# Debiasing Sequential Recommenders through Distributionally Robust
Optimization over System Exposure

Jiyuan Yang<EMAIL_ADDRESS>Shandong UniversityQingdaoChina ,
Yue Ding<EMAIL_ADDRESS>Shanghai Jiao Tong UniversityShanghaiChina ,
Yidan Wang<EMAIL_ADDRESS>Shandong UniversityQingdaoChina ,
Pengjie Ren<EMAIL_ADDRESS>Shandong UniversityQingdaoChina ,  Zhumin
Chen<EMAIL_ADDRESS>Shandong UniversityQingdaoChina ,  Fei Cai
<EMAIL_ADDRESS>National University of Defense TechnologyChangshaChina ,
Jun Ma<EMAIL_ADDRESS>Shandong UniversityQingdaoChina ,  Rui Zhang
<EMAIL_ADDRESS>ruizhang.infoShenzhenChina ,  Zhaochun Ren
<EMAIL_ADDRESS>Leiden UniversityLeidenNetherlands and  Xin Xin
<EMAIL_ADDRESS>Shandong UniversityQingdaoChina

(2024)

###### Abstract.

Sequential recommendation (SR) models are typically trained on user-item
interactions which are affected by the system exposure bias, leading to the
user preference learned from the biased SR model not being fully consistent
with the true user preference. Exposure bias refers to the fact that user
interactions are dependent upon the partial items exposed to the user.
Existing debiasing methods do not make full use of the system exposure data
and suffer from sub-optimal recommendation performance and high variance.

In this paper, we propose to debias sequential recommenders through
Distributionally Robust Optimization (DRO) over system exposure data. The key
idea is to utilize DRO to optimize the worst-case error over an uncertainty
set to safeguard the model against distributional discrepancy caused by the
exposure bias. The main challenge to apply DRO for exposure debiasing in
sequential recommendation lies in how to construct the uncertainty set and
avoid the overestimation of user preference on biased samples. Moreover, since
the test set could also be affected by the exposure bias, how to evaluate the
debiasing effect is also an open question. To this end, we first introduce an
exposure simulator trained upon the system exposure data to calculate the
exposure distribution, which is then regarded as the nominal distribution to
construct the uncertainty set of DRO. Then, we introduce a penalty to items
with high exposure probability to avoid the overestimation of user preference
for biased samples. Finally, we design a debiased self-normalized inverse
propensity score (SNIPS) evaluator for evaluating the debiasing effect on the
biased offline test set. We conduct extensive experiments on two real-world
datasets to verify the effectiveness of the proposed methods. Experimental
results demonstrate the superior exposure debiasing performance of proposed
methods. Codes and data are available at
https://github.com/nancheng58/DebiasedSR_DRO.

Sequential Recommendation, Distributionally Robust Optimization, Exposure
Bias, Recommendation Debiasing

††journalyear: 2024††copyright: rightsretained††conference: seventeenth ACM
International Conference on Web Search and Data Mining; March 4–8, 2024;
Mexico.††doi: 10.1145/3616855.3635848††booktitle: seventeenth ACM
International Conference on Web Search and Data Mining (WSDM ’24), March 4–8,
2024, Mexico.

##  1\. Introduction

Over the past decade, sequential recommendation (SR) has achieved great
success in the field of recommender systems (RSs) to predict user future
interests from sequential user-item interactions (Hu et al., 2018; Yuan et
al., 2019, 2022; Du et al., 2023). However, recent research has revealed that
RSs face different intractable bias issues (e.g., popularity bias (Zhang et
al., 2021), position bias (Collins et al., 2018), selection bias (Wang et al.,
2021) and exposure bias (Saito et al., 2020; Jiang et al., 2019; Yang et al.,
2018)). In particular, exposure bias occurs when user interactions are
dependent upon the partial items exposed to the user, also known as the
”previous model bias” (Liu et al., 2020). Since the RS model is trained on
user-item interaction data, the previously deployed RS model will dramatically
impact the current one, and the exposed data in the current model is largely
dependent on the previous recommendation policy, resulting in a biased
feedback loop. The RS may inadvertently exacerbate the bias since the agent is
trained using biased interaction data, which leads to false predictions about
user true preference. As shown in Fig. 1a, the user preference learned from
exposure biased data is not fully consistent with the distribution of true
user preference. Existing methods mainly utilize the inverse propensity score
(IPS) to perform exposure debias (Saito et al., 2020; Liu et al., 2023; Jiang
et al., 2019; Damak et al., 2022; Wang et al., 2022; Xu et al., 2022; Dai et
al., 2022; Wang et al., 2019b). However, we argue that such kinds of methods
do not make full use of system exposure data (Xin et al., 2023) and suffer
from unbounded high variance (Zheng et al., 2021; Bottou et al., 2013).

(a)

(b)

Figure 1. Illustration of the user preference distribution gap (a) and our
solution through DRO framework (b).

Distributionally Robust Optimization. In this paper, we propose to leverage
_Distributionally Robust Optimization_ (DRO) (Rahimian and Mehrotra, 2019;
Sagawa et al., 2019; Słowik and Bottou, 2022; Shen et al., 2021; Yang et al.,
2023; Zhou et al., 2023) to perform debiased sequential recommendation. The
motivation to utilize DRO is that DRO aims to optimize the worst-case error
over an _uncertainty set_ to safeguard the model against potential
distributional shifts within the uncertainty set (Shen et al., 2021), which
naturally fits the needs of debiasing sequential recommendation. Besides, DRO
also provides more stable and robust model training compared with high
variance IPS-based methods. More specifically, to address the issue of
preference discrepancy, the uncertainty set is required lying around the true
user preference distribution. A reasonable approach to construct the
uncertainty set is to introduce the _nominal distribution_ (Rahimian and
Mehrotra, 2019; Hu and Hong, 2013; Shen et al., 2021) which contains the prior
knowledge regarding the true user preference, as shown in Fig. 1b. Here, we
adopt the system exposure distribution as the nominal distribution. The
insight behind this choice lies in the following points: 1) system exposure
can be viewed as the user preference from the recommender perspective and lies
around the true user preference; and 2) system exposure contains prior
knowledge about both the recommender exposure mechanism and the true user
preference distribution. Besides, since exposure bias occurs when a
recommender system exposes items that are deemed by the system as preferred by
a user but are not actually liked by the user, there is an overestimation of
user preference on biased samples. Finally, due to the unavailability of
unbiased sequential recommendation datasets (Damak et al., 2022), how to
evaluate the debiasing effect on the offline biased test set is also a
problem. To this end, this paper aims to address the following research
challenges:

Research challenges. i). How to model the system exposure distribution as the
nominal distribution of DRO? To address this challenge, we pre-train an
exposure simulator by modeling the previous system behavior data (i.e.,
exposed items). The task of simulating system exposure is challenging since
the exposure mechanism typically involves the combination of multiple
recommenders. Besides, service providers frequently prioritize the
recommendation of popular (hot) items, further complicating the process of
simulating. To this end, we model the exposure distribution by the mixture of
multiple recommender models 111In this paper, we utilize three recommender
models to model the sequential exposure distribution. We leave the
investigation of more advanced exposure simulator as one of our future works..
Remarkably, this paper represents the first attempt, to the best of our
knowledge, to model the exposure distribution explicitly in the context of
sequential recommendation.

ii). How to eliminate the overestimation of user preference on biased samples?
For this challenge, we impose a penalty on items that the system deems as
highly preferred by the user. This penalty can reduce the influence of such
items and enable the system to make more accurate predictions of user
preference. To more accurately identify samples with exposure bias, we
penalize items according to their exposure distribution, applying a larger
penalty to items with high exposure probabilities.

iii). How to evaluate the debiasing effect on the offline biased test set? For
this challenge, we design a self-normalized inverse propensity score (SNIPS)
(Swaminathan and Joachims, 2015; Schnabel et al., 2016; Yang et al., 2018)
evaluator to evaluate the debiasing effect on the biased test set. The idea of
SNIPS is to down-weight frequently exposed samples and up-weight the rare
ones. Here we treat the exposure probability of each item as the corresponding
propensity score. Nevertheless, using the prediction of the pre-trained
exposure simulator as exposure probability may cause potential data leakage
for evaluation. To solve this issue, we construct an extra exposure simulator
based on another unseen part of the recommender exposure to generate the
propensity score.

Experiments. Extensive experiments and analyses on two real-world datasets
demonstrate the effectiveness of the proposed framework. We hope this work can
raise more community concern regarding improving the recommenders from the
system behavior perspective other than just focusing on debiasing from the
user behavior perspective.

Contributions. To summarize, the main contributions are:

  * •

We propose to use Distributionally Robust Optimization to conduct exposure
debiasing in sequential recommendation.

  * •

In contrast to only considering debiasing from the user perspective, we
incorporate the system behavior and alleviate the exposure bias from
perspectives of both users and systems.

  * •

We design a debiased self-normalized inverse propensity score (SNIPS)
evaluator for evaluating the debiasing sequential recommendation performance
in the biased test set.

##  2\. Related work

In this section, we provide a literature review regarding sequential
recommendation and exposure debiasing.

