# Graph Reasoning for Explainable Cold Start Recommendation

Jibril Frej
EPFL
<EMAIL_ADDRESS>
&Marta Knežević
EPFL
<EMAIL_ADDRESS>
&Tanja Käser
EPFL
<EMAIL_ADDRESS>

###### Abstract

The cold start problem, where new users or items have no interaction history,
remains a critical challenge in recommender systems (RS). A common solution
involves using Knowledge Graphs (KG) to train entity embeddings or Graph
Neural Networks (GNNs). Since KGs incorporate auxiliary data and not just
user/item interactions, these methods can make relevant recommendations for
cold users or items. Graph Reasoning (GR) methods, however, find paths from
users to items to recommend using relations in the KG and, in the context of
RS, have been used for interpretability. In this study, we propose GRECS: a
framework for adapting GR to cold start recommendations. By utilizing explicit
paths starting for users rather than relying only on entity embeddings, GRECS
can find items corresponding to users’ preferences by navigating the graph,
even when limited information about users is available. Our experiments show
that GRECS mitigates the cold start problem and outperforms competitive
baselines across 5 standard datasets while being explainable. This study
highlights the potential of GR for developing explainable recommender systems
better suited for managing cold users and items.

##  1 Introduction

With the growth of digital commerce and content platforms, users are often
overwhelmed by the number of choices available [20], negatively impacting user
experience and engagement. By recommending a small set of personalized items,
recommender systems (RS) can enhance user satisfaction and platform efficiency
[26, 5, 19]. Moreover, explainable RS can further increase the effectiveness
and persuasiveness of an RS [22, 39]. Since most of the modern RS uses
supervised learning and neural networks (NN) trained on user interactions to
make recommendations, two challenges these systems still face are the cold
start problem and the lack of explainability of the recommendations.

The cold start problem occurs when few to no historical interactions are
available for new users or items [28, 10, 11, 25]. The challenge extends to
both recommending items to users with no or sparse previous history data (cold
users) and suggesting new items that have not yet been interacted with by
users (cold items). Solutions include meta-learning [30, 31, 23, 35], using
large language models (LLM) to analyze new user preferences/review expressed
as natural language [10, 27], or using knowledge graphs (KGs) to include
additional information about users and items and make recommendations using
entity embeddings or graph neural networks (GNNs) [13, 41, 32]. However, most
of the aforementioned approaches rely on computing a similarity between a user
and all items in the dataset, ranking the items by their similarity, and
recommending the top-k items. This method of comparing a user to all items
makes these approaches more prone to the popularity bias [7] since popular
items tend to have a high similarity with users when supervised learning is
used. This can result in top recommendations that do not necessarily align
with the user’s preferences. Furthermore, the majority of the suggested
approaches provide no explanations for the recommendations.

The absence of explainability can diminish users’ trust and reduce their
willingness to follow the recommendation [22, 39]. This is especially
problematic in high-impact domains such as education where a learner needs to
be given a clear explanation when recommended with a course [22]. Enhancing
explainability in NN-based RS often involves using KGs that represent explicit
relations between understandable entities [4, 16, 38]. Moreover, recent work
shows that using graph reasoning (GR) to make a recommendation by finding a
path from a user to an item in a KG leads to explainable recommendations while
keeping performance competitive to black-box approaches [36, 29, 17, 6, 15].

In this paper, we leverage GR methods for explainable cold start
recommendation. Since GR relies not only on user-item similarity, but also on
the structure of the KG to move from a user to an item with a limited number
of steps, the set of recommendable items is effectively reduced to reachable
items only. We hence hypothesize that GR approaches are less susceptible to
the popularity bias and more likely to recommend relevant items in the absence
of interaction data.

