# Multi-Domain Recommendation to Attract Users via Domain Preference Modeling

Hyunjun Ju1, SeongKu Kang2, Dongha Lee3, Junyoung Hwang1, Sanghwan Jang1,
Hwanjo Yu1
Corresponding Author

###### Abstract

Recently, web platforms have been operating various service domains
simultaneously. Targeting a platform that operates multiple service domains,
we introduce a new task, Multi-Domain Recommendation to Attract Users (MDRAU),
which recommends items from multiple “unseen” domains with which each user has
not interacted yet, by using knowledge from the user’s “seen” domains. In this
paper, we point out two challenges of MDRAU task. First, there are numerous
possible combinations of mappings from seen to unseen domains because users
have usually interacted with a different subset of service domains. Second, a
user might have different preferences for each of the target unseen domains,
which requires that recommendations reflect the user’s preferences on domains
as well as items. To tackle these challenges, we propose DRIP framework that
models users’ preferences at two levels (i.e., domain and item) and learns
various seen-unseen domain mappings in a unified way with masked domain
modeling. Our extensive experiments demonstrate the effectiveness of DRIP in
MDRAU task and its ability to capture users’ domain-level preferences.

##  1 Introduction

Nowadays, web platforms are operating various service domains simultaneously
(e.g., music streaming, game store, and eBook subscription). They allow users
to experience diverse domains within a single platform and promote the mutual
growth of all service domains through the Recommender System (RS). For such
multi-domain platforms, recommending items from unseen domains with which each
user has not interacted yet plays an essential role in the platform’s growth,
user satisfaction, and business success. That is, users typically utilize a
few domains rather than all domains, and accurate recommendations that align
with user preference can attract users into unexplored domains. To this end,
Cross-Domain Recommendation (CDR), which recommends items from unseen (target)
domains based on user interaction history in seen (source) domains, has gained
significant research attention.111In this paper, the terms “seen” and “unseen”
are defined from the perspective of each user; as each user interacts with a
different subset of service domains, the seen and unseen domain sets vary for
each user. A user can be considered a cold-start user in the user’s unseen
service domain (Man et al. 2017; Kang et al. 2019; Zhu et al. 2022).

Figure 1: A conceptual illustration of MDRAU task. A platform operates five
different service domains, and each user partially interacts with a subset of
the entire service domains. MDRAU aims to provide recommendations from each
user’s unseen domains to attract users.

Most CDR studies (Man et al. 2017; Kang et al. 2019; Zhu et al. 2022, 2021b;
Fu et al. 2019) have focused on transferring user preference information from
a source domain to a target domain. Given a recommender system employed for
each domain, they learn a mapping function that acts as a bridge between the
representation spaces of the two domains. To provide unseen domain
recommendations, they transfer the user embedding from the source domain to
the target domain using the mapping function and generate recommendations
based on the transferred user embedding. More recently, (Cao et al. 2022b,
2023, a) have achieved improved recommendation accuracy by modeling domain-
specific and domain-shared information separately, and selectively
transferring the domain-shared information. Despite their effectiveness, the
existing studies have targeted the case of a single seen-unseen domain pair
(i.e., one-to-one), and the case of multiple seen-unseen domains (i.e., many-
to-many) has not been studied well. Especially, they do not consider making
unified recommendations that include items from multiple domains.

In practical scenarios, it is becoming increasingly common for platforms to
offer services in more than two domains. This creates a need to promote user
engagement across multiple unseen domains by attracting users with accurate
personalized recommendations. We refer to this problem as Multi-Domain
Recommendation to Attract Users (MDRAU) task (Fig. 1). Formally, MDRAU aims to
provide a recommendation list that consists of items from each user’s unseen
domain(s) that the user has not tried before. MDRAU brings several practical
values to multi-domain platforms. It encourages users to explore new content
beyond their previously interacted domains, fostering diverse and
serendipitous discoveries. This diversified user experience can lead to
enhanced user satisfaction and engagement, which in turn helps to provide more
accurate recommendations in each domain.

Addressing MDRAU task presents two major challenges. First, since each user
has interacted with different service domains, there are numerous possible
combinations of seen-unseen domains. With $K$ domains, the number of
combinations can reach up to $2^{K}-2$, except in the case that a user has
used all services. This large number of combinations makes it difficult to
apply the previous CDR methods that learn a one-to-one mapping function for
each domain pair. Second, a user naturally has different preference for each
unseen domain, and these varying domain preference need to be properly
reflected in the recommendation process. That is, the recommendation needs to
consider user preference in both domain-level, i.e., the inclination of a user
to explore each unseen domain, and item-level, i.e., the inclination of a user
to interact with a new item within a domain. The previous CDR methods have
focused on improving item-level preference for a specific unseen domain
without directly considering domain-level preference. As a result, they show
limited performance when applied to MDRAU task.

To effectively solve our new task MDRAU, we propose DRIP, a new framework that
learns various seen-unseen domain mappings in a unified way via masked domain
modeling and models user preference at the domain and item levels. We
formulate the training process of DRIP as a prediction task of missing
information based on its contexts (Devlin et al. 2019; Bao et al. 2022). Then,
we model the two-level preferences using a multi-domain encoder that
incorporates user preference across multiple domains. The key idea is to
randomly mask the user preference of some seen domains in the model input, and
train the model to predict the user preference in the masked domains. During
the training, we regard the masked domains as the user’s unseen domains,
allowing the model to simulate and learn from numerous scenarios involving
different combinations of seen and unseen domains. This enables the model to
achieve the generalization capability of inferring user preferences in unseen
domains from ones in seen domains. Furthermore, we introduce an adaptive
masking scheme to make the model more focused on learning domains that a user
is more likely to prefer. We validate the superiority of DRIP by extensive
experiments on real-world datasets and provide a thorough comparison with
various state-of-the-art methods.

##  2 Related Work

The existing CDR studies can be divided into two groups according to the type
of target domain for recommendations.

CDR for Seen Domain Recommendation.  It aims to improve the recommendation
quality of seen domains with which the user has already interacted. Many
studies alleviate the data sparsity problem in the sparse target domains by
utilizing information from the source domain (Hu, Zhang, and Yang 2018; Zhu et
al. 2019; Yuan, Yao, and Benatallah 2019; Zhu et al. 2020; Liu et al. 2020; Li
and Tuzhilin 2020; Cao et al. 2022a). To this end, they transfer knowledge
among domains via bridging information, such as overlapping users or items.
For example, CoNet (Hu, Zhang, and Yang 2018) introduces cross-connection
units to transfer and integrate knowledge between source and target domains.
DTCDR (Zhu et al. 2019) proposes a dual-target framework to improve the
recommendation accuracy in both two involved domains simultaneously. GA-DTCDR
(Zhu et al. 2020) extends DTCDR by adopting graph information. Recently,
several studies have focused on multi-domain cases having more than two
domains (Singh and Gordon 2008; Zhang, Cao, and Yeung 2010; Cao et al. 2023;
Li et al. 2023; Zhao, Yang, and Yu 2022; Cui et al. 2020; Zhu et al. 2023).
GA-MTCDR (Zhu et al. 2023) extends GA-DTCDR with element-wise attention to
integrating embeddings of overlapping users from multiple domains. CAT-ART (Li
et al. 2023) proposes a contrastive autoencoder to encode a global user
embedding and a mechanism to transfer user embeddings from each source domain
to the target domain. UniCDR (Cao et al. 2023) introduces domain-specific and
domain-shared embeddings along with aggregation schemes to make a universal
model for existing CDR scenarios.