###  2.1. Sequential Recommendation

Recently, sequential recommendation (SR) has become a hot research topic.
Compared with the other task in recommendation (Koren et al., 2009; Ning and
Karypis, 2011), the SR focuses on capturing the item’s chronological
correlations. Many sequential recommender methods have been proposed, such as
methods based on the Markov Chain (Rendle et al., 2010; He et al., 2016) and
factorization methods (Hidasi and Tikk, 2016). Over the past few years, plenty
of deep learning-based SR models have emerged, including Recurrent Neural
Networks (RNNs)-based methods (Hidasi et al., 2016a, b), Convolutional Neural
Networks (CNNs)-based methods (Yuan et al., 2019), and attention-based methods
(Li et al., 2017; Kang and McAuley, 2018). Besides, Graph Neural Networks
(GNNs) also demonstrated their capability to represent user-item high-order
interactions in the SR. Plenty of graph-based SR models have emerged, such as
SR-GNN (Wu et al., 2019), UGrec (Wang et al., 2019a), and SURGE (Chang et al.,
2021). Casual inference (Wang et al., 2022), reinforcement learning (Xin et
al., 2020), and self-supervised learning (Zhou et al., 2020) also demonstrated
the effectiveness to enhance SR.

In this paper, instead of designing a new recommender model, we focus on
mitigating the impact of exposure bias in the SR. To this end, we propose a
model-agnostic debiasing framework and adopt two representative models, SASRec
and GRU4Rec, as backbone sequential recommendation models for our experiments.

###  2.2. Exposure Debiasing in RSs

Exposure bias, also known as ”previous model bias” (Liu et al., 2020), occurs
when user interactions are dependent upon the partial items exposed to the
user. As it is not clear whether a lack of interaction between a user and an
item is due to genuine disinterest or simply a consequence of no exposure, a
non-exposed item may actually be favored by the user but unable to be
interacted with. Exposure bias would mislead both the model’s training and
evaluation (Chen et al., 2023). The common approach for debiasing recommender
system evaluation is incorporating the well-known _Inverse Propensity Scoring_
(IPS) (Schnabel et al., 2016) into the ranking evaluation metrics. More
specifically, the key idea of IPS-based evaluation is that items are down-
weighted by their propensity in the evaluation metrics. For instance, (Yang et
al., 2018) proposes an IPS-based unbiased evaluator to down-weight the
commonly observed interactions, while up-weighting the rare ones. Furthermore,
various strategies are being used to mitigate exposure bias during the
training phase. In early works, researchers aim to integrate a measure of
confidence into the unobserved interactions instead of considering them as
irrelevant. For example, (Pan and Scholz, 2009) utilizes user activity (e.g.,
the number of interacted items) to weigh the negative interactions. (Saito et
al., 2020) argues that early methods can not address exposure bias entirely
and designed the IPS-based unbiased estimator in the training phase to perform
debiasing. (Jiang et al., 2019) proposes an exposure-based propensity matrix
factorization framework to counteract the exposure bias.

Recently, there have been some works (Wang et al., 2022; Damak et al., 2022;
Xu et al., 2022) to remedy bias in SR. Since the interaction distribution in
SR evolves over time, it is reasonable to assume that exposure propensities
also vary over time (Damak et al., 2022). Thus, the traditional IPS does not
applicable to SR because it fails to account for the temporal nature of the
problem. To this end, (Wang et al., 2022) uses GRU (Cho et al., 2014) to
estimate temporal IPS, and derived an IPS-based loss function via potential
latent confounders in RS. (Xu et al., 2022) estimates the propensity scores
with two GRUs from the views of items and users in SR. (Damak et al., 2022)
proposes a temporal IPS-based framework for debiasing the Cloze task (Sun et
al., 2019) of SR.

While existing methods have explored alleviating the exposure bias problem,
they only rely on user interaction data to estimate the exposure policies and
neglect the system perspective. In this work, we propose to simulate the
exposure mechanism of the real-world recommendation system by considering both
interacted data from the user perspective and exposure data from the system
perspective. Besides, compared with the high variance IPS, the adopted DRO
framework provides more robust and stable model training. To the best of our
knowledge, our work is the first attempt to utilize DRO for exposure debiasing
in sequential recommendation.

##  3\. Notations and Problem Formulation

Sequential recommendation. Let $\mathcal{U}$ and $\mathcal{I}$ denote the user
set and the item set, respectively, where $u\in\mathcal{U}$ denotes a user and
$v\in\mathcal{I}$ denotes an item. We use $S^{u}$=($v^{u}_{1}$, $v^{u}_{2}$,
…, $v^{u}_{t}$) to denote the sequence of user $u$’s previous interactions
(e.g., views, clicks, or purchases) in the sequence, where $v^{u}_{j}$ is the
$j$-th item user $u$ has interacted with, $t$ is the length of the interaction
sequence. SR aims to predict the next item that the user is likely to interact
with at the $(t+1)$-th step, which can be formulated as the estimation of
$P(v_{t+1}|S^{u})$, where $P$ denotes the user’s preference score for the item
$v$ in the step $(t+1)$. The prediction error is measured by the prevalent
Binary Cross Entropy (BCE) (Kang and McAuley, 2018; Zhou et al., 2020) loss:

(1)
$\small\mathcal{L}_{\text{rec}}\\!=\\!-\\!\sum_{\\!u\\!\in\\!\mathcal{U}}\\!\sum_{j\\!\in[\\!2,\\!...,t]}\\![\log\sigma\\!\left(P\\!\left(\\!v_{j}^{+}|S^{u}_{<\\!j}\right)\right)+\\!\log\\!\sigma\\!\left(1-\\!P\\!\left(v_{j}^{-}|S^{u}_{<\\!j}\right)\right)],$

where $v_{j}^{+}$ and $v_{j}^{-}$ denote the positive sample and negative
sample at the $j$-th step, respectively. The $S^{u}_{<j}$ denotes the sequence
of user $u$ before $j$-th step. $\sigma$ denotes the Sigmoid activation
function.

System exposure data. Compared with the sparse user interaction data, the
large volume of exposure data generated by the recommender receives relatively
less research attention. Given an $n$-length exposure item sequence
$E^{u}=(e^{u}_{1},e^{u}_{2},...,e^{u}_{n})$, where $e^{u}_{j}$ represents the
$j$-th item exposed to user $u$ and $n$ is the length of exposure sequence.
For a user $u$, the user interaction data $\\{S^{u}\\}$ is a subset of
$\\{E^{u}\\}$ since the exposure data include both interacted and non-
interacted but exposed items. The exposed items in system exposure data are
selected by the recommender and thus can be regarded as a kind of system
behavior data. In this paper, we construct an exposure simulator by modeling
the system behavior, aiming to simulate the system exposure distribution.

Task formulation. The task of this paper is given the user-item interaction
sequence $S^{u}$ and the system exposure sequence $E^{u}$, eliminating the
impact of exposure bias and generating the recommendation list for user $u$.

##  4\. methodology

In this section, we present the detail of our proposed debiasing framework.
Fig. 2 provides the overview of our methods, which includes both the user and
system perspectives. From the _user_ perspective, users observe the exposed
items and interact with specific parts of them, generating biased user-item
interaction data. Therefore, the sequential recommender trained on such biased
data would lead to biased user preference. From the _system_ perspective, we
model the distribution of exposure data by pre-training an exposure simulator
to mimic the real-world exposure mechanism. The exposure simulator aims to
provide a system behavior distribution (i.e., the exposure probability of each
item). We then utilize the system exposure distribution as the nominal
distribution of Distributionally Robust Optimization (DRO) to infer the
debiased user preference and generate sequential recommendation. It is
important to note that the sequential recommender is jointly trained by user
interaction data and the DRO method, the exposure model is only pre-trained by
system exposure data and its parameters are fixed in the inference stage.

Figure 2. Framework overview. For the user side, users observe exposed items
from previous recommenders, generating biased interactions. For the system
side, exposure data is used to train the exposure simulator and obtain the
exposure distribution. During inference, the biased user preference and the
system exposure distribution are fed to the DRO block for debiasing.

###  4.1. Distributionally Robust Optimization

Distributionally Robust Optimization (DRO) (Rahimian and Mehrotra, 2019;
Sagawa et al., 2019; Słowik and Bottou, 2022) has been widely adopted as a
solution to the out-of-distribution (OOD) (Shen et al., 2021) generalization
problem (Wen et al., 2022). The key idea of DRO is to optimize the worst-case
error over an _uncertainty set_ to safeguard the model against potential
distributional shifts within the uncertainty set (Shen et al., 2021). The SR
model is typically trained on biased user-item interactions. It means that the
preference generated by the biased recommender may not align with the true
user preference. In this paper, we employ DRO to alleviate the impact of the
distribution discrepancy between biased user preference and unknown true user
preference in SR. The problem of distribution shifting is even more pronounced
in the context of SR, where users’ preference dynamically change.

