# Adaptive Fair Representation Learning for Personalized Fairness in
Recommendations via Information Alignment

Xinyu Zhu  School of Computer ScienceSichuan UniversityChengduChina
<EMAIL_ADDRESS>,  Lilin Zhang  School of Computer ScienceSichuan
UniversityChengduChina<EMAIL_ADDRESS>and  Ning Yang  School of
Computer ScienceSichuan UniversityChengduChina<EMAIL_ADDRESS>
(2024)

###### Abstract.

Personalized fairness in recommendations has been attracting increasing
attention from researchers. The existing works often treat a fairness
requirement, represented as a collection of sensitive attributes, as a hyper-
parameter, and pursue extreme fairness by completely removing information of
sensitive attributes from the learned fair embedding, which suffer from two
challenges: huge training cost incurred by the explosion of attribute
combinations, and the suboptimal trade-off between fairness and accuracy. In
this paper, we propose a novel Adaptive Fair Representation Learning (AFRL)
model, which achieves a real personalized fairness due to its advantage of
training only one model to adaptively serve different fairness requirements
during inference phase. Particularly, AFRL treats fairness requirements as
inputs and can learn an attribute-specific embedding for each attribute from
the unfair user embedding, which endows AFRL with the adaptability during
inference phase to determine the non-sensitive attributes under the guidance
of the user’s unique fairness requirement. To achieve a better trade-off
between fairness and accuracy in recommendations, AFRL conducts a novel
Information Alignment to exactly preserve discriminative information of non-
sensitive attributes and incorporate a debiased collaborative embedding into
the fair embedding to capture attribute-independent collaborative signals,
without loss of fairness. Finally, the extensive experiments conducted on real
datasets together with the sound theoretical analysis demonstrate the
superiority of AFRL. The codes and datasets are available on
https://github.com/zhuxinyu2700/AFRL.

Fair Recommendation, Personalized Fairness, Recommender Systems

††journalyear: 2024††copyright: acmlicensed††conference: Proceedings of the
47th International ACM SIGIR Conference on Research and Development in
Information Retrieval; July 14–18, 2024; Washington, DC, USA††booktitle:
Proceedings of the 47th International ACM SIGIR Conference on Research and
Development in Information Retrieval (SIGIR ’24), July 14–18, 2024,
Washington, DC, USA††doi: 10.1145/3626772.3657709††isbn:
979-8-4007-0431-4/24/07††ccs: Information systems††ccs: Information systems
Recommender systems

##  1\. Introduction

In the era of exponential information growth, recommender systems play a
critical role in alleviating the problem of information overloading (He et
al., 2017; Mnih and Salakhutdinov, 2007; Kang and McAuley, 2018). Despite the
great success of recommender systems, existing studies have shown that machine
learning based recommendation models often suffer from unfair recommendations
due to the bias in training data (Kleinberg et al., 2016; Pessach and Shmueli,
2022; Dwork et al., 2012; Xiao et al., 2017). In recent years, many efforts
have been made for fair recommendations from various perspectives (Beutel et
al., 2019; Fu et al., 2020; Zhu et al., 2021; Ge et al., 2021), among which
user-side fairness attracts special attention due to its significance to the
improvement of user experience.

A range of approaches have been proposed for user-side fair recommendations,
following various technical lines including Pareto optimization (Lin et al.,
2019), adversarial training (Li et al., 2021b; Wu et al., 2021, 2022), and
disentangled representation learning (Zhao et al., 2023; Park et al., 2021;
Gong et al., 2020; Sarhan et al., 2020). The common idea of the existing works
is to filter out the information of user sensitive attributes from the learned
fair user embeddings, so that recommendations can be made independently of
these sensitive attributes. However, the traditional approaches often assume
that all users share the common sensitive attributes and consider the user
fairness requirement, represented by a collection of user sensitive
attributes, as hyper-parameter specified in advance, which limits the model to
serving only one fairness requirement. In real world, however, it is the fact
that different users are sensitive to different attributes and have
personalized fairness requirements (Li et al., 2021b). For example, some users
may want the recommendations to be made for them without consideration of
their racial information, while some others want the recommendations to be
made without gender bias.

Recently, a few methods have been proposed for personalized fairness in
recommendations. For example, to meet diverse fairness requirements, Li et al.
(Li et al., 2021b) propose to train a filter for each possible combination of
sensitive attributes. Wu et al. (Wu et al., 2022) propose a model PFRec, which
builds a set of prompt-based bias eliminators and adapters with customized
attribute-specific prompts to learn fair embeddings for different attribute
combinations. Creager et al. (Creager et al., 2019) propose FFVAE, a
disentangled representation learning model that separates representations into
sensitive and non-sensitive subspaces. It addresses personalized fairness by
excluding from the learned fair embeddings the relevant semantic factors
corresponding to different sensitive attributes specified by user fairness
requirements. However, the problem of personalized fairness in recommendations
is still far from being well solved partly due to the following challenges:

(1) Unacceptable training cost caused by exponential combinations of
attributes Essentially, most existing methods for personalized fairness still
treat a fairness requirement as a hyper-parameter, which makes them have to
train and store a model for each combination of attributes in a brute force
way (Li et al., 2021b; Wu et al., 2022). Such inflexibility incurs a huge
training cost due to the explosion of attribute combinations, which leads to
the impracticability of the existing methods.

(2) Compromise on recommendation accuracy It is well-recognized by previous
works that gains in fairness necessarily come at the cost of losses in
accuracy (Gupta et al., 2021; Kearns et al., 2019). However, in order to
completely erase the sensitive attribute information from the fair embeddings,
the existing approaches also remove information that overlaps with non-
sensitive attributes (Li et al., 2021b; Wu et al., 2022; Creager et al.,
2019). This inevitably causes the loss of the discriminative information of
the non-sensitive attributes and results in a suboptimal trade-off between
accuracy and fairness. Therefore, it is worth exploring better solutions to
achieve personalized fairness with less compromise on recommendation accuracy.

In this paper, to address the above challenges, we propose a novel fair model
called Adaptive Fair Representation Learning (AFRL) for personalized fairness
recommendation. Particularly, to overcome the challenge of the unacceptable
training cost incurred by the explosion of attribute combinations, AFRL treats
a user fairness requirement as input, rather than hyper-parameter, by which
AFRL can adaptively generate the fair embeddings for different users by fusing
the corresponding embeddings of non-sensitive attributes specified by the
fairness requirement. The generation of fair embeddings is dynamically
controlled by the fairness requirements, which endows AFRL with the
adaptability during the inference phase to the exponential combinations of
attributes.

To strike a better trade-off between fairness and accuracy, we propose an
Information Alignment Module (IAlignM) for AFRL. This module is designed to
enable the learned fair embeddings to retain discriminative information from
non-sensitive attributes and unbiased collaborative signals from the user’s
interaction history. In contrast to existing approaches, where removing
sensitive attributes results in the loss of discriminative information from
non-sensitive attributes, IAlignM adopts a novel strategy. It learns
attribute-specific embeddings from the original user embeddings for each
attribute, ensuring the precise alignment of information between the
embeddings and their respective attributes. Here information alignment refers
to preserving and only preserving the discriminative information related to
the attributes within the corresponding attribute-specific embeddings. For
this purpose, we employ a bilevel optimization approach to ensure that an
attribute-specific embedding exactly encodes the information of its
corresponding attribute, with a theoretical guarantee rooted in information
bottleneck principle. At the same time, IAlignM will further improve the
recommendation accuracy by learning a debiased collaborative embedding to
explicitly capture into the fair user embeddings the collaborative signals
where bias to any user attribute is filtered out to avoid the loss of
fairness.

It is worth mentioning that AFRL is recommendation model-agnostic, which means
it can serve as a plugin for an off-the-shelf recommendation model. In this
paper, we will test our AFRL for non-sequential and sequential recommendation
tasks. In summary, our contributions can be outlined as follows:

  * •

We propose a novel fair model called Adaptive Fair Representation Learning
(AFRL) which achieves a real personalized fairness in recommendations due to
its advantage of training only one model to adaptively serve different
fairness requirements during inference phase.

  * •

To achieve a better trade-off between fairness and accuracy in
recommendations, we propose an Information Alignment Module (IAlignM). IAlignM
reduces the loss of recommendation accuracy by exactly preserving
discriminative information of non-sensitive attributes and incorporating a
debiased collaborative embedding into the fair embedding to capture attribute-
independent collaborative signals.

  * •

At last, the extensive experiments conducted on real datasets together with
the theoretical analysis demonstrate the superiority of AFRL.