Contributions. We propose GRECS: a lightweight Graph Reasoning for Explainable
Cold Start framework that adapts GR for cold start recommendations, while
keeping recommendations explainable. Specifically, we integrate cold entities
(users or items) into a KG by employing non-interaction relations and
computing relevant embeddings. GRECS can therefore be used on alreay optimized
models whithout any additional training. Our implementation is publicly
available111https://anonymous.4open.science/r/cold_rec-B765. We evaluate our
approach on five publicly available e-commerce and MOOC datasets and
demonstrate that GRECS:

  1. [1]

provides relevant recommendations to strict cold start users with no prior
interactions, outperforming state-of-the-art baseline methods,

  2. [2]

recommends relevant strict cold start items with no prior interactions, again
outperforming baselines on cold item coverage,

  3. [3]

is less sensitive to the popularity bias than existing methods,

  4. [4]

require few relations or interactions to make relevant recommendations.

##  2 Background

Cold Start Recommendation. A cold start scenario occurs when there is no
interaction data available for a user or an item. Common solutions include
meta-learning and KG-based approaches.

Meta-learning involves learning prior (or meta) knowledge by solving multiple
tasks to improve the generalization capacities of models on new examples or
new tasks [30]. In the context of cold start recommendation, each user is
treated as a different task, and the meta-knowledge enablse the RS to make
relevant recommendations to new users. To further improve performance in the
cold start-scenario, PDMA [31] proposes to distinguish new users and novel
preferences by decoupling the preference of a cold-start user into common
preference transfer and novel preference adaptation. M2eu [35] uses similar
warm user embeddings to enhance cold start user embeddings, and TAML [23]
proposes to consider the temporal factor of users’ preferences for cold items
in the context of news recommendations, where the time factor is crucial to
consider.

KG-based Approaches use additional information about users and items from a KG
to address the cold start problem. Since user-item interactions are not the
only types of information being used in a KG, the approaches can make
meaningful recommendations in a cold start scenario. MKR [32] trains entity
embeddings using multiple tasks over the KG to transfer knowledge between the
tasks. This approach produces embeddings that can be used for cold start
recommendation, KG completion, or cross-domain recommendation. UCC [24]
generates interactions for cold users that are distributed similarly to those
of warm users. SDCRec [13] uses GNN to cold start social recommendation while
reducing the popularity bias using contrastive learning. Metakg [14], a new
framework to use Meta-Learning on KG, combines both approaches for cold start
recommendation. Recently, several approaches have used Large Language Models
(LLMs) to make cold-start recommendations. ColdGPT [10] proposes to address
the strict cold-start item recommendation by using LLMs to find keywords in
item descriptions and reviews and include them in a KG to be used for
recommendation. [27] propose to tackle the user cold-start problem by
analyzing user preferences expressed in natural language with an LLM to make
cold-start recommendations.

Unfortunately, the aformentioned methods suffer from the popularity bias in
cold start scenarios and the majority of them do not provide explainable
recommendations.

Graph Reasoning for Explainable Recommendation. GR for recommendations
identifies paths from a user to the recommended item in a KG, utilizing the
relations between entities in the KG to provide human-understandable
explanations for recommendations. PGPR [36] was the first approach to use
graph reasoning for explainable recommendations, introducing a new
Reinforcement Learning (RL) framework for recommendation using GR and pre-
defined path patterns. Since PGPR, several approaches have been proposed to
improve the quality of the recommendations or explanations. EKAR [29] is a
framework similar to PGPR that uses a different reward to better guide the
agent towards items in the training set. CAFE [37] proposes to replace RL with
behavioral cloning to avoid some of the shortcomings emanating from RL. ReMR
[34] proposes to organize the KG into multiple abstraction levels to better
reveal users’ interests. Finally, UPGPR [15] adopts PGPR to educational use
cases and improves its generalizability by removing the pre-defined patterns.

Recent approaches, such as PLM-Rec [17] have proposed to move beyond explicit
GR by training LLMs over the relations triplets of the KG, avoiding the recall
bias caused by unreachable items. While providing better recommendations, the
explanations generated by the LLMs are not constrained by the KG, making them
less faithful. PEARLM [6] proposes to address this problem by introducing
constraints on the sequence decoding to guarantee path faithfulness.

To the best of our knowledge, GRECS is the first framework for adapting GR for
cold start recommendations, resulting in a decreased popularity bias and
explainable recommendations.