DRO replaces the expected risk under the empirical distribution (i.e., biased
interaction distribution) with the worst expected risk over a set of uncertain
distributions:

(2)
$\mathcal{L}_{DRO}(\theta)=\max_{\hat{\mathcal{D}}\in\mathcal{Q}}\mathbb{E}_{(S^{u},v)\sim\hat{\mathcal{D}}}\ell(S^{u},v;\theta),$

where $\theta$ refers to the parameters to be optimized and
$\ell(S^{u},v;\theta)$ is the surrogate loss and will be detailed in section
4.3. The DRO loss function $\mathcal{L}_{DRO}$ takes the maximum over all
distributions contained in a pre-defined _uncertainty set_ $\mathcal{Q}$.
$\mathcal{L}_{DRO}$ can be interpreted as an upper bound estimation of the
average loss on the true user preference distribution if the distribution lies
in $\mathcal{Q}$. A viable strategy is to form the uncertainty set
$\mathcal{Q}$ by stipulating that the distribution is within a certain
proximity to the nominal distribution $q_{0}$, which is an approximation of
the true user preference distribution and encapsulates important information
about user preference. To this end, we introduce the distance metric $D$
(i.e., the Kullback–Leibler Divergence) to the DRO loss function in Eq.(2), so
$\mathcal{Q}=\left\\{q:D\left(q\|q_{0}\right)\leq\eta\right\\}$, where $\eta$
is the robust radius to control the size of $\mathcal{Q}$. We can then
reformulate the DRO loss function as:

(3)
$\mathcal{L}_{DRO}^{{}^{\prime}}(\theta)=\max_{D\left(q\|q_{0}\right)\leq\eta}\mathbb{E}_{(S^{u},v)\sim
q}\ell(S^{u},v;\theta),$

To address the issue of preference discrepancy, the nominal distribution is
required to lie around the true preference distribution. In this paper, we
adopt system exposure distribution as the nominal distribution. The rationale
behind this choice lies in the following points: 1) system exposure can be
viewed as the user preference from the system perspective and lying around the
true user preference, and 2) system exposure distribution contains prior
knowledge about the recommender exposure mechanism that can be leveraged to
perform exposure debiasing. Specifically, the exposure probability for item
$v$ is denoted as $q_{0}(S^{u},v)$.

###  4.2. Modeling Exposure Distribution

The system exposure distribution can be considered as the system behavior
patterns and reflects the system’s understanding of user preference. Existing
exposure debiasing approaches in (Saito et al., 2020; Jiang et al., 2019; Yang
et al., 2018) rely solely on observed interaction data to estimate the
unobserved exposure mechanism in implicit feedback recommendation from the
user perspective. However, we argue that these approaches suffer from sub-
optimal performance as they did not introduce the large volume of exposure
data from the system perspective. In contrast to existing methods, we simulate
the exposure mechanism of the real-world recommender system by considering
both interacted data and exposed but non-interacted data.

Simulating the real-world exposure mechanism is a daunting task due to two key
factors: 1) the real-world exposure mechanism often entails a complex
interplay of multiple recommenders, making it challenging to accurately model
the precise exposure of individual items; 2) recommendation service providers
tend to prioritize popular items to increase the traffic, further complicating
the simulation process. To this end, we develop an exposure simulator that
consists the mixture of multiple recommenders. The simulator comprises a
Transformer-based (Vaswani et al., 2017) recommendation model (SASRec (Kang
and McAuley, 2018)), a GRU-based (Cho et al., 2014) recommendation model
(GRU4Rec (Hidasi et al., 2016b)), and a popularity-based recommender that
boosts popular items. The three recommenders in the simulator can be replaced
by other recommendation methods. We leave the investigation of a more advanced
exposure mechanism as one of our future works.

####  4.2.1. Training of the exposure simulator.

For the training stage, it is worth noting that the training of the exposure
simulator differs from that of sequential recommendation, primarily because:

  * •

The input of the exposure simulator in the training stage is the _system_
exposure data while the input for sequential recommendation is the _user_
interactions.

  * •

The output of the exposure simulator in the training stage is the _system_
exposure distribution while the output of sequential recommendation is the
predicted _user_ interests.

In the training stage, we use the system exposure data to train the SASRec
model (denoted as Expo-SASRec) and the GRU4Rec model (denoted as Expo-
GRU4Rec), separately. Then the parameters in the pre-trained Expo-SASRec and
Expo-GRU4Rec remain fixed in the following stages to provide stable exposure
simulation. More specifically, the Expo-SASRec model is based on a Transformer
decoder (Kang and McAuley, 2018). Expo-GRU4Rec is an RNN-based sequential
recommender that uses GRU to encode users’ interaction sequences, consisting
of an embedding layer, recurrent layers, and fully connected layers.

####  4.2.2. Exposure distribution inference.

It is important to note that, in the inference stage, the input to the
exposure simulator is the user interaction data rather than system exposure
data. The motivation is that during inference, the system exposure
distribution should depend on which items the user have interacted with. The
goal of such design is to gain insights into user sequential interests from a
system perspective.

Given a user-item interaction sequence $S^{u}$=($v^{u}_{1}$, $v^{u}_{2}$, …,
$v^{u}_{t}$), the hidden state of the Expo-SASRec encoder in the last
timestamp serves as the latent representation of the input sequence:
$\mathbf{F}^{u}_{t,1}=\text{Expo-SASRec}(S^{u})$. $\mathbf{F}^{u}_{t,1}$ can
be viewed as the user’s potential preference representation from the system’s
(Expo-SASRec) perspective at the $t$-th step. Similarly, we also leverage
Expo-GRU4Rec to encode user interaction data, The exposure representation
through Expo-GRU4Rec is denoted as: $\mathbf{F}^{u}_{t,2}=\text{Expo-
GRU4Rec}(S^{u})$. Additionally, we introduce a popularity-based model to
expose more popular items. We define the popularity score of item $i$ as
$f_{i}=\frac{s_{i}}{\max_{j\in\mathcal{I}}s_{j}}$ where $s_{i}$ denotes that
item $i$ appears $s_{i}$ times in the exposure data. Finally, we calculate the
recommender exposure score for the item $v$ at the step ($t$+1) as follows:

(4)
$\begin{split}\mu_{0}(S^{u},v_{t+1}=v)&=softmax(\mathbf{e}_{v}^{\top}\cdot\mathbf{F}^{u}_{t,1})+softmax(\mathbf{e}_{v}^{\top}\cdot\mathbf{F}^{u}_{t,2})\\\
&+\beta\ softmax(f_{v}),\end{split}$

where $\mathbf{e}_{v}$ is the embedding of item $v$ and $\beta$ is a
hyperparameter.

We calculate the exposure distribution as follows:

(5)
$q_{0}(S^{u},v)=\frac{\mu_{0}(S^{u},v)}{\sum_{i\in\mathcal{I}}\mu_{0}(S^{u},i)}.$

A high exposure probability $q_{0}(S^{u},v)$ indicates a significant level of
exposure. In summary, the proposed method of modeling exposure distribution
offers the following advantages:

  * •

Instead of relying on statistical methods to estimate exposure policy, we
choose to explicitly model the exposure distribution through exposure data.
Our methods provide more adaptive modeling of exposure distribution.

  * •

The simulator is based on the mixture of sequential models and item
popularity, which is more effective to capture both sequential dynamics and
popularity effects in the exposure distribution.

###  4.3. Mitigating Preference Overestimation

From a system perspective, exposure bias occurs when a recommender system
exposes items that are deemed by the system as preferred by a user but are not
actually preferred by the user, resulting in the failure to expose items that
are actually preferred by the user. Therefore previous system exposure can not
accurately obtain current user preference, i.e., the system assigns a higher
score to an item than the user’s true preference. In other words, the system
exposure distribution may overestimate the scores of biased samples that are
not aligned with the user’s true preference. To solve this issue, we optimize
the recommender to mitigate the risk of preference overestimation and pursue
conservative recommendation under the DRO framework.

Note that minimizing the DRO loss is an intractable min-max problem. To
address this limitation, we utilize the Kullback-Leibler (KL) Divergence as
the metric for measuring distance denoted as $D$ in Eq.(3). Through this
approach, we can derive a closed-form expression for Eq.(3) as a single-layer
optimization problem as:

(6)
$\mathcal{L}_{DRO}^{{}^{\prime\prime}}(\theta)=\log\mathbb{E}_{(S^{u},v)\sim
q_{0}}e^{\ell(S^{u},v;\theta)}.$

For detailed proof of the reformulation, please refer to Appendix A.1. The
surrogate loss $\ell(S^{u},v;\theta)$ is also called the risk function of DRO.
The risk can be categorized into the following two cases: 1) if ($S^{u}$, $v$)
is a positive sample, it means that the user is possibly to like the item, and
thus the risk is high if the sample receives a lower prediction score; 2) if
($S^{u}$, $v$) is a negative sample, a higher prediction score denotes a
higher risk of preference overestimation.

To this end, we define the surrogate loss $\ell(S^{u},v;\theta)$ as follows:

(7)
$\ell(S^{u},v;\theta)=\left\\{\begin{array}[]{ll}1-y(S^{u},v;\theta),&\text{if
}(S^{u},v)\text{ is a positive}\\\ y(S^{u},v;\theta),&\text{if
}(S^{u},v)\text{ is a negative},\end{array}\right.$

where $y(S^{u},v;\theta)$ denotes the prediction score of the $(S^{u},v)$ pair
in the DRO block. In our setting, the number of negative samples is
$|\mathcal{I}|-1$, which encompasses all items apart from positive samples. We
can see optimizing Eq.(6) equals to sample $(S^{u},v)$ from the nominal
exposure distribution $q_{0}$, then if the sampled $(S^{u},v)$ pair is a
negative sample, we would decrease its predicted score. Such the operation can
help the model to mitigate the risk of preference overestimation.

To conclude, optimizing Eq.(6) can enhance the robustness of the recommender
under the dynamic exposure bias, but pursuing robustness without considering
recommendation accuracy may significantly compromise the system’s performance.
To this end, we jointly consider the recommender robustness in Eq.(6) and
accuracy in Eq.(1), and the final optimization objective can be defined as:

(8)
$\begin{split}\mathcal{L}_{joint}&=\mathcal{L}_{rec}+a\mathcal{L}_{DRO}^{{}^{\prime\prime}}\\\
&=\mathcal{L}_{rec}+a\sum_{u\in\mathcal{U}}\sum_{j\in[2,...,t]}\log\mathbb{E}_{(S^{u}_{<j},v)\sim
q_{0}}e^{\ell(S^{u}_{<j},v;\theta)},\end{split}$

where $a$ is a hyperparameter, $v^{+}$ and $v^{-}$ denote positive and
negative samples, respectively. Note that the $P$ in $\mathcal{L}_{rec}$ and
$y$ in Eq.(7) are both predicted preference scores. $P$ is calculated from the
target sequential recommender, while $y$ is calculated from a model which has
a separate final prediction layer and shares all other parameters with the
target sequential recommender. The joint optimization objective can be viewed
as two tasks: recommendation and exposure debiasing. By optimizing the
recommender using the joint loss function, we can approximate the user’s true
preference meanwhile mitigate the exposure bias. It is worth noting that the
$\mathcal{L}_{joint}$ can serve as a surrogate for any sequential
recommendation model, making this approach model-agnostic.