CDR for Unseen Domain Recommendation.  It aims to provide recommendations in
unseen domains with which the user has not yet interacted. Their focus lies on
the method of obtaining user embeddings in the target domain space. For
example, EMCDR (Man et al. 2017) proposes an embedding and mapping framework,
which learns a mapping function that transfers user embeddings from the source
to the unseen target domain. SSCDR (Kang et al. 2019) proposes a semi-
supervised embedding and mapping framework to train a mapping function, even
when only a few labeled data are available. PTUPCDR (Zhu et al. 2022) uses a
meta-network that generates a personalized mapping function. UniCDR (Cao et
al. 2023) can also be applied to recommend unseen domains using domain-shared
embeddings. They mainly focus on a single unseen target domain rather than
multiple unseen target domains.

Despite their effectiveness, there is no method particularly designed for
MDRAU task. Existing CDR methods that handle unseen domains have only focused
on the case of a single seen-unseen domain pair. Also, CDR methods dealing
with multi-domain cases mainly focus on recommendations within seen domains.
To address MDRAU task, a method needs the ability to create an accurate,
unified recommendation list across multiple domains that users have not tried
before. We believe that a tailored solution for MDRAU task is required.

##  3 Problem Formulation

###  3.1 Notations

In this work, we focus on a scenario where a provider operates services for
multiple domains (e.g., music streaming, game store, and eBook subscription),
each of which employs a distinct recommender system. Each service domain has
its own user and item set. Items of each domain are mutually exclusive, while
users may use one or multiple service domain(s). Formally, given $K$ domains
$\mathcal{D}=\\{d_{1},\cdots,d_{K}\\}$, ${\mathcal{U}_{k}}$ and
${\mathcal{V}_{k}}$ denote the set of users and items for the $k$-th domain,
respectively. The user-item interaction history for $d_{k}$ is represented by
a matrix
${\bm{R}^{(k)}}\in\left\\{0,1\right\\}^{|{\mathcal{U}_{k}}|\times|{\mathcal{V}_{k}}|}$,
where $R_{u,v}=1$ if user $u$ has interacted with the item $v$, otherwise
$R_{u,v}=0$. Without loss of generality, we define an interaction matrix of
all domains ${\bm{R}}\in\\{0,1\\}^{|{\mathcal{U}}|\times|{\mathcal{V}}|}$,
where ${\mathcal{U}}=\bigcup_{k=1}^{K}{\mathcal{U}_{k}}$ and
${\mathcal{V}}=\bigcup_{k=1}^{K}{\mathcal{V}_{k}}$. We additionally define the
user-domain relations as
$\bm{G}\in\left\\{0,1\right\\}^{|\mathcal{U}|\times|\mathcal{D}|}$, where
$G_{u,k}=1$ if the user $u$ has interacted with items of domain $d_{k}$,
otherwise $G_{u,k}=0$. Overlapping users indicate users who have interacted
with at least two domains.

###  3.2 MDRAU Task

######  Definition 1 (Multi-Domain Recommendation to Attract Users)

Given user-item interaction history from multiple service domains, MDRAU
refers to the task of providing a ranking list (i.e., recommendation) that
consists of items from each user’s unseen domain(s) that the user has not
tried before.

In some cases, providers may have a need to promote a specific target domain
within the platform. We refer to the scenario with a single target domain as
MDRAU-ST, and the scenario with multiple target domains as MDRAU-MT. MDRAU
provides preferable items from each user’s unseen domains, encouraging the
exploration of new content beyond their previously interacted domains. By
doing so, MDRAU helps to diversify user experience and facilitate
serendipitous discoveries, enhancing user engagement. This enhanced
engagement, in turn, helps to provide more accurate recommendations in each
domain, ultimately contributing to the growth and revenue of the platform.

Figure 2: The overview of the proposed DRIP framework.

##  4 Proposed Framework

###  4.1 Overview

We present a unified framework for MDRAU task, named as DRIP (Domain
pReference-aware unseen domain Item Prediction). DRIP optimizes the parameters
of its model by maximizing the likelihood given the training data ${\bm{R}}$.
Let $\bm{R}_{u}\in\\{0,1\\}^{|\mathcal{V}|}$ denote a multi-hot vector
representing a user’s interaction with the items over all domains. We assume
the observed data are drawn from the Multinomial distribution, and the
likelihood is described by

$\begin{split}p(\bm{R}_{u})&=\prod_{v\in\mathcal{V}}p(v|u)^{R_{u,v}}\\\
\bm{R}_{u}&\sim\textnormal{Mult}(N_{u},p(v|u)),\end{split}$ (1)

where $N_{u}=\sum_{v}R_{u,v}$ and $p(v|u)$ is the probability that user $u$
prefers the item $v$ over the entire item set. We decompose the likelihood
based on the domain-level and item-level preference as follows:

$\displaystyle p(\bm{R}_{u})$
$\displaystyle=\prod_{v\in{\mathcal{V}}}p(v|u)^{R_{u,v}}=\prod_{d_{k}\in{\mathcal{D}}}\prod_{v\in{\mathcal{V}}_{k}}p(v,d_{k}|u)^{R_{u,v}}$
(2a)
$\displaystyle=\prod_{d_{k}\in{\mathcal{D}}}\prod_{v\in{\mathcal{V}}_{k}}\big{[}p(v|u,d_{k})\cdot
p(d_{k}|u)\big{]}^{R_{u,v}},$ (2b)

where $p(v|u,d_{k})$ denotes user $u$’s preference for item $v$ in domain
$d_{k}$ and $p(d_{k}|u)$ denotes the user’s preference for domain $d_{k}$. Eq.
(2a) holds because item sets from different domains are mutually exclusive
from each other. These preferences are modeled by a unified neural model with
a multi-domain encoder based on self-attention. Then, to maximize the
likelihood, we train the model via masked domain modeling that predicts the
item preference of the masked domains. The recommendations are produced by
considering both domain- and item-level preferences for unseen domains of each
user. Fig. 2 illustrates the overall DRIP architecture.

###  4.2 Domain-Specific Encoder

As aforementioned, we assume that a service platform operates multiple service
domains and has deployed its own RS for each domain. An RS model typically
contains encoders that encode the user and item information into
representation space, where the user-item similarity is measured for
recommendations. In specific, for each domain $d_{k}$, let
$f_{\bm{\theta}_{k}}:\mathbb{R}^{|\mathcal{U}_{k}|}\rightarrow\mathbb{R}^{d}$,
$f_{\bm{\xi}_{k}}:\mathbb{R}^{|\mathcal{V}_{k}|}\rightarrow\mathbb{R}^{d}$,
and $\text{sim}_{k}(\cdot,\cdot)$ denote a user encoder, an item encoder, and
similarity function, respectively. A variety of architectures can be adopted
for the encoders (e.g., id-based (Koren, Bell, and Volinsky 2009; Rendle et
al. 2009) and graph-based (Wang et al. 2019; He et al. 2020)), and
$\text{sim}_{k}(\cdot,\cdot)$ can be either a simple metric or a learnable
function. In this work, we use a simple id-based encoder with the inner
product similarity, as done in (Rendle et al. 2009; Man et al. 2017; Zhu et
al. 2022).