Figure 1.  The overview of AFRL. AFRL contains Information Alignment Module
(IAlignM) and Information Aggregation Module (IAggM). IAlignM generates $M$
attribute-specific embeddings $\\{\mathbf{z}_{u,i}\\}$ ($1\leq i\leq M$) and a
debiased collaborative embedding $\mathbf{z}_{u,0}$ from the user embedding
$\mathbf{u}$, using attribute encoders $\\{E_{i}\\}$ ($1\leq i\leq M$) and a
debiased collaborative signal encoder $F$, respectively. IAggM aggregates
these embeddings with respect to the personalized fairness requirement
$\mathbf{s}_{u}$ to produce the final fair user embedding $\mathbf{u}^{*}$ for
downstream recommendation.

##  2\. Preliminaries

###  2.1. Basic Notations and Definitions

We denote user set by $\mathcal{U}$ and item set by $\mathcal{V}$. Let
$\mathcal{O}\in\\{0,1\\}^{|\mathcal{U}|\times|\mathcal{V}|}$ be the
interaction matrix, where a cell $o_{u,v}=1$ indicates the observed
interaction of user $u\in\mathcal{U}$ with item $v\in\mathcal{V}$, and the
$u$th row $\mathcal{O}_{u,*}$ represents the historical user-item interaction
set of user $u$. Let $\mathcal{A}$ be the user attribute matrix of
$|\mathcal{U}|\times M$, where $M$ is the number of the attributes of a user,
and the cell at $u$th row and $i$th column, $a_{u,i}$, is the $i$th attribute
of user $u$.

###  2.2. Formulation of the Target Problem

Let $y_{u,v}=R(\mathbf{u},\mathbf{v})$ be a given recommendation model, which
infers the probability $y_{u,v}$ that user $u\in\mathcal{U}$ will interact
with item $v\in\mathcal{V}$ based on the user embedding
$\mathbf{u}\in\mathbb{R}^{d\times 1}$ and the item embedding
$\mathbf{v}\in\mathbb{R}^{d\times 1}$, where $d$ is the embedding
dimensionality. Let $\mathbf{s}_{u}\in\\{0,1\\}^{Md\times 1}$ representing the
fairness requirement of user $u$, where the $i$th piece
$\mathbf{s}_{u,[1+(i-1)d:i\times d]}=0$ means the $i$th attribute is a
sensitive attribute of user $u$, otherwise a non-sensitive attribute. The
target problem can be formulated as follow:

Given an unfair recommendation model $R$, the original user embeddings
$\\{\mathbf{u}\\}$ and item embeddings $\\{\mathbf{v}\\}$ generated by $R$,
the historical interaction matrix $\mathcal{O}$, and the user attribute matrix
$\mathcal{A}$, we want to train a fair model $FairR$ to generate the fair user
embedding $\mathbf{u}^{*}$ for user $u$ based on $u$’s original embedding
$\mathbf{u}$ and fairness requirement $\mathbf{s}_{u}$, i.e.,
$\mathbf{u}^{*}=FairR(\mathbf{u},\mathbf{s}_{u})$.

###  2.3. Counterfactual Fairness

In this paper, the recommendations made based on $\mathbf{u}^{*}$ are supposed
to be independent of the user’s sensitive attributes specified by
$\mathbf{s}_{u}$, which is a kind of counterfactual fairness (Kusner et al.,
2017). Intuitively, counterfactual fairness requires the recommendations made
in the imaginary counterfactual world, where only the user’s sensitive
attributes are modified, should be the same as in the real world. The formal
definition of counterfactual fairness in recommender systems is provided as
follow:

###### Definition 0 (Counterfactually fair recommendation (Li et al., 2021b)).

A recommender model is counterfactually fair if for any possible user with
non-sensitive attributes $A_{n}=a_{n}$ and sensitive attributes $A_{s}=a_{s}$:

$P\left(Y_{a_{s}}\middle|A_{n}=a_{n},A_{s}=a_{s}\right)=P\left(Y_{a_{s}^{\prime}}|A_{n}=a_{n},A_{s}=a_{s}\right)$

for all $Y$ and for any value $a_{s}$ attainable by $A_{s}$, where $Y$ denotes
the generated recommendation results.

##  3\. The Proposed Model

###  3.1. Overview

Fig. 1 gives an overview of the architecture of AFRL. As shown in Fig. 1, AFRL
takes as inputs the original user embedding $\mathbf{u}$ and the personalized
fairness requirement $\mathbf{s}_{u}$, and produces the fair embedding
$\mathbf{u}^{*}$. We can see that AFRL consists of two modules, the
Information Alignment Module (IAlignM) and the Information Aggregation Module
(IAggM). IAlignM is responsible for learning $M$ attribute-specific embeddings
$\\{\mathbf{z}_{u,i}\\}$ and one debiased collaborative embedding
$\mathbf{z}_{u,0}$ from the original user embedding $\mathbf{u}$ via $M$
attribute encoders $\\{E_{i}\\}$ ($1\leq i\leq M$) and a debiased
collaborative signal encoder $F$, respectively. In particular, to ensure the
information alignment between $\mathbf{z}_{u,i}$ and the $i$th attribute
$a_{u,i}$ of user $u$, IAlignM will maximize the mutual information between
$\mathbf{z}_{u,i}$ and $a_{u,i}$, and minimize the mutual information between
$\mathbf{z}_{u,i}$ and $\mathbf{u}$, using a bilevel optimization for
attribute encoder $E_{i}$ together with the auxiliary attribute classifier
$C_{i}$. At the same time, to generate the debiased collaborative embedding
$\mathbf{z}_{u,0}$, IAlignM will ensure $F$ to remove the correlation between
$\mathbf{z}_{u,0}$ and the user attributes via an adversarial training
together with $M$ attribute discriminators $\\{D_{i}\\}$ ($1\leq i\leq M$),
and encode the collaborative signals by maximizing the ability of
$\mathbf{z}_{u,0}$ to reconstruct the original user embedding $\mathbf{u}$.

Once the attribute-specific embeddings and the debiased collaborative
embedding are produced, IAggM will mask the embeddings of sensitive attributes
with respect to $\mathbf{s}_{u}$ and fuse the embeddings of non-sensitive
attributes with the debiased collaborative embedding using an MLP $G$ to
generate the fair embedding $\mathbf{u}^{*}$. To make $\mathbf{u}^{*}$ legal
for the given recommendation model $R$, the training of IAggM will be
supervised by the historical interactions $\mathcal{O}$ through $R$, which
locates $\mathbf{u}^{*}$ in the same embedding space as the original user
embedding $\mathbf{u}$. Finally, $\mathbf{u}^{*}$ and the item embedding
$\mathbf{v}$ are fed to $R$ to make a fair prediction of $y_{u,v}$.

###  3.2. Information Alignment Module

As mentioned before, IAlignM learns attribute-specific embeddings
$\\{\mathbf{z}_{u,1},$ $\cdots,\mathbf{z}_{u,M}\\}$ and debiased collaborative
embedding $\mathbf{z}_{u,0}$ from the original user embedding $\mathbf{u}$.
Since $\mathbf{u}$ is generated by the given recommendation model $R$, it is
reasonable to assume that $\mathbf{u}$ has encoded the attribute information
and the collaborative signals of user $u$ in an entangling and biased way.

(a) Larger $\beta$

(b) Smaller $\beta$

(c) Ideal $\beta$

Figure 2. Illustration of the attribute-specific embedding learning for
Information Alignment, where (a) and (b) are the cases of information
misalignment, while (c) is the optimal case of information alignment.

####  3.2.1. Attribute-Specific Embedding

The attribute-specific embedding $\mathbf{z}_{u,i}$ of the $i$th attribute of
user $u$ is extracted by the attribute encoder $E_{i}$ from the original user
embedding $\mathbf{u}$, $1\leq i\leq M$, i.e.,

(1) $\mathbf{z}_{u,i}=E_{i}(\mathbf{u}).$

To achieve information alignment, our objective is to make $E_{i}$ able to
encode and only encode the complete information of the $i$th attribute of
users. Since $E_{i}$ is shared by all users, the output of $E_{i}$ can be
represented by a stochastic variable $Z_{i}$ with various values
$\\{\mathbf{z}_{u,i}|u\in\mathcal{U}\\}$. Meanwhile, let $A_{i}$ be the
stochastic variable representing the $i$th column of the user attribute matrix
$\mathcal{A}$, of which the values are $\\{a_{u,i}|u\in\mathcal{U}\\}$, and
let $U$ be the stochastic variable representing different user embeddings
$\\{\mathbf{u}\\}$. Obviously, $Z_{i}=E_{i}(U)$. In the light of the
information bottleneck principle (Shwartz-Ziv and Tishby, 2017), the
optimization objective of $E_{i}$ is to maximize the mutual information
between $Z_{i}$ and $A_{i}$, and simultaneously minimize that between $Z_{i}$
and $U$, i.e.,

(2) $\min_{E_{i}}-I(Z_{i};A_{i})+{\beta}I(Z_{i};U),$

where $I(\cdot,\cdot)$ is mutual information function, $\beta$ is a balance
factor to control the amount of information from $U$ encoded by $Z_{i}$.