###  4.4. The Debiased Evaluator

To evaluate the debiasing effect, we need reliable debiased test set (Saito et
al., 2020; Damak et al., 2022). However, most existing benchmark test sets are
also affected by the exposure bias (Damak et al., 2022). An ideal case is to
access complete observations, i.e., user $u$ has the chance to interact with
the entire set of items (i.e., $\mathcal{I}$). Therefore, the ideal
recommendation evaluator calculates the following reward
$R_{\text{ideal}}(\hat{Z})$ for the predicted item ranking $\hat{Z}$:

(9)
$R_{\text{ideal}}(\hat{Z})=\frac{1}{|\mathcal{U}|}\sum_{u\in\mathcal{U}}\frac{1}{\left|\mathcal{I}\right|}\sum_{i\in\mathcal{I}}c\left(\hat{Z}_{u,i}\right),$

where $i\in\mathcal{I}$ is an item, and $\hat{Z}_{u,\,i}$ is the predicted
ranking of item $i$ (among all the items in $\mathcal{I}$) for user $u$.
$c(\cdot)$ represents any of the top-$K$ scoring metrics, such as Recall@$K$
or NDCG@$K$.

However, users have no chance to interact with the entire set of items,
leading to biased observations. To achieve a debiased evaluation from biased
observations, we employ a debiased self-normalized inverse propensity score
(SNIPS). The idea is to down-weight frequently exposed interactions and up-
weight the rare ones in the test set. The SNIPS evaluator is defined as
follows:

(10)
$\begin{split}\hat{R}_{\text{SNIPS}}(\hat{Z}|\rho)&=\frac{1}{\sum_{u\in\mathcal{U}}{\frac{1}{\rho^{k}_{v}}}}\sum_{u\in\mathcal{U}}\frac{c(\hat{Z}_{u,\,v)}}{\rho^{k}_{v}}\\\
&=\frac{1}{\sum_{u\in\mathcal{U}}{\frac{1}{\rho^{k}_{v}}}}\sum_{u\in\mathcal{U}}\sum_{i\in\mathcal{I}}\frac{c(\hat{Z}_{u,\,i)}}{\rho^{k}_{i}}\cdot
O_{u,i},\end{split}$

where $\rho$ is the propensity score of the SNIPS evaluator, $v$ is the target
item of each user $u$, and $O_{u,i}$ is an indicator function to indicate
whether the interaction $(u,i)$ is observed ($O_{u,i}=1$ if $(u,i)$ is
observed, and $O_{u,i}=0$ otherwise). Moreover, we propose the inclusion of a
hyperparameter $k\in[0,1]$, which enables control over the level of the
propensity score. We prove that given a propensity assignment $\rho$,
$\hat{R}_{\text{SNIPS}}(\hat{Z}|\rho)$ is a debiased estimator (More details
of proof can be found in Appendix A.2.):

(11)
$\begin{split}\mathbb{E}_{O}\\![\hat{R}_{\text{SNIPS}}\\!(\\!\hat{Z}|\rho)\\!]&=\\!\frac{|\mathcal{U}|\cdot|\mathcal{I}|}{\\!\sum_{u\in\mathcal{U}}{\frac{1}{\rho^{k}_{v}}}}\\!\sum_{u\in\mathcal{U}}\\!\sum_{i\in\mathcal{I}}\frac{1}{\rho^{1-k}_{i}}\\!\cdot\mathbb{E}_{O}[R_{\text{ideal}}(\hat{Z})].\end{split}$

The term
$\frac{|\mathcal{U}|\cdot|\mathcal{I}|}{\sum_{u\in\mathcal{U}}{\frac{1}{\rho^{k}_{v}}}}$
is a coefficient which not affect the unbiasedness of the evaluator. The
evaluator is a conventional biased one when the parameter $k$ is set to 0.
When the parameter $k$ is set to 1, the evaluator is completely unbiased, but
this comes at the cost of increased variance of the propensity score,
manifesting as noisier or less precise estimates. In our experiments, $k$ is
set to 0.1.

The key challenge in computing $\hat{R}_{SNIPS}(\hat{Z})$ is to predict the
propensity score $\rho$. Here we treat the exposure probability of each item
as the corresponding propensity score since we aim to evaluate the exposure
debiasing performance using the SNIPS evaluator. Nevertheless, using the
prediction of the pre-trained exposure model (as detailed in section 4.2) as
exposure probability may cause training data leakage. More concretely, if the
exposure model is trained by all the system exposure data, the testing user
interaction data would be leaked because all the test data is contained in
exposure data. To solve this issue, we construct an extra evaluation exposure
simulator based on another unseen part of system exposure to predict the
exposure probability in the testing phase.

##  5\. Experiments

In this section, we conduct experiments to demonstrate the effectiveness of
the proposed debiasing framework. We aim to answer the following research
questions:

  1. RQ1

How does our proposed debiasing framework perform compared to existing
debiasing methods?

  2. RQ2

How does the construction of the exposure simulator affect debiasing
performance?

  3. RQ3

How does the penalty term in the DRO loss affect the debiasing performance?

###  5.1. Dataset Description

We choose two real-world datasets:
ZhihuRec222https://github.com/THUIR/ZhihuRec-Dataset (Hao et al., 2021) and
Tenrec333https://github.com/yuangh-x/2022-NIPS-Tenrec (Yuan et al., 2022) to
conduct the experiments. Both datasets contain user interaction data (e.g.,
clicks) and system exposure data (e.g., impressions). All items in the
sequence are arranged chronologically based on their timestamp. More details
can be found in Appendix A.

###  5.2. Evaluation Protocols

We employ the debiased self-normalized inverse propensity score (SNIPS)
(Swaminathan and Joachims, 2015; Schnabel et al., 2016; Yang et al., 2018)
evaluator as detailed in section 4.4 to gauge the effectiveness of debiasing.
We adopt Recall and NDCG as the $c(\cdot)$ function metrics to evaluate the
ranking performance. We report the results with varying values of $K$ $\in$
{5, 10, 20} for both metrics. To prevent information leakage, it is crucial to
avoid any overlap in the system exposure data used for constructing the
exposure simulator and the evaluation simulator. We split the system exposure
data into two parts: with 70% being used to construct the exposure simulator
and the remaining 30% for constructing the evaluation simulator.

We adopt cross-validation to evaluate the performance of the models (including
the target recommender, exposure simulator, and evaluation simulator). For all
models, we choose 80% users’ data for training, 10% users’ data for
validation, and the rest 10% users’ data for test. Such user-based data split
can effectively avoid potential information leakage.

###  5.3. Implementation Detail

Backbone models. The proposed method is model-agnostic, we adopt the following
representative sequential recommender models as backbone models for our
experiments:

  * •

GRU4Rec (Hidasi et al., 2016b) is an RNN-based sequential recommender, which
leverages GRU (Cho et al., 2014) to encode users’ interaction sequences.

  * •

SASRec (Kang and McAuley, 2018) leverages a Transformer decoder to generate
sequential recommendation.

See Appendix A for hyperparameter settings of backbone models.

Baselines. We compare the exposure debiasing performance of our method with
the following state-of-the-art debiasing methods:

  * •

IPS (Schnabel et al., 2016; Zhu et al., 2023): IPS was first developed by
(Schnabel et al., 2016) to eliminate popularity bias by re-weighing each
interaction according to propensity score.

  * •

IPS-C (Zheng et al., 2021; Bottou et al., 2013): IPS-C adds a max-clipping
operation on the IPS value to reduce the variance of IPS.

  * •

RelMF (Saito et al., 2020): The method aims to use an effective unbiased
estimator to correct the matching score between items and users.

Note that the propensity scores in the original paper are solely estimated by
the user interaction data and fail to account for the temporal nature of the
problem. To solve this issue and adapt these methods to exposure debiasing in
SR, we define propensity scores $p(v|S^{u})=q_{0}(S^{u},v)$, where $q_{0}$ is
the system exposure distribution as detailed in subsection 4.2. Following
(Zheng et al., 2021), the clipping severity in IPS-C is set to the median
exposure probability of all the items. Besides, we also include the normal
training of GRU4Rec and SASRec without applying any debiasing methods for
comparison purposes.