###  4.3 Multi-Domain Encoder

The main component of our unified neural model is a multi-domain encoder that
aims to enrich user embedding from each domain-specific encoder with that from
the encoders for other domains. It adopts the self-attention mechanism to
aggregate information from other domains based on the similarity of user
preferences across multiple domains.

#### Constructing Masked Input.

Let $\bm{x}_{u,k}=f_{\bm{\theta}_{k}}(u)$ denote user embedding of user $u$ in
domain $d_{k}$. A user $u$ is represented as the set of the corresponding user
embeddings for all domains $\\{\bm{x}_{u,k}\\}_{k=1}^{K}$. Note that some
domains may have no interaction history with the user (i.e., $G_{u,k}=0$), as
users typically utilize a few domains rather than all domains. To handle this
case, we replace the embedding for the user’s unseen domains with
$\bm{e}_{\texttt{[M]}}$, which is the learnable embedding of a special mask
token [M] as follows:

$\bar{\bm{X}}_{u}=\\{\bar{\bm{x}}_{u,k}\\}_{k=1}^{K},\quad\bar{\bm{x}}_{u,k}=(1-G_{u,k})\bm{e}_{\texttt{[M]}}+G_{u,k}\bm{x}_{u,k}.$
(3)

Because the embeddings are obtained from independently trained domain-specific
RS models, they have different distributions. We align the distributions using
projectors $g_{\bm{\phi}_{k}}(\bm{x}_{u,k})$, where
$g_{\bm{\phi}_{k}}:\mathbb{R}^{d}\rightarrow\mathbb{R}^{m}$. Besides, we
insert $\bm{e}_{\texttt{[S]}}\in\mathbb{R}^{m}$ at the beginning of the input
for the encoder, which is the learnable embedding of a special token [S]; this
will be used to estimate each user’s domain-level preference. The final input
representation of user $u$ is constructed as

$\bm{H}_{u}^{0}=\big{[}\bm{e}_{\texttt{[S]}},g_{\bm{\phi}_{1}}(\bar{\bm{x}}_{u,1}),\cdots,g_{\bm{\phi}_{K}}(\bar{\bm{x}}_{u,K})\big{]}^{\top}\in\mathbb{R}^{(K+1)\times
m}.$ (4)

We do not use position embedding because spatial position information is
unnecessary for our target task.

#### Contextualizing User Embeddings over Multi-Domains.

The input $\bm{H}_{u}^{0}$ is forwarded into the multi-domain encoder to
contextualize each domain-specific user embedding over the user’s multiple
domains based on the self-attention mechanism. The multi-domain encoder is
basically a stack of $L$ transformer layers (Vaswani et al. 2017; Devlin et
al. 2019). The details are described in the Appendix. The $l$-th transformer
layer can be simply described by

$\bm{H}_{u}^{l+1}=\text{Transformer}(\bm{H}_{u}^{l}),\quad\forall
l\in\left\\{0,1,\cdots,L-1\right\\}.$ (5)

We denote a set of learnable parameters in the multi-domain encoder consisting
of transformer layers as $\bm{\Omega}$ for a consistent explanation. In the
end, the final output of $L$-th layer is obtained by

$\bm{H}_{u}^{L}=\big{[}\bm{h}_{u,\texttt{[S]}}^{L},\bm{h}_{u,1}^{L},\cdots,\bm{h}_{u,K}^{L}\big{]}^{\top}\in\mathbb{R}^{(K+1)\times
m}.$ (6)

Through the transformer layers, the user embedding from each domain gets
contextualized by attending to the embeddings from other domains based on the
embedding similarity across the domains. As a result, $\bm{h}_{u,k}^{L}$
encodes user preference for domain $d_{k}$, being enriched by preference
information from the other remaining domains.

###  4.4 Preference Modeling

#### Domain-level preference.

The domain-level preference can be inferred by using the contextualized
representation of the special token [S] for user $u$, denoted by
$\bm{h}_{u,\texttt{[S]}}^{L}$, which is generated by aggregating a user’s
preference information for multiple domains. We introduce a domain-preference
predictor
$q_{\bm{\psi}_{\texttt{[S]}}}:\mathbb{R}^{m}\rightarrow\mathbb{R}^{K}$ to
predict each user’s inclination to each domain:
$\bm{z}_{u,\texttt{[S]}}=q_{\bm{\psi}_{\texttt{[S]}}}(\bm{h}_{u,\texttt{[S]}}^{L})$.
The domain-level preference is defined by

$p(d_{k}|u;\bm{\Theta})=\frac{\exp{(\bm{z}_{{u,\texttt{[S]}}_{k}})}}{\sum_{{d}_{i}\in\mathcal{D}}\exp{(\bm{z}_{{u,\texttt{[S]}}_{i}})}},$
(7)

where $\bm{z}_{{u,\texttt{[S]}}_{k}}$ indicates $k$-th logit value in
$\bm{z}_{u,\texttt{[S]}}$.

#### Item-level preference.

The item-level preference in each domain is obtained from the similarity of
item embeddings to the contextualized user embedding for the domain. Using a
domain-specific projector
$q_{\bm{\psi}_{k}}:\mathbb{R}^{m}\rightarrow\mathbb{R}^{d}$, we first project
$\bm{h}_{u,k}^{L}$ to the representation space of domain $d_{k}$:
$\bm{z}_{u,k}=q_{\bm{\psi}_{k}}(\bm{h}_{k}^{L})$. We compute the in-domain
item-level preference based on user $u$’s similarity distribution over item
set ${\mathcal{V}}_{k}$,

$p(v|u,d_{k};\bm{\Theta})=\frac{\exp{\big{(}\textnormal{sim}_{k}(\bm{z}_{u,k},\bm{x}_{v,k})\big{)}}}{\sum_{\hat{v}\in{\mathcal{V}}_{k}}\exp{\big{(}\textnormal{sim}_{k}(\bm{z}_{u,k},\bm{x}_{\hat{v},k})}\big{)}},$
(8)

where $\bm{x}_{v,k}=f_{\bm{\xi}_{k}}(v)$ is the embedding of item $v$ in the
domain $d_{k}$.

###  4.5 Model Learning

#### Masked Domain Modeling

We formulate the training process of DRIP as a prediction task of missing
domain information based on its contexts (Devlin et al. 2019; Bao et al.
2022). Our key idea is to randomly mask some of the domain-specific user
embeddings (among the ones for a user’s seen domains) in the input, and train
the model to predict the user preference in the masked domains. That is, in
the training process, we regard randomly masked domains as the user’s unseen
domains, which allows our model to simulate and learn various scenarios of
mapping user preference from seen domains to unseen domains. As a result, the
model can capture the relations of user preferences across domains, eventually
achieving the generalization capability of inferring user preferences in
unseen domains from those in seen domains.

