cross-entropy loss. (3) NAM [
We use the classical ROC-AUC and NDCG@10 to measure model accuracy. As defined in section 3.2, we select reverse rate and irrelevant rate to measure monotonic fairness, where smaller values denotes better fairness performance. For parameter settings, is set to 0.1 as the weight of in loss function, while L2 regularization coeficient is set to 1e-6.
Unlike inherent attributes of human beings, such as gender, age and race, which segment users into subgroups, sensitive attributes related to monotonic fairness are more individual and quantifiable dimensions. Ensuring fairness along these dimensions in recommender systems is critical for platforms, as neglecting them can lead to a lose-lose scenario for both providers and platforms. For instance, price is a critical factor influencing user purchase. Consider a seller who lowers the price of his item. If the platform’s recommender system does not protect price attribute, the item’s model score might fail to increase as expected. This misalignment could result in lost transaction opportunities—a loss for both the seller and the platform. In summary, any attribute that may disrupt the online platform ecosystem if it fails to meet the monotonic fairness criteria in Definition 1, falls within the scope of sensitive attributes discussed in this paper. These include, but are not limited to, item prices for sellers, bids for advertisers, and movie ratings for filmmakers.
Before the real research begins, it is essential to clarify the current status of monotonic fairness in representative recommender systems. As previously defined, monotonic unfairness on protected attributes in recommendation is divided into reverse and irrelevant. We evaluate various baseline models on the same datasets to observe their fairness performance. Table 2 demonstrates that these baseline models still sufer from monotonic unfairness of varying degrees, despite good ranking metrics. Such results emphasize the importance of addressing monotonic unfairness from both the provider and system perspectives.
Theoretically, MNAM alone could eliminate all reverse cases, which is verified by experiments, as shown in Table 2. Nonetheless, MNAM still exhibits a certain number of irrelevant cases. According to Equation (5), ℎ () is trained as the weight factor for , influencing the contribution of protected attributes to the ifnal score. Therefore the irrelevant cases occur when ℎ () ⋅ |Θ ( ′) − Θ ( )| ≤ 1e-6. The reason why MNAM is powerless in reducing irrelevant cases is the absence of supervised constraints. In summary, MNAM cannot completely eliminate monotonic unfairness, indicating a need for improvement in reducing irrelevant cases.
We conduct additional experiments for investigating efectiveness of each component in MNAM-CL. Figure 3 presents the unfairness distribution of Beauty@price, illustrating that the base model (T2) has a relatively high occurrence of unfairness indiscriminately. In comparison, MNAM tends to generate unfairness only when the score is near the upper bound 1.0 or the change rate is small ( ′/ ≈ 1.0). This clearly demonstrates the alignment between the efect and design of MNAM. Compared with other ablation versions, MNAM-CL achieves improved monotonic fairness, particularly in alleviating irrelevant cases. The further reduction of unfairness from MNAM to MNAM-CL proves the efectiveness of data augmentation and contrastive learning. The remaining unfair cases are mostly caused by diminishing marginal efects, which is more acceptable from an ethical perspective. Furthermore, we evaluate monotonic fairness both on single and multiple attributes, where MNAM-CL consistently outperforms with stable performance.
In this paper, we study individual monotonic fairness in recommender systems, and propose MNAM-CL, a novel framework for reducing such unfairness. It has the capability to eliminate all reverse cases. Furthermore, it enhances fairness by data augmentation and contrastive learning according to specific scenarios and attributes. Extensive evaluations verify its efectiveness in modeling monotonic fairness while maintaining recommendation accuracy. Fairness in process is the premise of fairness in result. In the future work, more complex pairwise monotonic fairness would be further explored.
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