###  5.4. Overall Debiasing Performance (RQ1)

Table 1. Comaprison of debiased recommendation performance. Boldface denotes the highest score. “None” denotes the normal training. “DRO” denotes our method. Datasets | Backbone | Method | Recall@5 | NDCG@5 | Recall@10 | NDCG@10 | Recall@20 | NDCG@20
---|---|---|---|---|---|---|---|---
ZhihuRec | GRU4Rec | None | 0.0094 | 0.0072 | 0.0114 | 0.0079 | 0.0231 | 0.0108
IPS | 0.0083 | 0.0070 | 0.0137 | 0.0087 | 0.0244 | 0.0113
IPS-C | 0.0083 | 0.0057 | 0.0114 | 0.0067 | 0.0189 | 0.0085
RelMF | 0.0032 | 0.0021 | 0.0106 | 0.0046 | 0.0201 | 0.0069
DRO | 0.0103 | 0.0076 | 0.0146 | 0.0090 | 0.0200 | 0.0104
SASRec | None | 0.0119 | 0.0089 | 0.0162 | 0.0104 | 0.0241 | 0.0123
IPS | 0.0109 | 0.0079 | 0.0210 | 0.0112 | 0.0450 | 0.0171
IPS-C | 0.0151 | 0.0097 | 0.0174 | 0.0104 | 0.0261 | 0.0126
RelMF | 0.0095 | 0.0074 | 0.0138 | 0.0088 | 0.0257 | 0.0116
DRO | 0.0220 | 0.0131 | 0.0322 | 0.0162 | 0.0498 | 0.0205
Tenrec | GRU4Rec | None | 0.0335 | 0.0218 | 0.0524 | 0.0280 | 0.0735 | 0.0333
IPS | 0.0320 | 0.0210 | 0.0513 | 0.0273 | 0.0706 | 0.0322
IPS-C | 0.0381 | 0.0244 | 0.0533 | 0.0293 | 0.0802 | 0.0361
RelMF | 0.0382 | 0.0251 | 0.0523 | 0.0296 | 0.0767 | 0.0357
DRO | 0.0336 | 0.0225 | 0.0536 | 0.0290 | 0.0748 | 0.0343
SASRec | None | 0.0337 | 0.0216 | 0.0638 | 0.0313 | 0.1044 | 0.0414
IPS | 0.0365 | 0.0223 | 0.0647 | 0.0314 | 0.1041 | 0.0414
IPS-C | 0.0410 | 0.0266 | 0.0735 | 0.0370 | 0.1143 | 0.0473
RelMF | 0.0363 | 0.0238 | 0.0499 | 0.0282 | 0.0752 | 0.0346
DRO | 0.0517 | 0.0335 | 0.0902 | 0.0457 | 0.1439 | 0.0592

Table 1 shows the overall debiasing performance. We observe that the DRO
method outperforms both vanilla backbone models and debiasing baselines on two
datasets in most cases. These findings suggest that DRO is able to effectively
mitigate the risk of overestimating biased samples and conduct exposure
debiasing. Note that the data is partitioned by the user, with no overlap
between the users in the training and test sets. In other words, user
preference in the training and test data could have shifted in the sequential
recommendation scenario. If the recommender overly relies on the preference
learned from training users, it may raise the overestimation issue of the test
users’ preference and result in sub-optimal performance. Compared with other
methods, the proposed DRO framework compels the model to be less reliant on
the training data distribution and to make more conservative predictions
through the surrogate loss, resulting in better recommendation performance.

Exposure bias can amplify popularity bias, resulting in relevant but unpopular
items being overlooked and not recommended (Chen et al., 2023; Gupta et al.,
2021). Therefore, we also conduct experiments to see whether the proposed
framework generates more diverse recommendation. We use SASRec as the backbone
model. The coverage metric:$\text{ Coverage}@K=\frac{\left|\cup_{u\in\text{
test }}list_{@K}(u)\right|}{|\mathcal{I}|}$, where $list_{@K}(u)$ is the
top-$K$ recommendation list for user $u$, is used to measure the
recommendation diversity. As shown in Fig. 3, the reported results indicate
that the proposed method can significantly help to alleviate popularity bias.
We can see that the DRO, IPS, and IPS-C methods outperform the vanilla
backbone model (SASRec) on both datasets. Specifically, the IPS method
achieves the best performance. However, as reported in Table 1, the accuracy
of the IPS method cannot achieve satisfying results. Compared with vanilla
SASRec, the DRO method achieves better coverage performance, because the
recommender trained by DRO tends to make a conservative recommendation
regarding biased samples. More concretely, the DRO method tends to mitigate
the risk of continuously recommending high-exposed items. It indicates that
alleviating exposure bias could potentially reduce popularity bias as well. It
should be noted that the exposure simulator includes the use of a popularity-
based recommender to boost popular items, which may also contribute to the
success of these methods in alleviating popularity bias.

To conclude, the proposed DRO can effectively alleviate both exposure and
popularity bias, and meanwhile generate more accurate recommendation compared
with existing IPS-based methods.

(a) ZhihuRec

(b) Tenrec

Figure 3. Popularity debiasing effect with different methods.

###  5.5. Effect of the Exposure Simulator (RQ2)

In this subsection, we conduct experiments to verify the impact of the
exposure simulator on the Tenrec dataset. We first examine how the mixture of
recommenders affects the modeling of exposure data. It is important to
accurately simulate the exposure distribution since DRO relies on the system
exposure distribution to construct the uncertainty set. Besides, the
performance of IPS-based methods is also reliant on the propensity, which is
the exposure probability in our setting. Table 2 shows the simulator
performance comparison. Notably, “Expo-M” denotes the exposure simulator that
combines Expo-SASRec, Expo-GRU4Rec, and popularity-based recommenders as
detailed in subsection 4.2. “Expo-G” is short for Expo-GRU4Rec and “Expo-S” is
short for Expo-SASRec. We can see that the ”Expo-M” simulator outperforms the
other single model simulators, indicating its superior ability to accurately
model the exposure distribution.

Table 3 shows the debiasing performance comparison between IPS-C and the
proposed DRO method with different exposure simulators. We can see that the
debiasing performance with the “Expo-M” simulator achieves better performance
than vanilla SASRec and that with the “Expo-S” simulator. It indicates the
“Expo-M” simulator has remarkable ability to model exposure distribution and
thus provides better debiasing performance. Moreover, the performance of the
IPS-C method with the “Expo-S” simulator is inferior to that of the vanilla
SASRec recommender. It shows that establishing a good exposure simulator for
the propensity score is indispensable for IPS-based methods.

Table 2. Performance of exposure simulator. Boldface denotes the highest score. “R” and “N” are short for Recall and NDCG. “Expo-M” denotes the exposure simulator based on mixture of recommenders. “Expo-G” and “Expo-S” are short for Expo-GRU4Rec and Expo-SASRec, respectively. Simulator | R@5 | N@5 | R@10 | N@10 | R@20 | N@20
---|---|---|---|---|---|---
Expo-G | 0.0320 | 0.0210 | 0.0513 | 0.0273 | 0.0706 | 0.0322
Expo-S | 0.0335 | 0.0218 | 0.0524 | 0.0280 | 0.0735 | 0.0333
Expo-M | 0.0381 | 0.0244 | 0.0533 | 0.0293 | 0.0802 | 0.0361
Table 3. Debiasing performance $w.r.t$ different exposure simulators. Boldface denotes the highest score. “R” and “N” are short for Recall and NDCG. “Expo-M” denotes the exposure simulator based on mixture of multiple recommenders. “Expo-S” is short for Expo-SASRec. Simulator |  Method |  R@5 |  N@5 |  R@10 |  N@10 |  R@20 |  N@20
---|---|---|---|---|---|---|---
– |  SASRec |  0.033 |  0.021 |  0.063 |  0.031 |  0.104 |  0.041
Expo-S |  IPS-C |  0.027 |  0.017 |  0.047 |  0.024 |  0.079 |  0.032
|  DRO |  0.044 |  0.028 |  0.082 |  0.041 |  0.129 |  0.052
Expo-M |  IPS-C |  0.041 |  0.026 |  0.073 |  0.037 |  0.114 |  0.047
|  DRO |  0.052 |  0.032 |  0.088 |  0.044 |  0.141 |  0.057

###  5.6. Hyperparameter Study (RQ3)

(a) Recall@20, Tenrec

(b) NDCG@20, Tenrec

(c) Recall@20, ZhihuRec

(d) NDCG@20, ZhihuRec

Figure 4.  Effect of the weight of the DRO loss. The dash line denotes the
performance of SASRec.

In this subsection, we conduct experiments to demonstrate the impact of the
different weights of the DRO loss. We use SASRec as the backbone
recommendation model. Results on the GRU4Rec show the same trend. As discussed
in subsection 4.3, the recommender trained by joint optimization objective (as
detailed in Eq.(8)) with the suitable value of $a$ may approximate the user’s
true preference meanwhile mitigate the exposure bias. If $a\rightarrow 0$, the
optimization objective is reduced to the recommender loss, the recommender is
solely trained on biased user interactions and is likely to overestimate the
user preference over biased samples. If $a\rightarrow\infty$, the recommender
would have excessive attention to perform debiasing and lose recommendation
accuracy. Fig. 4 shows the performance of DRO with different $a$ tuned in the
range of [0.01, 0.1, 1, 10, 100, 1000] on both datasets.

As shown in Fig. 4a and 4b, we can observe the performance of DRO with $a$ in
[0.01, 0.1, 1,10] outperforms the SASRec on the Tenrec dataset. The results
show that DRO with suitable $a$ can perform exposure debiasing and better
obtain user preference compared with the backbone model SASRec. Regarding the
DRO with $a$ in [100, 1000], the recommendation performance drops
dramatically. The reason is that the recommender neglects user personalization
when it over-focuses on debiasing. The results on ZhihuRec are basically the
same as those in Tenrec. Different from the Tenrec, the performance of DRO
with $a=0.01$ is comparable with the SASRec on the ZhihuRec dataset.