Fig. 2 illustrates the insight of the attribute-specific embedding learning
for information alignment defined by Equation (2), where cycle areas represent
the information content of corresponding variables. We can see that the amount
of the information encoded in $Z_{i}$ can be regularized by $\beta$.
Particularly, as shown in Figs. 2(a) and 2(b), the smaller the $\beta$, the
more information about $U$ covered by $Z_{i}$. Ideally, by regularizing
$\beta$, the optimal solution $E_{i}$ to Equation (2) will cause that the area
of $Z_{i}$ exactly overlaps with the area of $A_{i}$, as shown in Fig. 2(c).
At this ideal time, (1) $Z_{i}$ covers the information of $A_{i}$, which makes
the discriminative information of $A_{i}$ be reserved completely in $Z_{i}$;
(2) $Z_{i}$ only covers the information of $A_{i}$, which is favorable to
fairness since the correlation between $Z_{i}$ and other attributes is reduced
to minimum. In sharp contrast, the existing works pursue extreme fairness by
completely removing the information of sensitive attributes, which will result
in information about $A_{i}$ not being preserved intact if it is a non-
sensitive attribute, because the parts of it that overlap with sensitive
information are also removed. As we will see later in the experiments, exactly
preserving the information of non-sensitive attributes, including the parts
overlapping with the information of sensitive attributes, will increase the
discriminability of the fair embeddings without loss of fairness, which helps
AFRL achieve a better trade-off between fairness and accuracy.

However, the evaluation of mutual information is difficult. To overcome this
challenge, we adopt different strategies to approximately maximize
$I(Z_{i};A_{i})$ and minimize $I(Z_{i};U)$, respectively.

(1) The minimization of $\boldsymbol{I(Z_{i};U)}$ At first, the definition of
$I(Z_{i};U)$ is

(3) $\displaystyle I(Z_{i};U)=\mathbb{E}_{(\mathbf{z}_{u,i},\mathbf{u})\sim
p(Z_{i},U)}\bigg{[}\log{\frac{p(\mathbf{z}_{u,i}|\mathbf{u})}{p(\mathbf{z}_{u,i})}}\bigg{]}.$

As previous works did (Liang et al., 2018; Liu et al., 2021), we first assume
$p(\mathbf{z}_{u,i})$ $\sim$ $\mathcal{N}(0,\mathbf{I})$. To make Equation (3)
tractable, our idea is to view the output of $E_{i}$ as a sample from a
special Gaussian distribution with 0 variance, i.e.,
$p(\mathbf{z}_{u,i}|\mathbf{u})$ $\sim$ $\mathcal{N}(\boldsymbol{\mu}_{u},0)$.
Then the optimal $E_{i}$ is

(4)
$\displaystyle\operatorname*{argmin}_{E_{i}}I(Z_{i};U)=\mathbb{E}_{\mathbf{u}\sim
p(U)}\frac{1}{2}{\|\boldsymbol{\mu}_{u}}\|_{2}^{2},$

where $\boldsymbol{\mu}_{u}=\mathbf{z}_{u,i}=E_{i}(\mathbf{u})$ and the
expectation can be evaluated via Monte Carlo method.

(2) The maximization of $\boldsymbol{I(Z_{i};A_{i})}$ The definition of
$I(Z_{i};A_{i})$ is

(5) $I(Z_{i};A_{i})=\mathbb{E}_{(\mathbf{z}_{u,i},a_{u,i})\sim
p(Z_{i},A_{i})}\bigg{[}\log{\frac{p(a_{u,i}|\mathbf{z}_{u,i})}{p(a_{u,i})}}\bigg{]},$

where $a_{u,i}$ represents the value of the $i$th attribute of a user $u$, and
$p(a_{u,i})$ and $p(a_{u,i}|\mathbf{z}_{u,i})$ are the priori and posterior
probabilities of $a_{u,i}$, respectively. Since $p(a_{u,i}|\mathbf{z}_{u,i})$
is intractable, we introduce the predicted probability
$q(a_{u,i}|\mathbf{z}_{u,i};C_{i})$ offered by the classifier $C_{i}$:

(6) $\displaystyle I(Z_{i};A_{i})$
$\displaystyle=\mathbb{E}_{(\mathbf{z}_{u,i},a_{u,i})\sim
p(Z_{i},A_{i})}\bigg{[}\log{\frac{p(a_{u,i}|\mathbf{z}_{u,i})q(a_{u,i}|\mathbf{z}_{u,i};C_{i})}{p(a_{u,i})q(a_{u,i}|\mathbf{z}_{u,i};C_{i})}}\bigg{]}$
$\displaystyle=\Phi(Z_{i},C_{i})+\Delta(Z_{i},C_{i}),$

where

(7) $\displaystyle\Phi(Z_{i},C_{i})$
$\displaystyle=\mathbb{E}_{(\mathbf{z}_{u,i},a_{u,i})\sim
p(Z_{i},A_{i})}\bigg{[}\log{\frac{q(a_{u,i}|\mathbf{z}_{u,i};C_{i})}{p(a_{u,i})}}\bigg{]},$
$\displaystyle\Delta(Z_{i},C_{i})$
$\displaystyle=\mathbb{E}_{\mathbf{z}_{u,i}\sim
p(Z_{i})}\big{[}\text{KL}\big{(}p(a_{u,i}|\mathbf{z}_{u,i})\|{q(a_{u,i}|\mathbf{z}_{u,i};C_{i})\big{)}}\big{]}.$

To maximize $I(Z_{i};A_{i})$, we borrow the idea of EM algorithm to
iteratively update $C_{i}$ and $Z_{i}$, i.e., at $t+1$ time step,

(8)
$C_{i}^{t+1}=\operatorname*{argmin}_{C_{i}^{t}}\Delta(Z_{i}^{t},C_{i}^{t}),$
(9)
$Z_{i}^{t+1}=\operatorname*{argmax}_{Z_{i}^{t}}\Phi(Z_{i}^{t},C_{i}^{t+1}).$

By some simple derivations, it is easy to know Equation (8) is equivalent to

(10)
$C_{i}^{t+1}=\operatorname*{argmin}_{C_{i}}\mathbb{E}_{(\mathbf{z}_{u,i},a_{u,i})\sim
p(Z_{i}^{t},A_{i})}[-\log{q(a_{u,i}|\mathbf{z}_{u,i};C_{i})}],\ $

and Equation (9) is equivalent to

(11)
$Z_{i}^{t+1}=\operatorname*{argmin}_{Z_{i}^{t}}\mathbb{E}_{(\mathbf{z}_{u,i},a_{u,i})\sim
p(Z_{i}^{t},A_{i})}[-\log{q(a_{u,i}|\mathbf{z}_{u,i};C_{i}^{t+1})}].$

By combining Equations (4),(10) and (11), and considering $Z_{i}$ is updated
through $E_{i}$ since $Z_{i}=E_{i}(U)$, we can obtain the following bilevel
optimization objective of the attribute encoders:

(12) $\displaystyle\min_{E_{i}}\min_{C_{i}}$
$\displaystyle\mathbb{E}_{\mathbf{u}\sim
p(U)}\frac{1}{2}{\|\mathbf{z}_{u,i}}\|_{2}^{2}$
$\displaystyle+\beta\mathbb{E}_{(\mathbf{z}_{u,i},a_{u,i})\sim
p(Z_{i},A_{i})}[-\log{q(a_{u,i}|\mathbf{z}_{u,i};C_{i})}].$

At the same time, note that the sampling process
$(\mathbf{z}_{u,i},a_{u,i})\sim p(Z_{i},A_{i})$ is fulfilled by first sampling
a user’s embedding $\mathbf{u}\sim p(U)$ and then obtaining
$(\mathbf{z}_{u,i}=E_{i}(\mathbf{u}),a_{u,i})$. Hence the sampling in the
second term in Equation (12) can be equivalently changed to be the same as
that in the first term, which leads to the following equivalent tractable
bilevel optimization:

(13) $\min_{E_{i}}\min_{C_{i}}\mathbb{E}_{\mathbf{u}\sim
p(U)}\bigg{[}\frac{1}{2}{\|\mathbf{z}_{u,i}}\|_{2}^{2}-\beta\log{q(a_{u,i}|\mathbf{z}_{u,i};C_{i})}\bigg{]}.$

####  3.2.2. Debiased Collaborative Embedding

As mentioned before, the original unfair user embedding $\mathbf{u}$ provided
by the given unfair recommendation model $R$ has encoded the collaborative
signals biased to user attributes. IAlignM employs a debiased collaborative
signal encoder $F$ to generate the debiased collaborative embedding
$\mathbf{z}_{u,0}$ to capture from $\mathbf{u}$ the collaborative signals
independent of user attributes. For this purpose, we optimize $F$ with two
objectives: (1) minimizing the discriminability of $\mathbf{z}_{u,0}$ to user
attributes for fairness, and (2) maximizing the information of $\mathbf{u}$
encoded in $\mathbf{z}_{u,0}$ to preserve the collaborative signals as much as
possible for recommendation accuracy.