##  3 Methodology

GRECS, our framework for Graph Reasoning for Explainable Cold Start, adapts GR
to cold start scenarios without requiring further training. In the following,
we first define the Knowledge Graph Reasoning for Explainable Recommendations
(KGRE-Rec) problem and then describe the GR models building the basis for the
recommendations. (PGPR [36] and UPGPR [15]). Finally, we detail how GRECS
integrates cold entities in the KG and assigns them with meaningful
embeddings.

###  3.1 Problem Formulation

We define a KG as a set of triplets composed of a head entity $e_{h}$, a tail
entity $e_{t}$, and a relation $r$:
$\mathcal{G}=\\{(e_{h},r,e_{t})|e_{h},e_{t}\in\mathcal{E},r\in\mathcal{R}\\}$.
$\mathcal{E}$ and $\mathcal{R}$ denote respectively the entity set and the
relations set associated with $\mathcal{G}$. We assume that the set of
entities contains a set of users $\mathcal{U}$ and items $\mathcal{I}$:
$\mathcal{U}\subset\mathcal{E}$ and $\mathcal{I}\subset\mathcal{E}$. If a user
$u$ has interacted with an item $i$, we add the triplet $(u,interacted,i)$ to
$\mathcal{G}$. We define a $k-$hop path in $\mathcal{G}$ as a sequence of
$k+1$ entities connected by $k$ relations:
$p=\left[e_{1},r_{1},e_{2},r_{2},\dots,r_{k},e_{k+1}\right]$, where all
entities in the path are unique (a path does not use the same entity twice)
and all triplets are in the KG: $\forall i\in 1...k:(e_{i},r_{i},e_{i+1})\in
p\rightarrow(e_{i},r_{i},e_{i+1})\in\mathcal{G}$. Given a user
$u\in\mathcal{U}$, KGRE-Rec aims to find a set of paths $\mathcal{P}_{u}$,
each starting from $u$ and terminating at a recommended item $i$, as
illustrated in Figure 1.

Figure 1: Illustration of the KGRE-REC problem on a KG with a warm user
$u_{1}$ (in red), who has already purchased a product and a cold user $u_{2}$
(in blue) who has not purchased any product, but whose preferences are assumed
to be known (e.g. through a questionnaire). The goal is to find paths from the
users to the items to be recommended. The red and blue arrows indicate the
paths chosen for the recommendations. While the agent uses past interactions
for the warm start user (purchased), only non-interaction relations are
leveraged to provide a recommendation for the cold start user. All
recommendations are explainable as they use entities and relations from the
KG.

###  3.2 Graph Reasoning Models

We use two GR models for explainable recommendations as a basis for GRECS:
PGPR and UPGPR.

PGPR. PGPR [36] consists of two main steps: (1) train a KG embedding model to
get entities and relations embeddings; (2) optimize an RL agent to find paths
in the KG from users to items. We refer the reader to the original paper [36]
for a full description of the agent optimization.

The goal of the first step is to embed every entity and relation in
$\mathcal{G}$. PGPR uses translational embeddings [8], trained by maximizing
the conditional probability of each triplet $(e_{t},r,e_{h})\in\mathcal{G}$:

$\mathbb{P}(e_{t}|e_{h},r)=\frac{\exp(f(e_{h},e_{t}|r))}{\sum_{e_{t}^{\prime}\in
E}\exp(f(e_{h},e_{t}^{\prime}|r))}$ (1)

where $f$ is a translation similarity function between entities $e_{h}$ and
$e_{t}$ connected with relation $r$:

$f(e_{h},e_{t}|r)=<\boldsymbol{e_{h}}+\boldsymbol{r},\boldsymbol{e_{t}}>+b_{e_{t}}$
(2)

where $\boldsymbol{e_{h}},\boldsymbol{r},\boldsymbol{e_{t}}$ are the
embeddings of $e_{h},r$ and $e_{t}$ respectively and $b_{e_{t}}$ is the bias
of $e_{t}$.