Let $\bm{m}_{u}\in\\{0,1\\}^{K}$ denote a random masking vector for user $u$,
where $m_{u,k}=1$ indicates that the user embedding for domain $d_{k}$ is
masked. We apply the making operation to the user embedding for the seen
domains (i.e., $G_{u,k}=1$) with the probability of $p_{u,k}$. In specific,
$m_{u,k}$ is drawn from a Bernoulli distribution:
$m_{u,k}\sim\text{Bern}(p_{u,k})$. At the beginning of training, we set the
equal masking probability for all seen domains (i.e., random masking). Then,
during the training process, we gradually adjust the probability based on the
domain-level preferences, i.e., $p_{u,k}\propto p(d_{k}|u;\Theta)$, to
encourage the model to more focus on learning domains that the user is more
likely to prefer (i.e, adaptive masking). The masked embedding set is
represented as $\tilde{\bm{X}}_{u}=\\{\tilde{\bm{x}}_{u,k}\\}_{k=1}^{K}$,
where its elements are obtained by

$\tilde{\bm{x}}_{u,k}=(1-G_{u,k})\bm{e}_{\texttt{[M]}}+G_{u,k}\big{(}m_{u,k}\bm{e}_{\texttt{[M]}}+(1-m_{u,k})\bm{x}_{u,k}\big{)}.$
(9)

During the training, we use $\tilde{\bm{X}}_{u}$ (Eq. (9)) instead of
$\bar{\bm{X}}_{u}$ (Eq. (3)) for the input of the multi-domain encoder, and
obtain their contextualized representations. Note that we discard the case in
which all seen domains are masked.

#### Learning objective

We train the model to predict the preference information of the masked domains
(i.e., $m_{u,k}=1$). Instead of predicting the masked embedding itself, we
directly maximize the likelihood of the user’s interaction history. This makes
the recommendation accuracy directly aligned with the optimization objective.
Based on the negative log-likelihood of Eq. (2) and the masking process, the
final loss is defined as follows:

$\mathcal{L}_{\textnormal{DRIP}}=-\sum_{u\in\mathcal{U}}\sum_{d_{k}\in\mathcal{D}}m_{u,k}\sum_{v\in\mathcal{V}_{k}}R_{u,v}\log[p(v|u,d_{k};\bm{\Theta})\cdot
p(d_{k}|u;\bm{\Theta})],$ (10)

where the learning parameters $\bm{\Theta}$ include the multi-domain encoder
$\bm{\Omega}$, two types of projectors $\\{\bm{\phi}_{k}\\}_{k=1}^{K}$ and
$\\{\bm{\psi}_{k}\\}_{k=1}^{K}$, and domain-preference predictor
$\bm{\psi}_{\texttt{[S]}}$.

###  4.6 MDRAU Recommendation

At the test phase, for each user, we construct the input representation with
the user’s unseen domains masked (Eq. (4)), and calculate the domain-level and
item-level preferences, $p(d_{k}|u;\bm{\Theta})$ and
$p(v|u,d_{k};\bm{\Theta})$. In the scenario where there are multiple target
service domains (MDRAU-MT), the recommendation is generated by sorting the
items by their score $p(v|u,d_{k};\bm{\Theta})\cdot p(d_{k}|u;\bm{\Theta})$.
Otherwise, in the scenario where we have a specific target service domain to
promote (MDRAU-ST), the recommendation is generated by considering only in-
domain item-level preference $p(v|u,d_{k};\bm{\Theta})$.

##  5 Experiments

###  5.1 Experimental Settings222More detailed experimental settings are in
the Appendix.

#### Datasets and Domain Setup

We use the widely-used Amazon dataset (He and McAuley 2016; Kang et al. 2019;
Zhu et al. 2021a), which consists of multiple item domains. To simulate the
platform environment, we select two subsets of these domains that have been
previously used in related studies (Zhu et al. 2021a). The first platform
scenario (P1) includes Book, Movie, CD, and Game domains, and the second
scenario (P2) includes Home, Health, Grocery, and Tools domains. The detailed
statistics of the datasets are described in Table 1 and the Appendix.

#### Evaluation Metrics

We focus on the top-$K$ recommendation task for implicit feedback. We evaluate
the recommendation accuracy of each method by using the two ranking metrics
(Hsieh et al. 2017; Liang et al. 2018): Recall (R@$K$) and Normalized
Discounted Cumulative Gain (N@$K$).

#### Compared Methods

We compare DRIP with various methods from related research fields. We have
modified the original methods to perform MDRAU, and the modified versions are
annotated with the suffix ‘+’. The first group of baselines learns a
recommendation model BPRMF (Rendle et al. 2009) while treating a union of
multiple domains as a single domain (Singh and Gordon 2008). The second group
includes multi-task learning methods (MMOE (Ma et al. 2018) and PLE (Tang et
al. 2020)), which define a single task as item-level preference learning for
each domain. They are widely used for RS in multi-domain cases (Cao et al.
2023). For each task (i.e., domain), they employ the binary cross-entropy loss
to predict user-item interactions from implicit feedback (He et al. 2017). The
third group includes CDR methods (EMCDR+ (Man et al. 2017) and PTUPCDR+ (Zhu
et al. 2022)) for unseen domain recommendation, which learn a mapping function
for each source-target domain pair. Due to a large number of seen-unseen
domain combinations, it is infeasible to directly apply them to MDRAU. For
this reason, we tailor their learning task for a many-to-one mapping. The last
group includes state-of-the-art methods (CAT-ART+ (Li et al. 2023) and UniCDR
(Cao et al. 2023)) that partially handle multi-domain cases. They are designed
to exploit information from multiple domains to improve recommendation
accuracy in each domain. For MDRAU-MT, recommendations from each unseen domain
are integrated into a unified recommendation list using post-processing (e.g.,
normalization).

| Domains | #Users | #Items | #Interaction | Density
---|---|---|---|---|---
P1 | Book | 35,987 | 39,049 | 1,726,231 | 0.12%
Movie | 17,056 | 15,620 | 609,552 | 0.23%
CD | 5,941 | 9,069 | 211,617 | 0.39%
Game | 1,049 | 1,064 | 20,568 | 1.84%
P2 | Home | 10,317 | 7,605 | 127,091 | 0.16%
Health | 8,690 | 5,750 | 123,905 | 0.25%
Grocery | 4,869 | 2,884 | 71,269 | 0.51%
Tools | 1,804 | 1,422 | 18,040 | 0.70%

Table 1: Statistics of the two platform scenarios of MDRAU.