To achieve the objective (1), we introduce a discriminator $D_{i}$ for $i$th
attribute, $1\leq i\leq M$, and adjust $F$ to fool $D_{i}$ with the following
adversarial training between $F$ and $D_{i}$:

(14) $\min_{F}\max_{D_{i}}-\mathbb{E}_{\mathbf{u}\sim
p(U)}\sum_{i=1}^{M}{\left[-\log{q(a_{u,i}|\mathbf{z}_{u,0};D_{i})}\right]},$

where $q(a_{u,i}|\mathbf{z}_{u,0};D_{i})$ is the probability that
$\mathbf{z}_{u,0}$ is classified as $a_{u,i}$ by $D_{i}$.

To achieve the objective (2), we minimize the following reconstruction loss:

(15) $\min_{F}\mathbb{E}_{\mathbf{u}\sim
p(U)}\|\mathbf{z}_{u,0}-\mathbf{u}\|_{2}^{2}.\\\ $

By combining Equations (14) and (15), we obtain the following optimization
objective of $F$:

(16) $\displaystyle\min_{F}\max_{D_{i}}\mathbb{E}_{\mathbf{u}\sim
p(U)}\|\mathbf{z_{u,0}-\mathbf{u}}\|_{2}^{2}-\lambda\sum_{i=1}^{M}{\left[-\log{q(a_{u,i}|\mathbf{z}_{u,0};D_{i})}\right]},$

where $\lambda$ controls the trade-off between recommendation accuracy and
fairness.

###  3.3. Information Aggregation Module

After obtaining attribute-specific embeddings $\\{\mathbf{z}_{u,i}\\}$ ($1\leq
i\leq M$) and the debiased collaborative embedding $\mathbf{z}_{u,0}$, the
Information Aggregation Module (IAggM), which is implemented as an MLP $G$,
combines these embeddings based on the personalized fairness requirement
$\mathbf{s}_{u}$ to produce the final fair embedding $\mathbf{u}^{*}$ as
follow:

(17)
$\mathbf{u}^{*}=G\bigg{\\{}\mathbf{z}_{u,0}\oplus\big{[}(\mathbf{z}_{u,1}\oplus\ldots\oplus\mathbf{z}_{u,M})\odot\mathbf{s}_{u}\big{]}\bigg{\\}},$

where $\oplus$ represents concatenation, $\odot$ represents element-wise
product, and $\mathbf{s}_{u}\in\\{0,1\\}^{Md\times 1}$ represents the fairness
requirement of user $u$. The $i$th part $\mathbf{s}_{u,[1+(i-1)d:i\times
d]}=0$ means the $i$th attribute is a sensitive attribute of user $u$,
otherwise a non-sensitive attribute.

To ensure $\mathbf{u}^{*}$ to be compatibility with the original
recommendation model $R$, $G$ will be adjusted with respect to the supervision
offered by $R$ as follow:

(18) $\min_{G}-\sum_{(u,v^{+},v^{-})}{\ln{\sigma(y_{u,v^{+}}-y_{u,v^{-}})}},$

where $v^{+}$ and $v^{-}$ are a positive example and a negative example of
$u$, respectively, $\sigma(\cdot)$ is the sigmoid function, and
$y_{u,v}=R(\mathbf{u}^{*},\mathbf{v})$. Note that Equation (18) is a function
of $G$ rather than $R$, which means it is $G$ that will be adjusted during the
optimization of Equation (18) with fixed $R$. Algorithm 1 gives the training
process of AFRL.

Algorithm 1 Training of AFRL

0: user-item interaction matrix $\mathcal{O}$, user attribute matrxi
$\mathcal{A}$, unfair recommendation model $R$, and the set of original user
embeddings $U$ and item embeddings $V$ generated by $R$;

0: $F$, $\\{E_{i}\\}$ ($1\leq i\leq M$), and $G$;

1: Randomly initialize $F$, $\\{D_{i}\\}$, $\\{E_{i}\\}$, $\\{C_{i}\\}$ and
$G$, $1\leq i\leq M$;

2: for $1$ to $T$ do

3: for each $\mathbf{u}\in U$ do

4: obtain $\mathbf{z}_{u,0}=F(\mathbf{u})$ and
$\\{\mathbf{z}_{u,i}=E_{i}(\mathbf{u})\\}$;

5: randomly sample an $\mathbf{s}_{u}$ from a uniform distribution over
different attribute combinations;

6: obtain $\mathbf{u}^{*}$ by Equation (17);

7: update $\\{C_{i}\\}$ by inner minimization of Equation (13);

8: update $\\{E_{i}\\}$ by outer minimization of Equation (13);

9: update $\\{D_{i}\\}$ by inner maximization of Equation (16);

10: update $F$ by outer minimization of Equation (16);

11: update G by Equation (18).

12: end for

13: end for

###  3.4. Theoretical Justification

####  3.4.1. Convergence Analysis

Now we analyze the convergence of the optimization of Equation (13), which is
the tractable approximation of Equation (2) to realize the information
alignment. At first, it is easy to see that $I(Z_{i};U)$ will achieve its
minimum as defined in Equation (4). So, we only justify the iterative
optimization defined Equations (8), (9) will lead to the maximum of
$I(Z_{i};A_{i})$, which equivalently to prove
$I(Z_{i}^{t+1};A_{i})-I(Z_{i}^{t};A_{i})\geq 0$. At first, according to
Equation (6), we can obtain

(19) $\displaystyle I(Z_{i}^{t+1},A_{i})-I(Z_{i}^{t},A_{i})$ $\displaystyle=$
$\displaystyle\underbrace{\Phi(Z_{i}^{t+1},C_{i})-\Phi(Z_{i}^{t},C_{i})}_{A}+\underbrace{\Delta(Z_{i}^{t+1},C_{i})-\Delta(Z_{i}^{t},C_{i})}_{B}.$

By taking a close look at Equation (6), we can observe that $I(Z_{i},A_{i})$
is independent of $C_{i}$. Based on this observation, we can set $C_{i}$ to
the optimal
$C_{i}^{t+1}=\operatorname*{argmin}_{C_{i}^{t}}\Delta(Z_{i}^{t},C_{i}^{t})$
(Equation (8)) without changing $I(Z_{i},A_{i})$, which gives:

(20) $\displaystyle I(Z_{i}^{t+1},A_{i})-I(Z_{i}^{t},A_{i})$ $\displaystyle=$
$\displaystyle\underbrace{\Phi(Z_{i}^{t+1},C^{t+1}_{i})-\Phi(Z_{i}^{t},C^{t+1}_{i})}_{A}+\underbrace{\Delta(Z_{i}^{t+1},C^{t+1}_{i})-\Delta(Z_{i}^{t},C^{t+1}_{i})}_{B}.$

Since $\Delta$ is a KL-divergence, the optimal $C_{i}^{t+1}$ makes
$\Delta(Z_{i}^{t}$, $C^{t+1}_{i})$ $=0$, and hence
$B=\Delta(Z_{i}^{t+1},C^{t+1}_{i})\geq 0$. At the same time, since
$Z_{i}^{t+1}$ maximizes $\Phi(Z_{i}^{t},C^{t+1}_{i})$ (see Equation (9)),
$\Phi(Z_{i}^{t+1}$, $C^{t+1}_{i})$ $\geq\Phi(Z_{i}^{t},C^{t+1}_{i})$, i.e.,
$A\geq 0$. Thus $I(Z_{i}^{t+1},A_{i})-I(Z_{i}^{t},A_{i})\geq 0$ holds.

####  3.4.2. Informativeness Analysis

Now we show that AFRL completely extracts the information of a non-sensitive
attribute into the fair embedding. Without loss of generality, let $A_{n}$,
$Z_{n}$, $U$, and $U^{*}$ be the stochastic variables representing a non-
sensitive attribute, the embedding of $A_{n}$, the original user embedding,
and the fair user embedding, respectively, $1\leq i\leq M$. Obviously, the
information encoded by $U$ can be divided into two parts:
$H(U)=I(U;A_{n})+H(U|A_{n})$, where $I(U;A_{n})$ is the part relevant to
$A_{n}$. We want to prove $U^{*}$ completely encodes $I(U;A_{n})$, which is
equal to proving $I(A_{n};U|U^{*})=0$.