The goal of the second step is to optimize the RL agent, formulating KGRE-Rec
as a Markov Decision Process (MDP). The state is a vector built by
concatenating all entities and relations in the agent’s path. The initial
state is always a user embedding. For example, if we consider the current path
the agent took as $\left[u,r_{1},e_{1}\right]$, the state $s_{1}$ is defined
as $u||r_{1}||e_{1}$, where $||$ is the concatenation operation. The action is
defined as the choice of the next hop from the current entity $e_{t}$. Hence,
the action space $A_{t}$ consists of all possible relations connected to
entity $e_{t}$ except the ones that lead to already visited graph entities.
The agent can also take the action self-loop that keeps it on the current
entity. KGRE-Rec has a deterministic state transition function, meaning that
when that agent takes the action corresponding to going from entity $e_{i}$ to
entity $e_{i+1}$ using relation $r$, the probability of the agent arriving on
$e_{i+1}$ for its next state is equal to 1. Finally, the reward is computed
using the similarity function $f$ defined in equation 2 and using a set of
predefined path patterns $\mathcal{P}$:

$R(u,e_{T},p_{T})=\begin{cases}\frac{f(u,e_{T}|r)}{\max_{i\in\mathcal{I}}f(u,i|r)}&\text{if
}p_{T}\in\mathcal{P}\\\ 0,&\text{otherwise}\end{cases}$ (3)

where $e_{T}$ is the final entity in the path taken by the agent, $r$ is the
relation $interacted$, and $\mathcal{P}$ is a set of predefined path patterns.
We define a $k-$hop path pattern in $\mathcal{G}$ as a sequence of $k+1$
entity types connected by $k$ relations. Using predefined path patterns in the
reward constrains the exploration of the agent toward paths that are relevant
for explainability and that end on an item. However, the manual path
definition requires time, expert-knowledge, and can be infeasible in practice
for long paths with a large number of possible patterns.

UPGPR. To address the issues arising with the use of predefined path patterns
in the reward, UPGPR [15] uses a new binary reward scheme, allowing to remove
the predefined patterns without hurting the performances. Specifically, the
agent receives a reward if it begins at user $u$ and the final entity $e_{T}$
is an item that $u$ interacted with:

$R_{0/1}(u,e_{T})=\begin{cases}1&\text{ if }e_{T}\in\mathcal{I}_{u}\text{ and
}n_{sl}<k-1\\\ 0,&\text{otherwise}\end{cases}$ (4)

where $\mathcal{I}_{u}\subseteq I$ is the set of items user $u$ interacted
with, $k$ is the number of hops in the path and $n_{sl}$ is the number of self
loops. A reward of 0 is assigned to the agent if it uses $k-1$ self-loops
because rewarding paths with only one effective hop would lead to poor
generalization. For example, if an agent was rewarded for the following path:
$\left[user_{1},~{}interacted,~{}item_{1},~{}\textit{self-
loop},~{}item_{1}\right]$, there would be a risk of overfitting to the
training interactions. The other components of UPGPR, namely the KG
embeddings, state, actions, state transitions, and agent optimization are the
same as PGPR.

###  3.3 Graph Reasoning for Explainable Cold Start Recommendation

Our GRECS framework adapts GR models for cold start recommendations after the
embeddings and agent are optimized. Hence, GRECS can be used on an already
optimized model, not requiring any additional training. Specifically, GRECS
follows two steps: (1) integrating the new entity (user or item) into the KG
using their known (non-interaction) relations; (2) assigning the entity with a
meaningful embedding using its neighboring entities’ embeddings.

KG integration. Given a new entity $e\notin\mathcal{E}$ related to a small set
of entities via non-interaction relations ($r\neq interacted$), we add all
triplets containing $e$ to $\mathcal{G}$. Thanks to this integration, the
agent will have the capacity to either start from a cold user or land on a
cold item using the non-interaction relations connected to these entities that
were added to the graph. It should be noted that we are assuming to know at
least one relation of the cold entity to integrate. For example, a new user
can indicate the brand(s) they like on a questionnaire. If a new entity is not
related to any existing entity in the KG, it will not be used by GRECS.