Methods (P1) | Book | Movie | CD | Game
---|---|---|---|---
R@20 | R@50 | N@20 | N@50 | R@20 | R@50 | N@20 | N@50 | R@20 | R@50 | N@20 | N@50 | R@20 | R@50 | N@20 | N@50
BPRMF | 0.0174 | 0.0176 | 0.0182 | 0.0205 | 0.0223 | 0.0357 | 0.0224 | 0.0279 | 0.0378 | 0.0613 | 0.0371 | 0.0471 | 0.0572 | 0.1315 | 0.0548 | 0.0868
MMOE | 0.0161 | 0.0183 | 0.0164 | 0.0171 | 0.0306 | 0.0423 | 0.0310 | 0.0352 | 0.0338 | 0.0535 | 0.0341 | 0.0408 | 0.0729 | 0.1467 | 0.0613 | 0.0941
PLE | 0.0103 | 0.0149 | 0.0108 | 0.0123 | 0.0307 | 0.0469 | 0.0296 | 0.0368 | 0.0375 | 0.0499 | 0.0337 | 0.0382 | 0.0750 | 0.1379 | 0.0592 | 0.0872
EMCDR+ | 0.0322 | 0.0460 | 0.0348 | 0.0396 | 0.0449 | 0.0647 | 0.0439 | 0.0523 | 0.0574 | 0.0767 | 0.0610 | 0.0673 | 0.0846 | 0.1600 | 0.0755 | 0.1093
PTUPCDR+ | 0.0311 | 0.0417 | 0.0338 | 0.0373 | 0.0426 | 0.0642 | 0.0427 | 0.0516 | 0.0559 | 0.0778 | 0.0589 | 0.0669 | 0.0875 | 0.1535 | 0.0836 | 0.1131
CAT-ART+ | 0.0325 | 0.0426 | 0.0339 | 0.0366 | 0.0472 | 0.0689 | 0.0445 | 0.0545 | 0.0566 | 0.0747 | 0.0578 | 0.0646 | 0.0770 | 0.1412 | 0.0745 | 0.0981
UniCDR | 0.0359 | 0.0485 | 0.0380 | 0.0424 | 0.0493 | 0.0700 | 0.0502 | 0.0581 | 0.0589 | 0.0851 | 0.0607 | 0.0697 | 0.0876 | 0.1620 | 0.0823 | 0.1102
DRIP | 0.0403* | 0.0535* | 0.0423* | 0.0472* | 0.0526* | 0.0758* | 0.0517 | 0.0619* | 0.0677* | 0.0958* | 0.0699* | 0.0813* | 0.0936* | 0.1785* | 0.0873* | 0.1193*
Improv. | 12.42% | 10.42% | 11.56% | 11.39% | 6.84% | 8.30% | 3.13% | 6.54% | 14.86% | 12.58% | 14.56% | 16.66% | 6.78% | 10.23% | 4.44% | 5.50%
Methods (P2) | Home | Grocery | Tools | Health
R@20 | R@50 | N@20 | N@50 | R@20 | R@50 | N@20 | N@50 | R@20 | R@50 | N@20 | N@50 | R@20 | R@50 | N@20 | N@50
BPRMF | 0.0363 | 0.0600 | 0.0328 | 0.0423 | 0.0781 | 0.1513 | 0.0655 | 0.0943 | 0.0981 | 0.1613 | 0.0647 | 0.0873 | 0.0466 | 0.0735 | 0.0415 | 0.0525
MMOE | 0.0305 | 0.0512 | 0.0279 | 0.0355 | 0.0966 | 0.1833 | 0.0928 | 0.1250 | 0.0799 | 0.1587 | 0.0678 | 0.0929 | 0.0494 | 0.0730 | 0.0520 | 0.0610
PLE | 0.0279 | 0.0487 | 0.0279 | 0.0354 | 0.0953 | 0.1850 | 0.0912 | 0.1251 | 0.0814 | 0.1510 | 0.0697 | 0.0918 | 0.0500 | 0.0765 | 0.0525 | 0.0623
EMCDR+ | 0.0464 | 0.0795 | 0.0423 | 0.0552 | 0.1049 | 0.1982 | 0.0968 | 0.1336 | 0.1045 | 0.1727 | 0.0827 | 0.1097 | 0.0640 | 0.1032 | 0.0639 | 0.0791
PTUPCDR+ | 0.0460 | 0.0788 | 0.0433 | 0.0557 | 0.1040 | 0.1945 | 0.0969 | 0.1329 | 0.1108 | 0.1857 | 0.0836 | 0.1100 | 0.0653 | 0.1050 | 0.0651 | 0.0810
CAT-ART+ | 0.0434 | 0.0801 | 0.0396 | 0.0535 | 0.1115 | 0.1938 | 0.0975 | 0.1286 | 0.1031 | 0.1758 | 0.0758 | 0.1018 | 0.0603 | 0.0967 | 0.0573 | 0.0712
UniCDR | 0.0468 | 0.0812 | 0.0436 | 0.0583 | 0.1181 | 0.2060 | 0.1068 | 0.1356 | 0.1206 | 0.1893 | 0.0863 | 0.1139 | 0.0674 | 0.1074 | 0.0647 | 0.0805
DRIP | 0.0527* | 0.0857* | 0.0472* | 0.0598 | 0.1184 | 0.2195* | 0.1086* | 0.1471* | 0.1229* | 0.1879* | 0.0919* | 0.1156* | 0.0726* | 0.1129* | 0.0715* | 0.0870*
Improv. | 12.57% | 5.53% | 8.33% | 2.63% | 2.70% | 6.52% | 3.23% | 8.48% | 11.10% | 6.08% | 14.97% | 10.75% | 7.78% | 5.07% | 9.82% | 7.40%

* denotes the improvement over the best baseline is statistically significant with $p<0.05$, using the paired t-test.

Table 2: Recommendation performance comparison for MDRAU-ST on the platform
scenario 1 (P1) and scenario 2 (P2).

###  5.2 Performance comparison for MDRAU-ST

We first compare the recommendation performance of various methods for MDRAU-
ST on our two simulated platforms, P1 and P2. In this task, we set each of the
domains as the target domain, and for evaluation, we consider only the users
who have not tried the domain yet as test users. The results for each target
domain are reported in Table 2.

We observe that DRIP consistently achieves higher recommendation performance
than all the other methods in each of the target domains. Specifically, the
CDR methods designed for a single pair of source-target domain based on one-
to-one mapping (i.e., EMCDR+ and PTUPCDR+) show lower performance compared to
the ones that can effectively handle multiple source domains based on many-to-
one mapping (i.e., CAT-ART+, UniCDR, and DRIP). They are not capable of
capturing the relevance among multiple source domains, whereas the multi-
domain CDR methods integrate the user preferences of multiple source domains
in advanced ways. In particular, the multi-domain encoder of DRIP
contextualizes domain-specific user embeddings over multiple source domains
with attention mechanism that is effective in capturing the inter-domain
relationship; this brings a significant performance improvement for MDRAU-ST.

Furthermore, unlike the CDR methods for recommending items in a user’s unseen
domain (i.e., EMCDR+, PTUPCDR+, and DRIP), the CDR baselines that aim to
enhance the recommendation in the user’s seen domains (i.e., CAT-ART+ and
UniCDR) have to rely on each user’s global embedding shared over multiple
domains to predict the user preference for a target unseen domain. This is
because they are suffering from the incapability of inferring a user’s unseen
domain embedding, caused by their training process aiming at only predicting
items in a user’s seen domains. In contrast, DRIP is good at inferring user
embedding of a target unseen domain, conferred by masked domain modeling. To
sum up, DRIP outperforms all existing methods in terms of MDRAU-ST, by (1)
effectively contextualizing user embeddings over multiple domains using
attention mechanism and (2) accurately inferring a user’s preference for a
target unseen domain via masked domain modeling.