In terms of the theory of information bottleneck (Shwartz-Ziv and Tishby,
2017), AFRL can be framed as a Markov Chain $A_{n}\rightarrow U\rightarrow
Z_{n}\rightarrow U^{*}$. Suppose the attribute encoder $E_{n}$ is the optimal
solution to the bilevel optimization defined in Equation (13), which means
$Z_{n}=E_{n}(U)$ completely encodes the $A_{n}$’s information from $U$, and
equivalently, $I(A_{n};U|Z_{n})=0$. Considering
$I(A_{n};U|Z_{n})=I(A_{n};U)-I(U;A_{n};Z_{n})=I(A_{n};U)-I(A_{n};Z_{n})$, we
have

(21) $I(A_{n};U)=I(A_{n};Z_{n}).$

Let $Z_{s}$ be the stochastic variable representing the embeddings of
sensitive attributes, and due to the Markov Chain $Z_{s}\leftarrow
U\rightarrow Z_{n}$, $Z_{n}$ and $Z_{s}$ are conditional independent, i.e.,
$Z_{n}\perp Z_{s}|U$. Meanwhile, the variable of debiased collaborative
embedding, $Z_{0}$, is optimized to be independent of any $Z_{n}$. Therefore,
removing $Z_{s}$ from and incorporating $Z_{0}$ to $U^{*}$ will not affect the
mutual information between $Z_{n}$ and $U^{*}$, $I(Z_{n};U^{*})$. When $E_{n}$
and $G$ are both optimal, $I(Z_{n};U^{*})$ achieves maximum, which results in

(22) $H(Z_{n}|U^{*})=0.$

Based on Equations (21) and (22), we have the following derivations:

(23) $\displaystyle I(A_{n};U|U^{*})=$ $\displaystyle
I(A_{n};U)-I(A_{n};U;U^{*})$ $\displaystyle=$ $\displaystyle
I(A_{n};Z_{n})-\big{(}I(A_{n};U^{*})-I(A_{n};U^{*}|U)\big{)}$ $\displaystyle=$
$\displaystyle I(A_{n};Z_{n})-I(A_{n};U^{*})$ $\displaystyle=$ $\displaystyle
I(A_{n};Z_{n})-\big{(}I(A_{n};U^{*}|Z_{n})+I(A;U^{*};Z_{n})\big{)}$
$\displaystyle=$ $\displaystyle I(A_{n};Z_{n})-I(A_{n};U^{*};Z_{n})$
$\displaystyle=$ $\displaystyle
I(A_{n};Z_{n})-I(Z_{n};U^{*})+I(Z_{n};U^{*}|A_{n})$ $\displaystyle=$
$\displaystyle\big{(}H(Z_{n})-H(Z_{n}|A_{n})\big{)}-\big{(}H(Z_{n})-H(Z_{n}|U^{*})\big{)}$
$\displaystyle+\big{(}H(Z_{n}|A_{n})-H(Z_{n}|U^{*},A_{n})\big{)}$
$\displaystyle=$ $\displaystyle H(Z_{n}|U^{*})-H(Z_{n}|U^{*},A_{n})$
$\displaystyle=$ $\displaystyle-H(Z_{n}|U^{*},A_{n})\geq 0.$

Note that during the above derivations, $I(A_{n};U^{*}|U)$ and
$I(A_{n};U^{*}|Z_{n})$ are both equal to 0 because of the Markov Chain
$A_{n}\rightarrow U\rightarrow Z_{n}\rightarrow U^{*}$. At the same time,
since entropy is non-negative, we also have $-H(Z_{n}|U^{*},A_{n})\leq 0$, and
thus $H(Z_{n}|U^{*},A_{n})=0$, and consequently $I(A_{n};U|U^{*})=0$.

##  4\. experiments

The experiments are designed to address the following research questions:

  * •

RQ1 How does AFRL perform as compared to the state-of-the-art models?

  * •

RQ2 How does AFRL make trade-off between fairness and accuracy as compared to
the state-of-the-art models?

  * •

RQ3 How do the attribute-specific embeddings and the debiased collaborative
embedding contribute to the performance of AFRL?

  * •

RQ4 How do the hyper-parameters affect the performance of AFRL?

###  4.1. Experimental Settings

####  4.1.1. Datasets.

We evaluate AFRL on two datasets:

  * •

MovieLens-1M111https://grouplens.org/datasets/movielens/ (ML-1M) This dataset
consists of 1,000,000 movie ratings provided by 6,040 users with attributes G
(Gender), A (Age) and O (Occupation). For simplicity, we convert the ratings
into binary values, where ratings not less than 4 are set to 1, while the rest
are set to 0.

  * •

Taobao Display Ad Click222https://tianchi.aliyun.com/dataset/56 (Taobao) This
dataset comprises more than 26,000,000 interactions between 1,140,000 users
and 840,000 advertisements on Taobao website. A user in Taobao is associated
with attributes G (Gender), A (Age), and C (Consumption level).

For each dataset, we remove the users with less than 10 instances. We generate
interaction sequences for a user with sliding window sizes 100 and 50 on ML-1M
and Taobao, respectively. As previous work did (Wu et al., 2022), for each
user, we choose the most recent sequence as a testing instance and the second
most recent sequence as a validation instance.

Table 1. Hyper-parameter setting of AFRL

$\mathbb{Method}$ |  $\mathbb{\beta\ is\ selected\ from}$ $\mathbb{\\{0.001,0.01,0.1,1,10,100\\}}$ |  $\mathbb{\lambda\ is\ selected\ from}$ $\mathbb{\\{0.001,0.01,0.1,1,10,100\\}}$
---|---|---
ML-1M | Taobao | ML-1M | Taobao
AFRL+PMF | 0.1 | 1 | 0.1 | 10
AFRL+DeepModel | 0.1 | 1 | 0.1 | 1
AFRL+SASRec | 1 | 1 | 1 | 10
AFRL+BERT4Rec | 1 | 1 | 1 | 10

####  4.1.2. Baselines

We will compare AFRL with following three state-of-the-art models for
personalized fairness in recommendations:

  * •

SM (Li et al., 2021b) To meet personalized fairness in recommendations, SM
trains a attribute filter for each possible combination of sensitive
attributes.

  * •

PFRec (Wu et al., 2022) PFRec builds a set of prompt-based bias eliminators
and adapters with predefined attribute-specific prompts to learn fair
representations for different attribute combinations.

  * •

FFVAE (Creager et al., 2019) FFVAE disentangles an unfair embedding into
latent factors, each of which corresponds to an attribute, and excludes
relevant sensitive latent factors based on different fairness requirements of
users.

We will check the performance of AFRL and the baseline models in combination
with the following four base recommendation models, including two non-
sequential models PMF (Mnih and Salakhutdinov, 2007) and DeepModel (Cheng et
al., 2016), and two sequential models SASRec (Kang and McAuley, 2018) and
BERT4Rec (Sun et al., 2019).

####  4.1.3. Evaluation Protocols.

We evaluate the accuracy of top-$N$ recommendations with two popular metrics
Normalized Discounted Cumulative Gain (N@$10$) and Hit rate (H@$10$).
Following the idea in (Kang and McAuley, 2018; Sun et al., 2019; Wu et al.,
2022), we sample 1 and 99 negative examples for a positive example during
training and testing, respectively. To evaluate the fairness, following the
popular method used in the existing works (Li et al., 2021b; Hua et al.,
2023), we first train a surrogate classifier for each attribute using the fair
embeddings generated by AFRL and the baseline models, respectively, and report
the average AUC over all classifiers as the fairness metric. The closer to 0.5
AUC, the better fairness.

Table 2.  Fairness (AUC) and Accuracy (N@10, H@10) comparison on ML-1M. A
fairness requirement is represented by an attribute combination where each
attribute is assumed to be sensitive to users. For instance, G+A+O represents
Gender, Age and Occupation are sensitive attributes. The best runs per metric
are marked in boldface.