Cold Embeddings. While the agent can navigate the KG from a cold user (or to a
cold item) via their integration in the KG, it needs meaningful embeddings in
its state representation to take an action that will lead to a relevant
recommendation. To this end, we propose to calculate the embedding for a new
entity by using the average translations from its related entities:

$\boldsymbol{e}=\sum_{(r^{\prime},e^{\prime}_{t})\in\mathcal{G}_{e}}\left(\boldsymbol{e^{\prime}_{t}}-\boldsymbol{r^{\prime}}\right)/|\mathcal{G}_{e}|$
(5)

where $\mathcal{G}_{e}$ is the subset of all triplets in $\mathcal{G}$ whose
head entity is $e$. This choice is motivated by the KG embeddings being
trained using a translation method as described in equation (2). To evaluate
our cold embeddings assignment strategy, we will also compare it to using null
embeddings (zeros values everywhere) that correspond to no prior knowledge
about users or items. In the following sections, we denote models using the
average translation embeddings as PGPRa/UPGPRa, null embeddings as
PGPR0/UPGPR0, and both methods regardless of the embeddings as PGPR/UPGPR.

##  4 Datasets

We evaluated GRECS on four e-commerce datasets [18] and one education dataset
[12].

E-commerce Datasets. The four e-commerce datasets [18] are: Amazon’s Beauty,
CDs and Vinyl, Clothing, and Cellphones.222Datasets can be downloaded here.
These datasets consist of user purchases, product reviews, and meta-
information about products. In the context of the e-commerce datasets, we are
interested in recommending a Product to a User and we use the relation
purchase as the interaction. The full list of entities, relations, and
statistics of the e-commerce datasets are displayed in Table 6 in Appendix A.
To integrate cold start users in the KG, we added 2 relations to the original
KG: interested_in and like. We connect a User with a Category using the
relation interested_in if the user purchased a product belonging to that
category. Similarly, we connect a User with a Brand using the relation like if
the user purchased a product belonging to that brand.

Education Dataset. COCO [12] consists of online course from the
Udemy333https://www.udemy.com/. platform. This dataset provides user
enrollments, course descriptions, instructors, and categories. On the COCO
dataset, we recommend a Course to a User using the enroll relation as the
interaction. The full list of entities, relations, and statistics of the
dataset are in Table 6 in Appendix A. To include cold start users in the KG,
we added the entity Skill and the relations know and cover to the original KG.
Skills taught in each course were extracted from the course description using
skillNER444https://github.com/AnasAito/SkillNER. If a Skill is mentioned in a
Course description, we connect them in the KG using the relation cover. If a
user enrolled in a Course with the relation cover with a Skill, we connect the
User and the Skill using the relation know.

Datasets Splits. All datasets were split into training, validation, and test
sets at the user level. For each user, the first $80\%$ of their interactions
(purchase for the e-commerce datasets and enroll for COCO) were selected to be
in the training set, the next $10\%$ were added to the validation set, and the
last $10\%$ were added to the test set. Additionally, we randomly selected
$20\%$ of users and items to be strict cold start users and items and removed
them from the training set. Half of the strict cold start users were assigned
to the validation set and the other half to the test set. When adding them to
the validation and test sets, we integrated cold start users into the
e-commerce KG using the relations interested_in and like and into the COCO KG
using the relation has_skills. Similarly, cold start items were integrated
into the e-commerce KG using the relations belong_to and produced_by and into
the COCO KG using the relation cover. To study the impact of the number of
known relations and to have realistic cold start users, we limited the
occurrences of the relations in the validation and the test KG. Specifically,
we uniformly sampled a random integer $k$ from 1 to 10 for each cold start
user and relation and connected the user only to the top $k$ entities in terms
of relation frequency. For example, on the e-commerce datasets, this is
similar to asking a new user to indicate their $k$ favorite brands, and
including the user using the like relation with their favorite brands.