##  6\. Conclusions and Future Work

In this paper, we have investigated the task of exposure debiasing in
sequential recommendation. We have proposed to adopt Distributionally Robust
Optimization (DRO) to perform exposure debiasing in SR. More specifically, we
have introduced an exposure simulator trained upon the system exposure data to
calculate exposure distribution, which is then regarded as the nominal
distribution to construct the uncertainty set of DRO. Besides, we have
introduced the penalty to items with high exposure probability to avoid the
overestimation issue for the preference scores of biased samples. Furthermore,
we have designed a debiased self-normalized inverse propensity score (SNIPS)
evaluator for evaluating the debiasing sequential recommendation performance
in the biased test set. Extensive experiments and analysis on two real-world
datasets have demonstrated the effectiveness of the proposed framework.

In future work, we plan to design more advanced exposure simulators to better
model the system exposure distribution. In the real-world recommendation
scenario, items are exposed page-by-page. To this end, developing exposure
simulators to model page-wise exposure data would be a potential research
direction. Additionally, the system exposure data is also highly affected by
other kinds of biases (e.g., the popularity bias). Exploring the relationship
between exposure bias and other biases would also be an interesting research
direction. We hope this work can raise more community concern to conduct
recommendation debiasing from a more wide range of perspectives, other than
just focusing on the user interaction data.

## Acknowledgements

This work was supported by the National Key R&D Program of China with grants
No. 2020YFB1406704 and No. 2022YFC3303004, the Natural Science Foundation of
China (62202271, 61902219, 61972234, 61672324, 62072279, 62102234, 62272274),
the Natural Science Foundation of Shandong Province (ZR2021QF129,
ZR2022QF004), the Key Scientific and Technological Innovation Program of
Shandong Province (2019JZZY010129), the Fundamental Research Funds of Shandong
University, the Tencent WeChat Rhino-Bird Focused Research Program (WXG-
FR-2023-07). All content represents the opinion of the authors, which is not
necessarily shared or endorsed by their respective employers and/or sponsors.

## References

  * (1)
  * Bottou et al. (2013) Léon Bottou, Jonas Peters, Joaquin Quiñonero-Candela, Denis X Charles, D Max Chickering, Elon Portugaly, Dipankar Ray, Patrice Simard, and Ed Snelson. 2013.  Counterfactual Reasoning and Learning Systems: The Example of Computational Advertising.  _Journal of Machine Learning Research_ 14, 11 (2013).
  * Chang et al. (2021) Jianxin Chang, Chen Gao, Yu Zheng, Yiqun Hui, Yanan Niu, Yang Song, Depeng Jin, and Yong Li. 2021.  Sequential recommendation with graph neural networks. In _SIGIR_. 378–387.
  * Chen et al. (2023) Jiawei Chen, Hande Dong, Xiang Wang, Fuli Feng, Meng Wang, and Xiangnan He. 2023.  Bias and debias in recommender system: A survey and future directions.  _ACM Transactions on Information Systems_ 41, 3 (2023), 1–39.
  * Cho et al. (2014) Kyunghyun Cho, Bart Van Merriënboer, Dzmitry Bahdanau, and Yoshua Bengio. 2014.  On the properties of neural machine translation: Encoder-decoder approaches.  _arXiv preprint arXiv:1409.1259_ (2014).
  * Collins et al. (2018) Andrew Collins, Dominika Tkaczyk, Akiko Aizawa, and Joeran Beel. 2018.  A study of position bias in digital library recommender systems.  _arXiv preprint arXiv:1802.06565_ (2018).
  * Dai et al. (2022) Quanyu Dai, Haoxuan Li, Peng Wu, Zhenhua Dong, Xiao-Hua Zhou, Rui Zhang, Rui Zhang, and Jie Sun. 2022.  A generalized doubly robust learning framework for debiasing post-click conversion rate prediction. In _KDD_. 252–262.
  * Damak et al. (2022) Khalil Damak, Sami Khenissi, and Olfa Nasraoui. 2022.  Debiasing the Cloze Task in Sequential Recommendation with Bidirectional Transformers. In _KDD_. 273–282.
  * Du et al. (2023) Yali Du, Yinwei Wei, Wei Ji, Fan Liu, Xin Luo, and Liqiang Nie. 2023.  Multi-queue Momentum Contrast for Microvideo-Product Retrieval. In _WSDM_. 1003–1011.
  * Gupta et al. (2021) Shantanu Gupta, Hao Wang, Zachary Lipton, and Yuyang Wang. 2021.  Correcting exposure bias for link recommendation. In _International Conference on Machine Learning_. PMLR, 3953–3963.
  * Hao et al. (2021) Bin Hao, Min Zhang, Weizhi Ma, Shaoyun Shi, Xinxing Yu, Houzhi Shan, Yiqun Liu, and Shaoping Ma. 2021.  A Large-Scale Rich Context Query and Recommendation Dataset in Online Knowledge-Sharing.  arXiv:2106.06467 [cs.IR]
  * He et al. (2016) Ruining He, Chen Fang, Zhaowen Wang, and Julian McAuley. 2016.  Vista: A visually, socially, and temporally-aware model for artistic recommendation. In _Proceedings of the 10th ACM conference on recommender systems_. 309–316.
  * Hidasi et al. (2016a) Balázs Hidasi, Alexandros Karatzoglou, Linas Baltrunas, and Domonkos Tikk. 2016a.  Session-based Recommendations with Recurrent Neural Networks. In _ICLR (Poster)_.
  * Hidasi et al. (2016b) Balázs Hidasi, Massimo Quadrana, Alexandros Karatzoglou, and Domonkos Tikk. 2016b.  Parallel recurrent neural network architectures for feature-rich session-based recommendations. In _Proceedings of the 10th ACM conference on recommender systems_. 241–248.
  * Hidasi and Tikk (2016) Balázs Hidasi and Domonkos Tikk. 2016.  General factorization framework for context-aware recommendations.  _Data Mining and Knowledge Discovery_ 30, 2 (2016), 342–371.
  * Hu et al. (2018) Yujing Hu, Qing Da, Anxiang Zeng, Yang Yu, and Yinghui Xu. 2018.  Reinforcement learning to rank in e-commerce search engine: Formalization, analysis, and application. In _KDD_. ACM, 368–377.
  * Hu and Hong (2013) Zhaolin Hu and L Jeff Hong. 2013.  Kullback-Leibler divergence constrained distributionally robust optimization.  _Available at Optimization Online_ 1, 2 (2013), 9.
  * Jiang et al. (2019) Ray Jiang, Silvia Chiappa, Tor Lattimore, András György, and Pushmeet Kohli. 2019.  Degenerate feedback loops in recommender systems. In _Proceedings of the 2019 AAAI/ACM Conference on AI, Ethics, and Society_. 383–390.
  * Kang and McAuley (2018) Wang-Cheng Kang and Julian McAuley. 2018.  Self-attentive sequential recommendation. In _ICDM_. IEEE, 197–206.
  * Kingma and Ba (2015) Diederik P. Kingma and Jimmy Ba. 2015.  Adam: A Method for Stochastic Optimization. In _ICLR (Poster)_.
  * Koren et al. (2009) Yehuda Koren, Robert Bell, and Chris Volinsky. 2009.  Matrix factorization techniques for recommender systems.  _Computer_ 42, 8 (2009), 30–37.
  * Li et al. (2017) Jing Li, Pengjie Ren, Zhumin Chen, Zhaochun Ren, Tao Lian, and Jun Ma. 2017.  Neural attentive session-based recommendation. In _CIKM_. 1419–1428.
  * Liu et al. (2020) Dugang Liu, Pengxiang Cheng, Zhenhua Dong, Xiuqiang He, Weike Pan, and Zhong Ming. 2020.  A General Knowledge Distillation Framework for Counterfactual Recommendation via Uniform Data. In _SIGIR_. 831–840.
  * Liu et al. (2023) Dugang Liu, Pengxiang Cheng, Zinan Lin, Xiaolian Zhang, Zhenhua Dong, Rui Zhang, Xiuqiang He, Weike Pan, and Zhong Ming. 2023.  Bounding System-Induced Biases in Recommender Systems with a Randomized Dataset.  _ACM Transactions on Information Systems_ 41, 4 (2023), 1–26.
  * Ning and Karypis (2011) Xia Ning and George Karypis. 2011.  Slim: Sparse linear methods for top-n recommender systems. In _ICDM_. IEEE, 497–506.
  * Pan and Scholz (2009) Rong Pan and Martin Scholz. 2009.  Mind the gaps: weighting the unknown in large-scale one-class collaborative filtering. In _KDD_. 667–676.
  * Rahimian and Mehrotra (2019) Hamed Rahimian and Sanjay Mehrotra. 2019.  Distributionally robust optimization: A review.  _arXiv preprint arXiv:1908.05659_ (2019).
  * Rendle et al. (2010) Steffen Rendle, Christoph Freudenthaler, and Lars Schmidt-Thieme. 2010.  Factorizing personalized Markov chains for next-basket recommendation. In _WWW_. ACM, 811–820.
  * Sagawa et al. (2019) Shiori Sagawa, Pang Wei Koh, Tatsunori B. Hashimoto, and Percy Liang. 2019.  Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization.  _CoRR_ abs/1911.08731 (2019).  arXiv:1911.08731 http://arxiv.org/abs/1911.08731
  * Saito et al. (2020) Yuta Saito, Suguru Yaginuma, Yuta Nishino, Hayato Sakata, and Kazuhide Nakata. 2020.  Unbiased Recommender Learning from Missing-Not-At-Random Implicit Feedback. In _WSDM_. ACM, 501–509.
  * Schnabel et al. (2016) Tobias Schnabel, Adith Swaminathan, Ashudeep Singh, Navin Chandak, and Thorsten Joachims. 2016.  Recommendations as treatments: Debiasing learning and evaluation. In _international conference on machine learning_. PMLR, 1670–1679.
  * Shen et al. (2021) Zheyan Shen, Jiashuo Liu, Yue He, Xingxuan Zhang, Renzhe Xu, Han Yu, and Peng Cui. 2021.  Towards Out-Of-Distribution Generalization: A Survey.  _CoRR_ abs/2108.13624 (2021).  arXiv:2108.13624 https://arxiv.org/abs/2108.13624
  * Słowik and Bottou (2022) Agnieszka Słowik and Léon Bottou. 2022.  On distributionally robust optimization and data rebalancing. In _International Conference on Artificial Intelligence and Statistics_. PMLR, 1283–1297.
  * Sun et al. (2019) Fei Sun, Jun Liu, Jian Wu, Changhua Pei, Xiao Lin, Wenwu Ou, and Peng Jiang. 2019.  BERT4Rec: Sequential recommendation with bidirectional encoder representations from transformer. In _CIKM_. 1441–1450.
  * Swaminathan and Joachims (2015) Adith Swaminathan and Thorsten Joachims. 2015.  The self-normalized estimator for counterfactual learning.  _NIPS_ 28 (2015).
  * Vaswani et al. (2017) Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. 2017.  Attention is All you Need. In _NIPS_. 5998–6008.
  * Wang et al. (2019a) Pengfei Wang, Hanxiong Chen, Yadong Zhu, Huawei Shen, and Yongfeng Zhang. 2019a.  Unified collaborative filtering over graph embeddings. In _SIGIR_. 155–164.
  * Wang et al. (2019b) Xiaojie Wang, Rui Zhang, Yu Sun, and Jianzhong Qi. 2019b.  Doubly robust joint learning for recommendation on data missing not at random. In _International Conference on Machine Learning_. PMLR, 6638–6647.
  * Wang et al. (2021) Xiaojie Wang, Rui Zhang, Yu Sun, and Jianzhong Qi. 2021.  Combating selection biases in recommender systems with a few unbiased ratings. In _WSDM_. 427–435.
  * Wang et al. (2022) Zhenlei Wang, Shiqi Shen, Zhipeng Wang, Bo Chen, Xu Chen, and Ji-Rong Wen. 2022.  Unbiased sequential recommendation with latent confounders. In _WWW_. 2195–2204.
  * Wen et al. (2022) Hongyi Wen, Xinyang Yi, Tiansheng Yao, Jiaxi Tang, Lichan Hong, and Ed H Chi. 2022.  Distributionally-robust Recommendations for Improving Worst-case User Experience. In _www_. 3606–3610.
  * Wu et al. (2019) Shu Wu, Yuyuan Tang, Yanqiao Zhu, Liang Wang, Xing Xie, and Tieniu Tan. 2019.  Session-based recommendation with graph neural networks. In _Proceedings of the AAAI conference on artificial intelligence_ , Vol. 33. 346–353.
  * Xin et al. (2020) Xin Xin, Alexandros Karatzoglou, Ioannis Arapakis, and Joemon M Jose. 2020.  Self-supervised reinforcement learning for recommender systems. In _SIGIR_. 931–940.
  * Xin et al. (2023) Xin Xin, Jiyuan Yang, Hanbing Wang, Jun Ma, Pengjie Ren, Hengliang Luo, Xinlei Shi, Zhumin Chen, and Zhaochun Ren. 2023.  On the user behavior leakage from recommender system exposure.  _ACM Transactions on Information Systems_ 41, 3 (2023), 1–25.
  * Xu et al. (2022) Chen Xu, Jun Xu, Xu Chen, Zhenghua Dong, and Ji-Rong Wen. 2022.  Dually Enhanced Propensity Score Estimation in Sequential Recommendation. In _CIKM_. 2260–2269.
  * Yang et al. (2018) Longqi Yang, Yin Cui, Yuan Xuan, Chenyang Wang, Serge Belongie, and Deborah Estrin. 2018.  Unbiased offline recommender evaluation for missing-not-at-random implicit feedback. In _Proceedings of the 12th ACM conference on recommender systems_. 279–287.
  * Yang et al. (2023) Zhengyi Yang, Xiangnan He, Jizhi Zhang, Jiancan Wu, Xin Xin, Jiawei Chen, and Xiang Wang. 2023.  A generic learning framework for sequential recommendation with distribution shifts. In _SIGIR_. 331–340.
  * Yuan et al. (2019) Fajie Yuan, Alexandros Karatzoglou, Ioannis Arapakis, Joemon M Jose, and Xiangnan He. 2019.  A Simple Convolutional Generative Network for Next Item Recommendation. In _WSDM_. ACM, 582–590.
  * Yuan et al. (2022) Guanghu Yuan, Fajie Yuan, Yudong Li, Beibei Kong, Shujie Li, Lei Chen, Min Yang, Chenyun Yu, Bo Hu, Zang Li, et al. 2022\.  Tenrec: A Large-scale Multipurpose Benchmark Dataset for Recommender Systems.  _NIPS_ 35 (2022), 11480–11493.
  * Zhang et al. (2021) Yang Zhang, Fuli Feng, Xiangnan He, Tianxin Wei, Chonggang Song, Guohui Ling, and Yongdong Zhang. 2021.  Causal intervention for leveraging popularity bias in recommendation. In _SIGIR_. 11–20.
  * Zheng et al. (2021) Yu Zheng, Chen Gao, Xiang Li, Xiangnan He, Yong Li, and Depeng Jin. 2021.  Disentangling user interest and conformity for recommendation with causal embedding. In _www_. 2980–2991.
  * Zhou et al. (2020) Kun Zhou, Hui Wang, Wayne Xin Zhao, Yutao Zhu, Sirui Wang, Fuzheng Zhang, Zhongyuan Wang, and Ji-Rong Wen. 2020.  S3-Rec: Self-Supervised Learning for Sequential Recommendation with Mutual Information Maximization. In _CIKM_. ACM, 1893–1902.
  * Zhou et al. (2023) Rui Zhou, Xian Wu, Zhaopeng Qiu, Yefeng Zheng, and Xu Chen. 2023.  Distributionally Robust Sequential Recommnedation. In _SIGIR_. 279–288.
  * Zhu et al. (2023) Yaochen Zhu, Jing Ma, and Jundong Li. 2023.  Causal Inference in Recommender Systems: A Survey of Strategies for Bias Mitigation, Explanation, and Generalization.  _arXiv preprint arXiv:2301.00910_ (2023).