###  5.3 Performance Comparison for MDRAU-MT

We also evaluate DRIP and various methods for MDRAU-MT on two simulated
platforms, P1 and P2. In this task, the set of target domains varies depending
on users, because each user has different unseen domains. For each user, we
assess the accuracy of recommendations for the user’s multiple unseen domains,
and report the averaged accuracy over all test users as the final performance.
Note that MDRAU-MT scenario differs from MDRAU-ST (in Sec. 5.2) in that it
evaluates the models’ ability to make aggregated recommendations over multiple
unseen domains. In this sense, MDRAU-MT requires to properly capture domain-
level preference with item-level preference. Table 3 presents overall
performances for MDRAU-MT.

We observe that DRIP outperforms the best baseline method more in MDRAU-MT
than in MDRAU-ST. The limited MDRAU-MT performance of baselines stems from two
factors. First, they focus on predicting items in single domains without
considering multi-domain preferences, unlike DRIP, which captures both domain
and item-level preferences. Second, most baseline methods need a post-
processing step to merge recommended item lists over multiple target domains,
limiting final accuracy. On the contrary, DRIP optimizes a unified model that
makes recommendations for multiple target domains in an end-to-end manner,
improving MDRAU-MT performance by reducing its gap from the training process.
In conclusion, DRIP achieves the best performance among all the baselines with
the help of its item-level preference accurately predicted for each of the
target domains as well as its capability of inferring domain-level preference
obtained by the training process.

###  5.4 Domain-level Preference Analysis

We analyze the models’ ability to capture domain-level preference, essential
for accurate recommendations in multiple unseen domains (i.e., MDRAU-MT). We
compare two domain distributions obtained from (1) a user’s interaction
history and (2) the recommendation list generated by each method for the
user.444In this analysis, we assume that the domain distributions in each
user’s interaction history reflect the user’s actual domain-level preferences
to a considerable extent. Let $P$ and $Q$ denote the ground-truth distribution
in user history and the predicted distribution, respectively. We calculate the
Kullback-Leibler Divergence (KLD@$K$) between the two distributions
$D_{KLD}(P\|Q)=\sum_{i}P_{i}\log(P_{i}/Q_{i})$ to measure how closely the
model’s prediction captures the distribution of actual domain preferences.
Note that KLD only measures the domain-level accuracy, not in-domain item
prediction accuracy.

In Fig. 3, we assess the KLD@$K$ score for the top-$K$ recommendation and
observe the following: (1) In comparison to other competing methods, BPRMF
exhibits significantly better KLD scores. BPRMF treats a union of all domains
as a single domain and learns the pair-wise ranking of item-level preference
over the entire domains. This makes a user’s domain-level preference
implicitly captured during the training process. This result can be also
interpreted with the previous performance comparison for MDRAU-MT/ST. The
performance of BPRMF is highly limited in MDRAU-ST due to its limited
capability of capturing item-level preferences. However, BPRMF achieves
comparable performance with the state-of-the-art methods in MDRAU-MT. We
interpret that this improvement mainly comes from its capability of capturing
domain-level preferences. (2) Other competing methods show considerably worse
KLD scores compared to DRIP. As discussed earlier, they need a post-processing
step to generate the unified ranking list encompassing all unseen domains
(e.g., z-score normalization), which may not yield optimal recommendation
accuracy. This result highlights the importance of holistic model training
that considers both domain-level and item-level preferences in MDRAU task. (3)
Among all baseline methods, DRIP achieves the best KLD scores in both
scenarios. This result shows that DRIP indeed effectively captures user’s
domain-level preferences, and also supports its superior performance in MDRAU-
MT.

Methods | P1 | P2
---|---|---
R@20 | R@50 | N@20 | N@50 | R@20 | R@50 | N@20 | N@50
BPRMF | 0.0249 | 0.0315 | 0.0256 | 0.0278 | 0.0528 | 0.0835 | 0.0503 | 0.0625
MMOE | 0.0188 | 0.0230 | 0.0191 | 0.0203 | 0.0486 | 0.0691 | 0.0513 | 0.0581
PLE | 0.0190 | 0.0249 | 0.0190 | 0.0212 | 0.0491 | 0.0722 | 0.0516 | 0.0595
EMCDR+ | 0.0362 | 0.0507 | 0.0374 | 0.0434 | 0.0531 | 0.0832 | 0.0525 | 0.0659
PTUPCDR+ | 0.0367 | 0.0482 | 0.0377 | 0.0422 | 0.0546 | 0.0866 | 0.0538 | 0.0665
CAT-ART+ | 0.0395 | 0.0517 | 0.0395 | 0.0441 | 0.0522 | 0.0827 | 0.0497 | 0.0620
UniCDR | 0.0434 | 0.0571 | 0.0446 | 0.0497 | 0.0588 | 0.0958 | 0.0574 | 0.0719
DRIP | 0.0545* | 0.0698* | 0.0556* | 0.0612* | 0.0780* | 0.1170* | 0.0773* | 0.0919*
Improv. | 25.64% | 22.25% | 24.55% | 23.14% | 32.66% | 22.11% | 34.80% | 27.78%

* denotes the improvement over the best baseline is statistically significant with $p<0.05$, using the paired t-test.

Table 3: Recommendation performance comparison for MDRAU-MT. Figure 3: Domain-
level preference analysis. KL-divergence scores of each method (Best viewed in
color).

Designs | R@20 | R@50 | N@20 | N@50
---|---|---|---|---
DRIP | 0.0545 | 0.0698 | 0.0556 | 0.0612
Training Paradigm |  |  |  |
Single-domain learning | 0.0281 | 0.0371 | 0.0272 | 0.0310
Many-to-one learning w/ post-processing A | 0.0432 | 0.0593 | 0.0447 | 0.0511
Many-to-one learning w/ post-processing B | 0.0409 | 0.0520 | 0.0424 | 0.0463
Domain Preference Modeling
Uniform dist. | 0.0122 | 0.0210 | 0.0120 | 0.0164
Domain activeness dist. | 0.0409 | 0.0534 | 0.0419 | 0.0466
Masking Scheme
w/o Adaptive Masking | 0.0513 | 0.0663 | 0.0520 | 0.0576

Table 4: Performance comparison of different design choices. Results for
MDRAU-MT on P1.

###  5.5 Design Choice Analysis

We analyze alternative design choices for DRIP in Table 4 to verify the
effectiveness of our design choice. We report the performance for MDRAU-MT on
platform scenario P1.