##  5 Results

We performed four experiments to demonstrate the advantages of GRECS. [1]
GRECS outperforms all baselines on cold start users in terms of nDCG and HR.
[2] GRECS outperforms all baselines in cold item coverage. [3] GRECS mitigates
popularity bias. [4] GRECS needs only a small number of relations (not
interactions) to provide an accurate recommendation, and providing few
interactions increases the relevance of recommendations even further. Note
that while being adopted for the cold start scenario, GR methods also match or
outperform all the baselines on 4/5 datasets on warm users who already
interacted with items. We report the full detailed results in Table 7 in
Appendix B.

Baselines. We compared GRECS to eight competitive baselines with
implementations publicly available on Recbole [40]. Pop ranks items based on
their popularity, defined by their frequency in the training set. ItemKNN [5]
uses k-nearest-neighbor to recommend items similar to those a user has
previously selected. BPR [26] optimizes user-item similarity using a ranking-
based Bayesian method. NeuMF [19] combines matrix factorization and a multi-
layer perceptron to compute a user-item matching score. CFKG [4] uses the
similarity between users and items KG embeddings for recommendations and
constructs a path from users to items to generate a post-hoc explanation. KGCN
[33] uses Knowledge Graph Convolutional Networks (KGCN) to train an end-to-end
model for recommendation, directly on the KG.
SpectralCF${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char
94\relax}}}$ [41] proposes to address the cold start problem by structuring
the interactions between users and items as a bipartite graph and using
information in the spectral domains to make relevant recommendations.
MKR${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$
[32] addresses the cold start problem by a multi-task approach that optimizes
a model jointly on KG embeddings and for recommendation.

Evaluation Metrics. To assess recommendation relevance, we used two standard
ranking metrics: nDCG@$K$ and Hit Ratio@$K$. We use the POPB@$K$ [9] to
measure the popularity bias. To evaluate the ability of the models to
recommend strict cold items, we adapt 2 metrics from previous literature on
long tail recommendation [2, 3]: (1) the Cold Item Coverage
(Cov.${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char
94\relax}}}$) reports the proportion of recommended cold items among all cold
items across all users in the test set; (2) the Average Cold Item
Proportion@$K$
(Prop.${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char
94\relax}}}$) reports the average proportion of item recommended for each
user. All metrics are computed on the top 10 recommended items for each user
($K=10$). We define the Long Tail items as the 80% of items with the lowest
number of interactions in the training set. We report the average and standard
deviation of the metric across 3 runs with different seeds.

Implementation. For GRECS, we set PGPR and UPGPR embedding dimensions to 100
and trained them for 30 epochs. Other hyperparameters (learning rate, batch
size, etc…) were the same as in the original PGPR
implementation555https://github.com/orcax/PGPR. We used the full path history
for the agent’s state with a path length fixed to 3, making our state composed
of six KG entities embedding, each of size 100. RL agents were trained for 50
epochs using the Adam optimizer [21] with a learning rate of 0.001. Baselines
were implemented and evaluated with Recbole666https://recbole.io/ [40] with
batches of size 512 and Adam optimizer [21] with a learning rate of 0.001 for
50 epochs with early stopping on the validation set with a patience of 10
epochs. Baselines with embeddings had their dimensions set to 100, and all
other hyperparameters were set to their default values. Training and
evaluation took 2-4 hours on a single Intel Xeon Gold 6132 CPU on all datasets
except CDs (the largest dataset), which took up to 48 hours per model.

###  5.1 Exp. 1: GRECS outperforms baselines on strict cold start users

Table 1 presents the performance of GRECS and baselines in a strict cold start
scenario across all datasets using user-centric metrics. We observe that: (1)
GRECS outperforms all baselines across all datasets, showing the ability of GR
to make recommendations to users with no prior interactions that are more
relevant than baselines that rely on heuristics (Pop), matrix factorization
(NeuMF) or entity embeddings (CFKG). (2) Neither of the two cold embedding
strategies shows a definitive advantage over the other. For instance, null
embeddings prove more effective on the Beauty and Cellphones datasets, while
the average translation strategy performs better on the Clothing dataset. (3)
Despite being designed for cold start recommendations,
MKR${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$
and SpectralCF${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char
94\relax}}}$ underperform against the popularity-based recommender, which does
not make personalized recommendations nor use the KG. This highlights the
challenge of developing personalized recommendation models that outperform
simple heuristic approaches for strict cold-start users. (4) UPGPR performs
better than PGPR on all E-commerce datasets and both methods display similar
performances on the COCO dataset.