##  Appendix A PROOF OF THEOREMS

###  A.1. Proof 1

###### Proof.

In this proof, we follow the deviation from (Hu and Hong, 2013). Set $D$ as
KL-divergence, minimizing the Eq. (3) can be formulated as:

(12) $\begin{split}\min_{\theta}\max_{q}\mathbb{E}_{(S^{u},v)\sim
q}\ell(S^{u},v,\theta)\\\ \text{subject to
}D_{KL}\left(q\|q_{0}\right)\leq\eta.\end{split}$

Note that $q_{0}$ is the nominal distribution. Assume that the distributions
$q$ and $q_{0}$ have densities denoted by $p(S^{u},v)$ and $p_{0}(S^{u},v)$,
respectively.

Let the Radon-Nikodym derivative $L(S^{u},v)=p(S^{u},v)/p_{0}(S^{u},v)$, and
by applying the change-of-measure technique, we obtain:

(13)
$\begin{split}D_{KL}\left(q\|q_{0}\right)&=\int\frac{p(S^{u},v)}{p_{0}(S^{u},v)}\log\frac{p(S^{u},v)}{p_{0}(S^{u},v)}p_{0}(S^{u},v)\mathrm{d}s\mathrm{d}v\\\
&=\int L(S^{u},v)\log L(S^{u},v)p_{0}(S^{u},v)\mathrm{d}s\mathrm{d}v\\\
&=\mathbb{E}_{(S^{u},v)\sim q_{0}}[L(S^{u},v)\log L(S^{u},v)].\end{split}$

Similarly,

(14) $\mathbb{E}_{(S^{u},v)\sim
q}\ell(S^{u},v,\theta)=\mathbb{E}_{(S^{u},v)\sim
q_{0}}[\ell(S^{u},v,\theta)L(S^{u},v)].$

Then, the inner maximization problem in Eq.(12) can be reformulated as

(15) $\begin{split}\max_{L}\mathbb{E}_{(S^{u},v)\sim
q_{0}}[\ell(S^{u},v,\theta)L(S^{u},v)]\\\ \text{subject to
}\mathbb{E}_{(S^{u},v)\sim q_{0}}[L\log L]\leq\eta.\end{split}$

To formulate the dual problem of Eq.(15), we formulate the Lagrangian
functional is

(16) $l(\alpha,L)=\mathbb{E}_{(S^{u},v)\sim
q_{0}}[\ell(S^{u},v,\theta)L]-\alpha(\mathbb{E}_{(S^{u},v)\sim q_{0}}[L\log
L]-\eta)$

Then, Eq.(15) is equivalent to

(17) $\max_{L}\min_{\alpha\geq 0}l(\alpha,L).$

Interchanging the order of the maximum and minimum operators, we obtain the
Lagrangian dual of Eq.(17), which is represented as

(18) $\min_{\alpha\geq 0}\max_{L}l(\alpha,L).$

The strong duality for Eq.(17) and Eq.(18) have proved in (Hu and Hong, 2013).
It is easy to see the $\mathbb{E}_{(S^{u},v)\sim q_{0}}[L]=1$. Omitting the
term $\alpha\eta$, the inner maximization problem in Eq.(18) can be expressed
as