First, we compare alternative training paradigms for DRIP: Single-domain
learning, where all domains are treated as one, and the model is trained to
maximize the likelihood of the training data; Many-to-one learning, where a
single model is trained for each target domain to predict item-level
preferences. To generate a unified recommendation list encompassing all
domains, we apply a post-processing step. Post-processing A uses
z-normalization, performing best in our test. We also consider emphasizing
active domains in post-processing; specifically, for post-processing B, we
multiply the ratio of the total number of interactions in each domain by the
z-normalized scores and use the scores for the recommendation.

We observe that the alternative training paradigms show considerably degraded
performance. Single-domain learning achieves a highly limited performance,
showing the necessity of proper domain modeling in MDRAU task. Also, the many-
to-one learning neglects the domain-level preference during the training, and
the post-processing is applied independently from the training process, which
results in limited MDRAU performance. Further, in our experiments,
sophisticated designs for post-processing do not bring further improvements.
These results support the superiority of our training strategy that decomposes
user preference into domain- and item-level preferences and jointly learns
them through a unified model.

Second, we compare ablations for the domain-level preference modeling. Instead
of estimating personalized domain-level preference, they use globally fixed
distributions: the uniform and domain activeness distribution (the latter
assumes users prefer more active domains). Both fixed domain preference
approaches yield suboptimal recommendation performance. This result supports
the effectiveness of our strategy that models the domain-level preference for
each individual user considering their different preference.

Lastly, we provide the results without the adaptive masking. For the ablation,
we use random masking with the same masking ratio as adaptive masking. The
adaptive masking brings slight improvements to the final performance,
indicating that our masking strategy is well-aligned with our masked domain
modeling. We also provide the sensitivity analysis in the Appendix.

##  6 Conclusion

This paper highlights the importance of MDRAU task based on its practical
advantages in multi-domain platforms. We propose DRIP, a new framework to
provide accurate unseen domain recommendations to attract users into new
service domains that they have not interacted with yet. The DRIP decomposes
user preference into domain-level preference and in-domain item-level
preference and then jointly learns them via a unified model with the help of a
training strategy based on masked domain modeling. We conduct extensive
comparisons with a wide range of CDR methods. DRIP consistently achieves
superior performance compared to all competing methods in both cases of a
specific target domain (MDRAU-ST) and multiple target domains (MDRAU-MT). We
expect that DRIP can enhance the user experience by fostering diverse and
serendipitous discoveries and potentially promote the influx of new users to
each service domain, benefiting providers in multi-domain service platforms.

## Acknowledgements

This work was supported by Institute of Information & communications
Technology Planning & Evaluation (IITP) grant funded by the Korea government
(MSIT) (No.2018-0-00584, No.2019-0-01906), and the National Research
Foundation of Korea (NRF) grant funded by the MSIT (No.2020R1A2B5B03097210,
No.RS-2023-00217286).

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##  Appendix A Transformer Layer

The multi-domain encoder is basically a stack of $L$ transformer layers
(Vaswani et al. 2017; Devlin et al. 2019), each of which consists of two
blocks: multi-head self-attention (MSA) and position-wise two-layered feed-
forward neural network (FFN). Given the input representation
$\bm{H}\in\mathbb{R}^{(K+1)\times m}$, the MSA block computes its output as
follows:

$\begin{split}\textnormal{MSA}(\bm{H})&=\left[\textnormal{SAttH}_{1},\textnormal{SAttH}_{2},\cdots,\textnormal{SAttH}_{h}\right]\bm{W}^{O}\\\
\textnormal{SAttH}_{i}&=\textnormal{SAtt}(\bm{H}\bm{W}_{i}^{Q},\bm{H}\bm{W}_{i}^{K},\bm{H}\bm{W}_{i}^{V})\\\
\textnormal{SAtt}(\bm{Q},\bm{K},\bm{V})&=\text{Softmax}\left(\bm{Q}\bm{K}^{\top}/\sqrt{m/h}\right)\bm{V},\end{split}$
(11)

where
$\bm{W}_{i}^{Q},\bm{W}_{i}^{K},\bm{W}_{i}^{V}\in\mathbb{R}^{m\times(m/h)}$ and
$\bm{W}^{O}\in\mathbb{R}^{m\times m}$ are learnable parameters, and $h$
denotes the number of heads. The output of each block is applied dropout
(Srivastava et al. 2014), then added to the block’s input for the residual
connection, and finally normalized with Layer Norm (Ba, Kiros, and Hinton
2016). Transformer Layer calculates the MSA block, and then the output is
forwarded to the FFN block.

##  Appendix B Algorithm

For a better understanding of DRIP (Sec. 4), we provide the algorithms for
DRIP. Algorithm 1 shows the training procedure, while Algorithm 2 shows the
procedure for making a recommendation list of a user for each scenario (i.e.,
MDRAU-MT/ST).

Algorithm 1 DRIP Training

Input: Interaction data $\bm{R}$, $K$ domain-specific encoders (i.e., RSs)
(Sec. 4.2)
Output: A trained DRIP model

1: while not converged do

2: for each batch users $\mathcal{B}(u)\in\mathcal{U}$ do

3: Construct inputs according to users’ interaction information (Eq. (3))

4: Calculate the domain-level preferences: $p(d_{k};u;\bm{\Theta})$ (Eq. (7))

5: Select masking probability with selection probability (Sec. 4.5, C.3)

6: Mask inputs for training (Eq. (9))

7: Compute $\mathcal{L}_{\textnormal{DRIP}}$ (Eq. (10))

8: Update model by minimizing $\mathcal{L}_{\textnormal{DRIP}}$

9: end for

10: end while

Algorithm 2 DRIP Inference

Input: A trained DRIP model, a user $u$, and recommendation size $N$
Output: A recommendation list

1: Construct an input according to the user’s interaction information (Eq.
(3))

2: Calculate $p(d_{k}|u;\bm{\Theta})$ and $p(v|u,d_{k};\bm{\Theta})$ (Eq. (7),
(8))

3: if MDRAU-MT Scenario then

4: Calculate the preferences: $p(d_{k}|u;\bm{\Theta})\cdot
p(v|u,d_{k};\bm{\Theta})$

5: Sort the preferences and select top-$N$ items for top-$N$ recommendation

6: else if MDRAU-ST Scenario (domain $d_{k}$) then

7: Calculate the preferences: $p(v|u,d_{k};\bm{\Theta})$

8: Sort the preferences and select top-$N$ items for top-$N$ recommendation
for domain $d_{k}$

9: end if

##  Appendix C Detailed Descriptions for Experiments

###  C.1 Experimental Settings

#### Dataset and Domain Settings

We filter out users who interacted with at least two domains with less than 10
(P1) & 5 (P2) interactions in each domain and users who interacted with only
one domain and items with less than 20 (P1) & 10 (P2) interactions in each
domain (Kang et al. 2019; Fu et al. 2019). We report overlapping user
information for our datasets in Table 5.

#### Evaluation Setup

To assess MDRAU accuracy, we remove interaction history of overlapping users
in certain domains and treat the removed interactions as ground-truth for
evaluation. In specific, for each overlapping user, we randomly select a
subset of interacted domains and hide all interactions in the selected
domains555We select the domain to be hidden with the probability of $0.3$.
Note that the hidden interactions are completely excluded from the training
data.. The selected domains are regarded as ground-truth unseen domains that
the user is likely to interact with, and the hidden interacted items are
regarded as ground-truth items in the domains. For MDRAU-ST, we evaluate the
quality of recommendation for each unseen domain, respectively, and for MDRAU-
MT, we evaluate the quality of recommendation encompassing all unseen domains.