$\mathbb{Method}$ | $\mathbb{Fairness\ Requirement}$
---|---
$\mathbb{G}$ | $\mathbb{A}$ | $\mathbb{O}$ | $\mathbb{G+A}$ | $\mathbb{G+O}$ | $\mathbb{A+O}$ | $\mathbb{G+A+O}$
AUC$\downarrow$ | N@10$\uparrow$ | H@10$\uparrow$ | AUC$\downarrow$ | N@10$\uparrow$ | H@10$\uparrow$ | AUC$\downarrow$ | N@10$\uparrow$ | H@10$\uparrow$ | AUC$\downarrow$ | N@10$\uparrow$ | H@10$\uparrow$ | AUC$\downarrow$ | N@10$\uparrow$ | H@10$\uparrow$ | AUC$\downarrow$ | N@10$\uparrow$ | H@10$\uparrow$ | AUC$\downarrow$ | N@10$\uparrow$ | H@10$\uparrow$
PMF | 0.7890 | 0.4157 | 0.6918 | 0.7908 | 0.4157 | 0.6918 | 0.6703 | 0.4157 | 0.6918 | 0.7863 | 0.4157 | 0.6918 | 0.7211 | 0.4157 | 0.6918 | 0.7220 | 0.4157 | 0.6918 | 0.7438 | 0.4157 | 0.6918
SM+PMF | 0.6547 | 0.3733 | 0.6492 | 0.6394 | 0.3739 | 0.6496 | 0.5703 | 0.3690 | 0.6467 | 0.6382 | 0.3703 | 0.6471 | 0.5890 | 0.3711 | 0.6498 | 0.5828 | 0.3682 | 0.6440 | 0.5915 | 0.3699 | 0.6464
FFVAE+PMF | 0.6433 | 0.3122 | 0.5625 | 0.6843 | 0.2993 | 0.5409 | 0.6036 | 0.2772 | 0.5048 | 0.7261 | 0.2979 | 0.5418 | 0.6553 | 0.2765 | 0.5034 | 0.6258 | 0.2684 | 0.4874 | 0.6394 | 0.2664 | 0.4844
AFRL+PMF | 0.5310 | 0.3944 | 0.6707 | 0.5238 | 0.3908 | 0.6655 | 0.5112 | 0.3945 | 0.6729 | 0.5274 | 0.3884 | 0.6622 | 0.5211 | 0.3915 | 0.6669 | 0.5175 | 0.3881 | 0.6601 | 0.5220 | 0.3846 | 0.6555
DeepModel | 0.7656 | 0.3683 | 0.6397 | 0.7365 | 0.3683 | 0.6397 | 0.6542 | 0.3683 | 0.6397 | 0.7589 | 0.3683 | 0.6397 | 0.7113 | 0.3683 | 0.6397 | 0.6876 | 0.3683 | 0.6397 | 0.7202 | 0.3683 | 0.6397
SM+DeepModel | 0.6529 | 0.3403 | 0.6063 | 0.6319 | 0.3346 | 0.6047 | 0.5709 | 0.3356 | 0.6009 | 0.6495 | 0.3299 | 0.5949 | 0.6169 | 0.3314 | 0.5952 | 0.6024 | 0.3263 | 0.5906 | 0.6158 | 0.3205 | 0.5802
FFVAE+DeepModel | 0.6289 | 0.2981 | 0.5204 | 0.6491 | 0.2954 | 0.5137 | 0.5000 | 0.2955 | 0.5145 | 0.6258 | 0.2957 | 0.5125 | 0.5647 | 0.2925 | 0.5095 | 0.5000 | 0.2928 | 0.509 | 0.5798 | 0.2902 | 0.5029
AFRL+DeepModel | 0.5358 | 0.3504 | 0.6151 | 0.5018 | 0.3474 | 0.6103 | 0.5231 | 0.3525 | 0.6202 | 0.5188 | 0.3430 | 0.6024 | 0.5295 | 0.3471 | 0.6108 | 0.5125 | 0.3438 | 0.6050 | 0.5203 | 0.3377 | 0.5921
SASRec | 0.7554 | 0.5709 | 0.8103 | 0.7259 | 0.5709 | 0.8103 | 0.6143 | 0.5709 | 0.8103 | 0.7284 | 0.5709 | 0.8103 | 0.6879 | 0.5709 | 0.8103 | 0.6634 | 0.5709 | 0.8103 | 0.6883 | 0.5709 | 0.8103
SM+SASRec | 0.6366 | 0.4808 | 0.7474 | 0.6183 | 0.4792 | 0.7447 | 0.5917 | 0.4803 | 0.7454 | 0.6021 | 0.4790 | 0.7427 | 0.5947 | 0.4813 | 0.7486 | 0.5968 | 0.4773 | 0.7378 | 0.6229 | 0.4746 | 0.7382
PFRec+SASRec | 0.5179 | 0.4784 | 0.7418 | 0.5159 | 0.4684 | 0.7341 | 0.5288 | 0.4499 | 0.7044 | 0.5146 | 0.4420 | 0.7002 | 0.5179 | 0.4478 | 0.7069 | 0.5073 | 0.3798 | 0.5825 | 0.5173 | 0.4187 | 0.6830
FFVAE+SASRec | 0.5677 | 0.4190 | 0.6585 | 0.6540 | 0.4035 | 0.6376 | 0.6029 | 0.3728 | 0.5995 | 0.6433 | 0.4027 | 0.6383 | 0.6513 | 0.3727 | 0.5966 | 0.5631 | 0.3598 | 0.5785 | 0.5962 | 0.3614 | 0.5829
AFRL+SASRec | 0.5543 | 0.5571 | 0.7980 | 0.5346 | 0.5543 | 0.7953 | 0.5200 | 0.5595 | 0.7982 | 0.5445 | 0.5518 | 0.7945 | 0.5372 | 0.5559 | 0.7953 | 0.5273 | 0.5526 | 0.7934 | 0.5463 | 0.5493 | 0.7903
BERT4Rec | 0.7257 | 0.5657 | 0.8103 | 0.6946 | 0.5657 | 0.8103 | 0.6331 | 0.5657 | 0.8103 | 0.7171 | 0.5657 | 0.8103 | 0.6894 | 0.5657 | 0.8103 | 0.6686 | 0.5657 | 0.8103 | 0.6922 | 0.5657 | 0.8103
SM+BERT4Rec | 0.5485 | 0.4764 | 0.7393 | 0.5674 | 0.4731 | 0.7370 | 0.5668 | 0.4744 | 0.7373 | 0.6200 | 0.4660 | 0.7297 | 0.6007 | 0.4702 | 0.7299 | 0.6112 | 0.4587 | 0.7244 | 0.6063 | 0.4606 | 0.7235
PFRec+BERT4Rec | 0.5258 | 0.4875 | 0.7400 | 0.5147 | 0.4576 | 0.7113 | 0.5277 | 0.4699 | 0.7183 | 0.5351 | 0.4438 | 0.6963 | 0.5139 | 0.4510 | 0.7037 | 0.5179 | 0.3868 | 0.5936 | 0.5278 | 0.4247 | 0.6765
FFVAE+BERT4Rec | 0.6506 | 0.4229 | 0.6790 | 0.5933 | 0.4090 | 0.6595 | 0.5963 | 0.3528 | 0.5817 | 0.6263 | 0.4080 | 0.6592 | 0.6018 | 0.3549 | 0.5850 | 0.5567 | 0.3431 | 0.5625 | 0.5765 | 0.3434 | 0.5691
AFRL+BERT4Rec | 0.5461 | 0.5390 | 0.7906 | 0.5066 | 0.5326 | 0.7830 | 0.5248 | 0.5405 | 0.7903 | 0.5264 | 0.5285 | 0.7798 | 0.5354 | 0.5381 | 0.7897 | 0.5157 | 0.5310 | 0.7817 | 0.5258 | 0.5207 | 0.7770

Table 3. Fairness and Accuracy comparison on Taobao.