(19) $\begin{split}\max_{L}\mathbb{E}_{(S^{u},v)\sim
q_{0}}[\ell(S^{u},v,\theta)L-\alpha L\log L])\\\ \text{subject to
}\mathbb{E}_{(S^{u},v)\sim q_{0}}[L]=1.\end{split}$

Define the functionals of Eq.(19)

(20) $\begin{split}\mathcal{J}(L)&=\mathbb{E}_{(S^{u},v)\sim
q_{0}}[\ell(S^{u},v,\theta)L-\alpha L\log L])\\\
\mathcal{J}_{c}(L)&=\mathbb{E}_{(S^{u},v)\sim q_{0}}[L]-1.\end{split}$

Let $D\mathcal{J}(L(S^{u},v))$ denote the derivative of
$\mathcal{J}(L(S^{u},v))$, and for any feasible direction $V(S^{u},v)$ at
$L(S^{u},v)$, we have:

$\displaystyle D\mathcal{J}(L(S^{u},v))V(S^{u},v)$ $\displaystyle=$
$\displaystyle\lim_{t\rightarrow
0}\frac{\mathcal{J}(L(S^{u},v)+tV(S^{u},v))-\mathcal{J}(L(S^{u},v))}{t}$
$\displaystyle=$ $\displaystyle\lim_{t\rightarrow
0}\frac{\mathbb{E}_{(S^{u},v)\sim
q_{0}}[\ell(S^{u},v,\theta)(L+tV)-\alpha(L+tV)\log(L+tV)]}{t}$
$\displaystyle-$ $\displaystyle\lim_{t\rightarrow
0}\frac{\mathbb{E}_{(S^{u},v)\sim q_{0}}[\ell(S^{u},v,\theta)L-\alpha L\log
L]}{t}$ $\displaystyle=\mathbb{E}_{(S^{u},v)\sim
q_{0}}[\ell(S^{u},v,\theta)V]$ (21) $\displaystyle-$
$\displaystyle\alpha\lim_{t\rightarrow 0}\mathbb{E}_{(S^{u},v)\sim
q_{0}}\left[\frac{(L+tV)\log(L+tV)-L\log L}{t}\right].$

Using the monotone convergence theorem, we can rearrange the operators in
Eq.(A.1):

$\displaystyle D\mathcal{J}(L(S^{u},v))V(S^{u},v)$
$\displaystyle=\mathbb{E}_{(S^{u},v)\sim q_{0}}[\ell(S^{u},v,\theta)V]$
$\displaystyle-\alpha\mathbb{E}_{(S^{u},v)\sim q_{0}}\lim_{t\rightarrow
0}\left[\frac{(L+tV)\log(L+tV)-L\log L}{t}\right]$ (22)
$\displaystyle=\mathbb{E}_{(S^{u},v)\sim
q_{0}}[(\ell(S^{u},v,\theta)-\alpha(\log L+1))V].$

Similarly, we have:

(23) $D\mathcal{J}_{c}(L(S^{u},v))V=\mathbb{E}_{(S^{u},v)\sim q_{0}}[V].$

We construct Lagrangian functional associated with Eq.(16) as follows:

(24) $\displaystyle Y(L,\lambda)$ $\displaystyle=\mathbb{E}_{(S^{u},v)\sim
q_{0}}[\ell(S^{u},v,\theta)L-\alpha L\log L]+\lambda(\mathbb{E}_{(S^{u},v)\sim
q_{0}}[L]-1)$ $\displaystyle=\mathbb{E}_{(S^{u},v)\sim
q_{0}}[\ell(S^{u},v,\theta)L-\alpha L\log L+\lambda L]-\lambda.$

Similarly, it is also straightforward to obtain that

(25) $\displaystyle DY(S^{u},v)V=\mathbb{E}_{(S^{u},v)\sim
q_{0}}[(\ell(S^{u},v,\theta)-\alpha(\log L+1)+\lambda)V].$

To acquire an optimal solution $L^{*}(S^{u},v)$, let $DY(L(S^{u},v))=0$ for
the all feasible direction $V(S^{u},v)$:

(26) $\ell(S^{u},v,\theta)-\alpha(\log L+1)+\lambda=0.$

Solving the equation, we get

(27)
$L^{*}(s,v,\lambda)=e^{\ell(S^{u},v,\theta)/\alpha+(\lambda-\alpha)/\alpha}.$

From Eq.(19) and Eq.(20) we have $\mathbb{E}_{(S^{u},v)\sim q_{0}}[L^{*}]=1$
and $\mathcal{J}_{c}(L^{*})=0$, then we can obtain
$\lambda^{*}=-\alpha\mathbb{E}_{(S^{u},v)\sim
q_{0}}[e^{\ell(S^{u},v,\theta)/\alpha}]+\alpha$. Therefore,

(28)
$L^{*}(S^{u},v)=L^{*}(s,v,\lambda^{*})=\frac{e^{\ell(S^{u},v,\theta)/\alpha}}{\mathbb{E}_{(S^{u},v)\sim
q_{0}}[e^{\ell(S^{u},v,\theta)/\alpha}]}$

Put $L^{*}(S^{u},v)$ into Eq.(16), we obtain the close from of Eq.(15):

(29) $l^{*}(\alpha,L)=\alpha\mathbb{E}_{(S^{u},v)\sim
q_{0}}[e^{\ell(S^{u},v,\theta)/\alpha}]+\alpha\eta$

Finally, the $\alpha=1$ in our setting and omitting constant terms, we can
obtain:

(30) $\mathcal{L}_{DRO}^{{}^{\prime\prime}}(\theta)=\mathbb{E}_{(S^{u},v)\sim
q_{0}}[e^{\ell(S^{u},v,\theta)}],$

which completes the proof. ∎

###  A.2. Proof 2

###### Proof.

In this proof, we follow (Yang et al., 2018) to prove the following SNIPS
evaluator is a debiased evaluator.

(31)
$\begin{split}\mathbb{E}_{O}[\hat{R}_{\text{SNIPS}}(\hat{Z}|\rho)]&=\frac{1}{\sum_{u\in\mathcal{U}}{\frac{1}{\rho^{k}_{v}}}}\sum_{u\in\mathcal{U}}\sum_{i\in\mathcal{I}}\frac{c(\hat{Z}_{u,\,i)}}{\rho^{k}_{i}}\cdot\mathbb{E}_{O}[O_{u,i}]\\\
&=\frac{1}{\sum_{u\in\mathcal{U}}{\frac{1}{\rho^{k}_{v}}}}\sum_{u\in\mathcal{U}}\sum_{i\in\mathcal{I}}\frac{c(\hat{Z}_{u,\,i)}}{\rho^{k}_{i}}\cdot\rho_{i}\\\
&=\frac{1}{\sum_{u\in\mathcal{U}}{\frac{1}{\rho^{k}_{v}}}}\sum_{u\in\mathcal{U}}\sum_{i\in\mathcal{I}}\frac{c(\hat{Z}_{u,\,i)}}{\rho^{1-k}_{i}}\\\
&=\frac{|\mathcal{U}|\cdot|\mathcal{I}|}{\sum_{u\in\mathcal{U}}{\frac{1}{\rho^{k}_{v}}}}\sum_{u\in\mathcal{U}}\sum_{i\in\mathcal{I}}\frac{1}{\rho^{1-k}_{i}}\cdot\mathbb{E}_{O}[R_{\text{ideal}}(\hat{Z})].\end{split}$

∎

##  Appendix A statistics of datasets

In this work, we conduct experiments on two datasets, Zhihu (Hao et al., 2021)
and Tenrec (Yuan et al., 2022). Table 4 summarizes the statistics of the two
datasets.

ZhihuRec. This dataset is obtained from Zhihu, a knowledge-sharing platform.
The original data includes question information, answer information, and user
profiles. Our focus is on the scenario of answer recommendation, where a slate
of answers (i.e., the items in our setting) is presented to the user during
the recommender’s serving period. The dataset contains the show time and click
time of all answers, with a value of 0 for non-clicked answers. In total, the
dataset contains 771,550 impressions and 214,853 user clicks, covering 9,223
items from 7,862 users.

Tenrec. This is a large-scale dataset and is collected from two feeds, namely
articles and videos, on Tenrec’s recommendation platforms. Our primary focus
for this study is on the video recommendation scenario. The data we used
comprises 1,738,116 recommended impressions for 31,722 users, covering 24,653
videos and a total of 912,812 user clicks.

Table 4. Dataset statistics. Dataset | ZhihuRec | Tenrec
---|---|---
#users | 7,862 | 31,722
#items | 9,223 | 24,653
#impressions | 771,550 | 1,738,116
#clicks | 214,853 | 912,812

##  Appendix A reproducibility

Hyperparameter settings. For each user interaction, we preserve the last 50
click items as the historical interaction sequence to avoid too long
sequences. We pad the sequence with an additional padding item if the sequence
length is less than 50. For the system exposure, we preserve the last 200
exposed items and pad the sequence with an additional padding item if the
sequence length is less than 200. For a fair comparison, the item embedding
size is set to 64 across all models. We train all models with the Adam
optimizer(Kingma and Ba, 2015). The learning rate is tuned to 0.005. For
SASRec, the number of heads in self-attention is set to 2, with a total of 64
hidden neurons. For GRU4Rec, the number of layers in GRU is set to 1. The size
of hidden layers in the feedforward network is also set to 64 for two backbone
models. The $\beta$ in Eq.(4) to boost popular items is set to 0.3. Each
experiment is conducted 3 times and the average result is reported.