#### Evaluation Metrics

| Domains | Book | Movie | CD | Game
---|---|---|---|---|---
P1 | Book | 35,987 | 5,243 | 1,678 | 316
Movie | - | 17,056 | 2,884 | 548
CD | - | - | 5,941 | 222
Game | - | - | - | 1,049
| Domains | Home | Health | Grocery | Tools
P2 | Home | 10,317 | 5,444 | 3,072 | 1,399
Health | - | 8,690 | 3,441 | 1,338
Grocery | - | - | 4,857 | 891
Tools | - | - | - | 1,804

Table 5: Count of users who interact with each domain pair.

We focus on the top-$K$ recommendation task for implicit feedback. We evaluate
the recommendation accuracy of each method by using the two ranking metrics
(Hsieh et al. 2017; Liang et al. 2018): Recall (R@$K$) and Normalized
Discounted Cumulative Gain (N@$K$). R@$K$ equally treats all items within a
top-$K$ list, while N@$K$ assigns a higher score on upper-ranked test items.
We use 50% of overlapping users for validation purposes. We use the full-
ranking evaluation (Krichene and Rendle 2020) rather than the sampling-based
evaluation (e.g., leave-one-out (Hu, Zhang, and Yang 2018; Kang et al. 2019;
Cao et al. 2023)).

###  C.2 Compared Methods

We compare DRIP with various methods from related research fields. As
discussed in the paper, MDRAU task has not been studied well in previous
literature, and many existing methods cannot be directly applied. Therefore,
we have modified the original methods to perform MDRAU, and the modified
versions are annotated with the suffix ‘+’. The following are our competing
methods.

  * •

BPRMF (Rendle et al. 2009) is a representative method for implicit feedback.
It learns pair-wise ranking in the latent space.

  * •

MMOE (Ma et al. 2018) utilizes multiple experts that share user embeddings
over multiple domains, and it adopts a domain-specific gating module to
effectively capture inter-domain relationships.

  * •

PLE (Tang et al. 2020) also utilizes multiple experts, but it separates
domain-specific and domain-shared experts for more balanced training.

Note that the above methods learn global user embeddings that are shared
across all domains, so that the global user embeddings can be directly used
for recommendation in any target domain.

EMCDR and PTUPCDR learn a mapping function for each source-target domain pair.
Due to a large number of seen-unseen domain combinations, it is infeasible to
directly apply them to MDRAU. For this reason, we tailor their learning task
for a many-to-one mapping. That is, for each target domain, we learn a mapping
function that takes concatenated domain-specific user embeddings as input666If
a user does not exist in a specific domain, we substitute the user embedding
by the average user embedding in that domain. and predicts user preference in
the target domain.

  * •

EMCDR+ (Man et al. 2017) is a representative CDR method based on the
embedding-and-mapping approach for unseen domain recommendation (or cold-start
recommendation). It trains a mapping function to predict user embedding in the
target domain from the source domain. The ‘+’ version (i.e., EMCDR+) is
modified according to the above description.

  * •

PTUPCDR+ (Zhu et al. 2022) improves EMCDR+ by employing a meta-network as its
personalized mapping function. It trains the mapping function to predict
ratings in the target domain.

  * •

CAT-ART+ (Li et al. 2023) generates shared user embeddings that summarize user
preferences from all interacted domains and exploits the shared embeddings to
improve the recommendation quality in the target domain. As user embeddings do
not exist for unseen domains, we use the reconstructed user embedding from the
autoencoder module used to generate the shared embedding.

  * •

UniCDR (Cao et al. 2023) is the state-of-the-art CDR method that can handle
various CDR scenarios. It models domain-specific and domain-shared user
embeddings separately and transfers the knowledge from other domains based on
the domain-shared embeddings.

All the compared methods except BPRMF were proposed to recommend items for a
single target domain. To evaluate such single target methods in the MDRAU-MT,
the recommendations for each unseen domain need to be integrated over multiple
unseen domains. For effective integration, we generate a unified
recommendation list by using the scores normalized within each domain.777We
found that the performance of the single target methods drastically drops
without normalization. We report their best performance among the cases of
using z-score normalization and min-max normalization.

###  C.3 Implementation Details

We use Xeon Gold 6226R CPU and A5000 24GB GPU on Ubuntu 20.04 LTS for
experiments. We implement DRIP and other competing methods with PyTorch
(Paszke et al. 2019) and use Adam optimizer (Kingma and Ba 2014) with
$\beta_{1}=0.9,\beta_{2}=0.999$. For domain-specific encoders, we use BPR
(Rendle et al. 2009) with embedding size 64. We ran five times for each
experiment. We tune all hyperparameters by grid search using the validation
set. The learning rates are searched in the range of
$\\{0.0001,0.0005,0.001,0.005,0.01\\}$. The weight decay is searched in the
range of $\\{0.0001,0.0005,0.001,0.005,0.01\\}$. For MMOE and PLE, the number
of experts is searched in the range of $\\{2,3,5,8,10\\}$. For the mapping
function in EMCDR, we use multi-layer perception (MLP) with one-hidden layer:
$[64\times 4\rightarrow 2\times 64\times 4\rightarrow 64\times 4]$ and $tanh$
activation (Man et al. 2017; Kang et al. 2019). For CAT-ART and UniCDR, we
follow the recommended values from the public implementation and from the
original papers (Li et al. 2023; Cao et al. 2023). For DRIP, the number of
heads, the number of layers, and random masking probabilities are searched in
the range of $\\{2^{0},2^{1},2^{2},2^{3}\\}$, $\\{1,2,3,4\\}$,
$\\{0,1,0.2,0.3,0.4,0.5,0.6,0.7,0.9\\}$, respectively. The results are
reported in Sec. D. For the masking process, we introduce a selection
probability $\epsilon_{i}$ in epoch $i$. When $\epsilon_{i}=1$, we use only
random masking, while when $\epsilon_{i}=0$, we only use adaptive masking. We
linearly decrease the $\epsilon_{i}=\text{max}(0.5,1-0.002i)$ in training
phase.

Figure 4: Sensitivity analysis of DRIP.

##  Appendix D Sensitivity Analysis

We provide a sensitivity analysis to guide the hyperparameter selection of
DRIP. In Fig 4, we report the recommendation accuracy (R@20) with varying
random masking probabilities, the number of heads, and the number of layers
for MDRAU-MT on P1. Similar tendencies are observed in the other scenario. We
first observe that the masking probability has a small impact within the range
of [0.1, 0.7]. However, the performance drastically drops when the masking
probability exceeds 0.7. If the masking probability is too high, the model
cannot obtain sufficient information from other domains, leading to degraded
performance. Also, we observe stable performances with varying numbers of
heads and layers of the multi-domain encoder. DRIP achieves a slightly
improved performance with more number of heads, and a slightly degraded
performance when the number of layers exceeds 3.