$\mathbb{Method}$ | $\mathbb{Fairness\ Requirement}$
---|---
$\mathbb{G}$ | $\mathbb{A}$ | $\mathbb{C}$ | $\mathbb{G+A}$ | $\mathbb{G+C}$ | $\mathbb{A+C}$ | $\mathbb{G+A+C}$
AUC$\downarrow$ | N@10$\uparrow$ | H@10$\uparrow$ | AUC$\downarrow$ | N@10$\uparrow$ | H@10$\uparrow$ | AUC$\downarrow$ | N@10$\uparrow$ | H@10$\uparrow$ | AUC$\downarrow$ | N@10$\uparrow$ | H@10$\uparrow$ | AUC$\downarrow$ | N@10$\uparrow$ | H@10$\uparrow$ | AUC$\downarrow$ | N@10$\uparrow$ | H@10$\uparrow$ | AUC$\downarrow$ | N@10$\uparrow$ | H@10$\uparrow$
PMF | 0.7144 | 0.5329 | 0.7839 | 0.6872 | 0.5329 | 0.7839 | 0.6406 | 0.5329 | 0.7839 | 0.7007 | 0.5329 | 0.7839 | 0.6785 | 0.5329 | 0.7839 | 0.6707 | 0.5329 | 0.7839 | 0.6829 | 0.5329 | 0.7839
SM+PMF | 0.5979 | 0.4892 | 0.7420 | 0.5345 | 0.5001 | 0.7546 | 0.5577 | 0.4701 | 0.7270 | 0.5798 | 0.4811 | 0.7364 | 0.6089 | 0.4654 | 0.7271 | 0.5832 | 0.4538 | 0.7169 | 0.5783 | 0.4797 | 0.7313
FFVAE+PMF | 0.6867 | 0.4382 | 0.6939 | 0.6212 | 0.4209 | 0.6734 | 0.5360 | 0.3806 | 0.6068 | 0.6325 | 0.4168 | 0.6653 | 0.5767 | 0.3762 | 0.6032 | 0.5456 | 0.3783 | 0.6058 | 0.5722 | 0.3720 | 0.5983
AFRL+PMF | 0.5659 | 0.4998 | 0.7529 | 0.5443 | 0.4983 | 0.7521 | 0.5073 | 0.5014 | 0.7550 | 0.5551 | 0.4908 | 0.7445 | 0.5366 | 0.4943 | 0.7473 | 0.5258 | 0.4929 | 0.7469 | 0.5391 | 0.4856 | 0.7492
DeepModel | 0.6582 | 0.4972 | 0.7485 | 0.6016 | 0.4972 | 0.7485 | 0.5652 | 0.4972 | 0.7485 | 0.6301 | 0.4972 | 0.7485 | 0.6095 | 0.4972 | 0.7485 | 0.5835 | 0.4972 | 0.7485 | 0.6082 | 0.4972 | 0.7485
SM+DeepModel | 0.6057 | 0.4714 | 0.7244 | 0.5541 | 0.4734 | 0.7248 | 0.6066 | 0.4725 | 0.7237 | 0.5800 | 0.4715 | 0.7244 | 0.6010 | 0.4728 | 0.7256 | 0.5803 | 0.4723 | 0.7247 | 0.5845 | 0.4615 | 0.7136
FFVAE+DeepModel | 0.6221 | 0.4185 | 0.6624 | 0.6392 | 0.4158 | 0.6573 | 0.5175 | 0.3997 | 0.6304 | 0.6133 | 0.4166 | 0.6582 | 0.5441 | 0.4009 | 0.6331 | 0.5337 | 0.3990 | 0.6345 | 0.5447 | 0.4011 | 0.6336
AFRL+DeepModel | 0.5237 | 0.4879 | 0.7444 | 0.5335 | 0.4897 | 0.7389 | 0.5085 | 0.4894 | 0.7380 | 0.5310 | 0.4831 | 0.7303 | 0.5166 | 0.4828 | 0.7292 | 0.5204 | 0.4847 | 0.7359 | 0.5209 | 0.4801 | 0.7273
SASRec | 0.7080 | 0.5399 | 0.7888 | 0.6656 | 0.5399 | 0.7888 | 0.5591 | 0.5399 | 0.7888 | 0.6832 | 0.5399 | 0.7888 | 0.6264 | 0.5399 | 0.7888 | 0.6171 | 0.5399 | 0.7888 | 0.6418 | 0.5399 | 0.7888
SM+SASRec | 0.6305 | 0.4827 | 0.7346 | 0.5868 | 0.4889 | 0.7393 | 0.5762 | 0.4860 | 0.7373 | 0.6121 | 0.4845 | 0.7377 | 0.6042 | 0.4848 | 0.7377 | 0.5826 | 0.4841 | 0.7365 | 0.6011 | 0.4854 | 0.7379
PFRec+SASRec | 0.6160 | 0.4957 | 0.7478 | 0.6027 | 0.4848 | 0.7373 | 0.5373 | 0.4945 | 0.7457 | 0.6086 | 0.4808 | 0.7318 | 0.5703 | 0.4860 | 0.7380 | 0.5655 | 0.4851 | 0.7375 | 0.5789 | 0.4794 | 0.7314
FFVAE+SASRec | 0.6506 | 0.4429 | 0.6990 | 0.5933 | 0.4290 | 0.6795 | 0.5500 | 0.3728 | 0.6017 | 0.6000 | 0.4280 | 0.6792 | 0.5700 | 0.3749 | 0.6050 | 0.5567 | 0.3631 | 0.5825 | 0.5765 | 0.3634 | 0.5891
AFRL+SASRec | 0.5942 | 0.5266 | 0.7767 | 0.5699 | 0.5263 | 0.7765 | 0.5133 | 0.5271 | 0.7773 | 0.5821 | 0.5211 | 0.7712 | 0.5537 | 0.5216 | 0.7717 | 0.5416 | 0.5212 | 0.7714 | 0.5691 | 0.5161 | 0.7663
BERT4Rec | 0.7119 | 0.5417 | 0.7900 | 0.6752 | 0.5417 | 0.7900 | 0.5863 | 0.5417 | 0.7900 | 0.6895 | 0.5417 | 0.7900 | 0.6331 | 0.5417 | 0.7900 | 0.6282 | 0.5417 | 0.7900 | 0.6543 | 0.5417 | 0.7900
SM+BERT4Rec | 0.6305 | 0.4627 | 0.7246 | 0.5868 | 0.4689 | 0.7293 | 0.5762 | 0.4660 | 0.7273 | 0.6121 | 0.4645 | 0.7277 | 0.6042 | 0.4648 | 0.7277 | 0.5826 | 0.4641 | 0.7265 | 0.6011 | 0.4654 | 0.7279
PFRec+BERT4Rec | 0.6020 | 0.4938 | 0.7449 | 0.5810 | 0.4891 | 0.7389 | 0.5451 | 0.4964 | 0.7491 | 0.5803 | 0.4938 | 0.7451 | 0.5724 | 0.4934 | 0.7456 | 0.5544 | 0.4709 | 0.7206 | 0.5737 | 0.4873 | 0.7323
FFVAE+BERT4Rec | 0.6638 | 0.4269 | 0.6760 | 0.6519 | 0.4254 | 0.6746 | 0.5784 | 0.3740 | 0.6045 | 0.6462 | 0.4174 | 0.6644 | 0.6027 | 0.3714 | 0.6015 | 0.6014 | 0.3721 | 0.6042 | 0.5972 | 0.3660 | 0.5945
AFRL+BERT4Rec | 0.5879 | 0.5273 | 0.7772 | 0.5799 | 0.5263 | 0.7784 | 0.5082 | 0.5307 | 0.7810 | 0.5839 | 0.5212 | 0.7725 | 0.5480 | 0.5220 | 0.7720 | 0.5440 | 0.5213 | 0.7730 | 0.5586 | 0.5111 | 0.7618

(a) ML-1M G

(b) ML-1M A

(c) ML-1M O

(d) ML-1M G+A

(e) ML-1M G+O

(f) ML-1M A+O

(g) Taobao G

(h) Taobao A

(i) Taobao C

(j) Taobao G+A

(k) Taobao G+C

(l) Taobao A+C

Figure 3. Pareto front curves under different fairness requirements with
SASRec (Kang and McAuley, 2018) as base model. In each curve, the points from
left to right correspond to
$\boldsymbol{\lambda}\in\\{100,10,1,0.1,0.01,0.001\\}$, respectively.

(a) ML-1M G

(b) ML-1M A

(c) ML-1M O

(d) ML-1M G+A

(e) ML-1M G+O

(f) ML-1M A+O

(g) Taobao G

(h) Taobao A

(i) Taobao C

(j) Taobao G+A

(k) Taobao G+C

(l) Taobao A+C

Figure 4. Pareto front curves under different fairness requirements with
BERT4Rec (Sun et al., 2019) as base model. In each curve, the points from left
to right correspond to $\boldsymbol{\lambda}\in\\{100,10,1,0.1,0.01,0.001\\}$,
respectively.

####  4.1.4. Parameter Setting.

We set the batch size to 256, the initial learning rate to 5e-5, and the
embedding dimensionality to 64 on both datasets. We employ early stopping as
the regularizer for avoiding overfitting, and Adam algorithm as the optimizer.
$F$ and $\\{E_{i}\\}$ are implemented as a six-layer MLP using ReLU as the
activation function. $\\{D_{i}\\}$ and $\\{C_{i}\\}$ are implemented as a two-
layer MLP using ReLU as the activation function. Table 1 gives the settings of
the hyper-parameters $\beta$ and $\lambda$ in Equations (2) and (16) in
different scenarios. For fairness, the hyper-parameters of the baseline models
are set to their optimal configuration tuned on validation sets.

###  4.2. Fairness and Accuracy (RQ1)

Tables 2 and 3 show the performaces of AFRL and the baseline models on ML-1M
and Taobao, respectively. We can see that on both datasets, compared with the
AUC of original model, the AUC after applying any fair model decreases, which
means all the fair models can improve the fairness of the original
recommendation models. However, the AUC after applying AFRL is closest to 0.5
for most fairness requirements, by which we can conclude that compared with
the baseline fair models, AFRL can achieve the best personalized fairness of a
recommendation model, due to its capability of learning the attribute-specific
embeddings of attributes based on information alignment.

For accuracy, we can observe that the applying of AFRL and the baseline fair
models will reduce the accuracy of the original recommendation models in terms
of NDCG and Hit rate, which is reasonable because of the loss of information
in the fair embeddings learned by the fair models. However, we see that in
most cases, AFRL outperforms the baseline fair models, which indicates that
AFRL can achieve less accuracy loss, due to its ability to capture more
discriminative information from non-sensitive attributes and collaborative
signals in the fair representations learned by it.

(a) ML-1M

(b) Taobao

Figure 5. Contributions to accuracy by $\mathbf{z}_{u,0}$ and
$\mathbf{z}_{u,i}$.

###  4.3. Trade-off (RQ2)

AFRL uses $\lambda$ in Equation (16) to control the trade-off between fairness
and accuracy, similar to the baseline fair models. Figures 3 and 4 show the
pareto front curves of AFRL and the baseline methods over different $\lambda$
and different fairness requirements on both datasets, with SASRec (Kang and
McAuley, 2018) and BERT4Rec (Sun et al., 2019) as the base recommendation
models, respectively.

We can first see that in most cases, the point of the curve of AFRL at a
specific $\lambda$ basically locates in the uppermost-left position compared
to all other points, i.e., there are no points of the curves of the baseline
models in its upper-left region. This result confirms the advantage of AFRL to
achieve a better trade-off between fairness and accuracy than the baseline
fair models. At the same time, we also note that as $\lambda$ is decreasing,
the points of the curve of AFRL move to upper-right region, i.e., the accuracy
improves while the fairness degrades. This is because in Equation (16), the
smaller $\lambda$ will cause more information from original user embedding to
be preserved in the fair embedding, which is favorable to its discriminability
but unfavorable to its fairness.

###  4.4. Ablation Study (RQ3)

Now we investigate the contributions of the attribute-specific embeddings
$\mathbf{z}_{u,i}$ ($1\leq i\leq M$) and the debiased collaborative embedding
$\mathbf{z}_{u,0}$. For this purpose, we compare AFRL with its two variants,
AFRL-w/o-$\mathbf{z}_{u,i}$ where the embeddings $\mathbf{z}_{u,i}$ of non-
sensitive attributes are removed from the fair user embedding
$\mathbf{u}^{*}$, and AFRL-w/o-$\mathbf{z}_{u,0}$ where the debiased
collaborative embedding $\mathbf{z}_{u,0}$ is removed from $\mathbf{u}^{*}$.
The results are shown in Figures 3, 4 and 5.

(a) $\beta$

(b) $\lambda$ on ML-1M

(c) $\lambda$ on Taobao

Figure 6. Tuning of hyper-parameters.

At first, from Figures 3 and 4 we can see that basically at the same
$\lambda$, AFRL and AFRL-w/o-$\mathbf{z}_{u,i}$ can achieve almost the same
fairness, but AFRL has higher accuracy. This indicates that due to the
information alignment, the fair embedding learned by AFRL through
$\mathbf{z}_{u,i}$ preserves more discriminability compared to the fair
embedding learned by AFRL-w/o-$\mathbf{z}_{u,i}$, without sacrificing
fairness. At the same time, Fig. 5 shows that AFRL achieves the higher
accuracy than both AFRL-w/o-$\mathbf{z}_{u,0}$ and
AFRL-w/o-$\mathbf{z}_{u,i}$, which indicates both $\mathbf{z}_{u,0}$ and
$\mathbf{z}_{u,i}$ contribute to the accuracy because of the discriminative
information encoded by them. However, we also note that the accuracy of
AFRL-w/o-$\mathbf{z}_{u,i}$ is higher than that of
AFRL-w/o-$\mathbf{z}_{u,0}$, which suggests the debiased collaborative signals
encoded by $\mathbf{z}_{u,0}$ contribute more to the discriminability of the
fair embedding.

###  4.5. Hyper-parameter Tuning (RQ4)

To determine the appropriate value of $\beta$, we train a classifier for each
attribute $A_{i}$ using the attribute embeddings $Z_{i}$ and utilize AUC to
evaluate the amount of information of $A_{i}$ encoded by $Z_{i}$. Fig. 6(a)
shows the average AUC curves over all surrogate classifiers on both datasets.
We can see that basically the smaller $\beta$, the higher AUC, and the more
information of $A_{i}$ encoded, which is consistent with our analysis of Fig.
2 in Section 3.2.1. We also note that after $\beta$ reaches 1, AUC begins to
drop sharply. Since our objective is information alignment, i.e., making the
information encoded by $Z_{i}$ exactly cover that of attribute $A_{i}$ rather
than maximize or minimize it, we heuristically choose $\beta=1$ to approximate
the ideal case shown in Fig. 2(c).

As $\lambda$ controls the trade-off between accuracy and fairness, we need to
consider both accuracy and fairness to determine its optimal value. As
mentioned in Section 4.1.3, we train a set of surrogate classifiers employing
the final fair user embedding $\mathbf{u}^{*}$ as input to predict the
sensitive attribute value, with AUC as the metric for fairness performance.
Accuracy is evaluated by N@$10$. Fig. 6(b) and Fig. 6(c) show the impact of
$\lambda$ on recommendation accuracy and fairness on ML-1M and Taobao,
respectively. We see that the larger $\lambda$, the more the fairness (the
smaller the AUC), and the less the accuracy (the smaller the NDCG). We choose
$\lambda=1$ for the ML-1M dataset and $\lambda=10$ for Taobao, because they
are a balance point beyond which the accuracy will drastically drop but
without significant rise of the fairness.

##  5\. related work

The fairness challenge in recommender systems is complex due to the
involvement of multiple stakeholders, generally categorized into item-side
fairness and user-side fairness. Item-side fairness seeks that different types
of items have an equitable opportunity to be recommended, by minimizing
prediction errors for various item categories (Rastegarpanah et al., 2019) or
allocating exposure based on item relevance (Biega et al., 2018). User-side
fairness aims to make fair recommendations to different users (Ekstrand et
al., 2018; Andrus and Villeneuve, 2022; Ge et al., 2022), or ensure that
similar users receive similar treatments (Fu et al., 2020; Li et al., 2023;
Hua et al., 2023).

A range of approaches have been proposed for user-side fairness, following
various technical lines including Pareto optimization (Lin et al., 2019; Yao
and Huang, 2017; Zhu et al., 2018; Beutel et al., 2019; Burke et al., 2018),
adversarial training (Bose and Hamilton, 2019; Wu et al., 2021; Li et al.,
2021a, c), and disentangled representation learning (Zhao et al., 2023; Park
et al., 2021; Gong et al., 2020; Sarhan et al., 2020). The common idea of them
is to filter out the information of user sensitive attributes from the learned
fair embeddings, so that recommendations can be made without bias to sensitive
attributes. At the same time, some works apply reinforcement learning to fair
recommendations, which usually impose fairness constraints to the cumulative
return function for long-term and dynamic fairness (Ge et al., 2021; Liu et
al., 2020).

The traditional methods often assume all users share the same sensitive
attributes, which is not true in real world where different users have
personalized fairness requirements. To address this issue, recently, some
models have been proposed for personalized fairness in recommendations. For
example, Li et al. (Li et al., 2021b) propose to train a filter for each
possible combination of sensitive attributes, while Wu et al. (Wu et al.,
2022) propose a model PFRec to build a set of prompt-based bias eliminators
and adapters with customized attribute-specific prompts to learn fair
embeddings for different attribute combinations. However, they treat a
fairness requirement as a hyper-parameter, and train a mode for each
combination of attributes, which makes them implement the personalized
fairness in a brute force way with unacceptable training cost. Creager et al.
(Creager et al., 2019) propose the FFVAE model, which disentangles an unfair
embedding into latent factors, each of which corresponds to an attribute, and
excludes relevant sensitive latent factors based on different fairness
requirements of users. Nevertheless, the existing methods often pursue an
extreme fairness by completely removing the information of sensitive
attributes from the fair embeddings, which makes them suffer from a suboptimal
trade-off between accuracy and fairness.

##  6\. Conclusion

In this paper, we propose a novel model, called Adaptive Fair Representation
Learning (AFRL), for personalized fairness in recommendations. AFRL can
overcome the challenge of the explosion of attribute combinations and achieve
a better trade-off between accuracy and fairness. At first, AFRL treats
fairness requirements as inputs and can learn an attribute-specific embedding
for each attribute from the unfair user embedding, which endows AFRL with the
adaptability during inference phase to dynamically determine the non-sensitive
attributes that should be encoded into the fair embedding under the guidance
of the user’s unique fairness requirement. With the novel information
alignment offered by the proposed Information Alignment Module (IAlignM), AFRL
can reduce the loss of recommendation accuracy, without loss of fairness, by
exactly preserving discriminative information of non-sensitive attributes and
incorporating a debiased collaborative embedding into the fair embedding to
capture attribute-independent collaborative signals. At last, the extensive
experiments conducted on real datasets together with the sound theoretical
analysis demonstrate the superiority of AFRL.

###### Acknowledgements.

This work is supported by National Natural Science Foundation of China under
grant 61972270.

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