| Beauty | CDs | Cellphones | Clothing | COCO
---|---|---|---|---|---
Measures (%) | nDCG | HR | nDCG | HR | nDCG | HR | nDCG | HR | nDCG | HR
Pop |  1.03 $\pm$ 0.0 |  1.92 $\pm$ 0.0 | 0.28 $\pm$ 0.0 | 0.76 $\pm$ 0.0 |  1.67 $\pm$ 0.0 |  3.24 $\pm$ 0.0 |  0.48 $\pm$ 0.0 | 0.87 $\pm$ 0.0 |  1.33 $\pm$ 0.0 | 2.61 $\pm$ 0.0
ItemKNN | 0.04 $\pm$ 0.0 | 0.10 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.01 $\pm$ 0.0 | 0.01 $\pm$ 0.0 | 0.04 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.01 $\pm$ 0.0
BPR | 0.18 $\pm$ 0.0 | 0.40 $\pm$ 0.1 | 0.01 $\pm$ 0.0 | 0.03 $\pm$ 0.0 | 0.36 $\pm$ 0.2 | 0.68 $\pm$ 0.3 | 0.10 $\pm$ 0.0 | 0.19 $\pm$ 0.1 | 0.07 $\pm$ 0.0 | 0.16 $\pm$ 0.0
NeuMF | 0.80 $\pm$ 0.1 | 1.67 $\pm$ 0.0 | 0.24 $\pm$ 0.0 | 0.63 $\pm$ 0.0 | 1.63 $\pm$ 0.0 | 3.23 $\pm$ 0.0 |  0.48 $\pm$ 0.0 |  0.88 $\pm$ 0.0 | 0.26 $\pm$ 0.0 | 0.78 $\pm$ 0.2
CFKG | 0.69 $\pm$ 0.0 | 1.48 $\pm$ 0.1 |  0.30 $\pm$ 0.0 |  0.78 $\pm$ 0.1 | 0.64 $\pm$ 0.1 | 1.50 $\pm$ 0.3 | 0.17 $\pm$ 0.0 | 0.33 $\pm$ 0.1 | 1.01 $\pm$ 0.4 | 2.32 $\pm$ 0.7
KGCN | 0.04 $\pm$ 0.0 | 0.10 $\pm$ 0.0 | 0.02 $\pm$ 0.0 | 0.08 $\pm$ 0.0 | 0.10 $\pm$ 0.0 | 0.21 $\pm$ 0.0 | 0.03 $\pm$ 0.0 | 0.07 $\pm$ 0.0 | 0.11 $\pm$ 0.1 | 0.24 $\pm$ 0.1
MKR${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | 0.74 $\pm$ 0.1 | 1.46 $\pm$ 0.2 | 0.17 $\pm$ 0.0 | 0.39 $\pm$ 0.0 | 1.46 $\pm$ 0.1 | 3.02 $\pm$ 0.2 | 0.38 $\pm$ 0.0 | 0.83 $\pm$ 0.1 | 0.53 $\pm$ 0.2 | 1.46 $\pm$ 0.6
SpectralCF${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | 0.81 $\pm$ 0.2 | 1.76 $\pm$ 0.4 | 0.21 $\pm$ 0.0 | 0.54 $\pm$ 0.1 | 1.54 $\pm$ 0.1 | 3.17 $\pm$ 0.1 | 0.45 $\pm$ 0.1 | 0.80 $\pm$ 0.2 | 1.27 $\pm$ 0.4 |  2.63 $\pm$ 0.8
PGPRa | 1.65 $\pm$ 0.3 | 4.30 $\pm$ 0.8 | 0.83 $\pm$ 0.1 | 1.49 $\pm$ 0.2 | 0.78 $\pm$ 0.2 | 1.77 $\pm$ 0.3 | 1.07 $\pm$ 0.1 | 2.55 $\pm$ 0.3 | 2.98 $\pm$ 0.5 | 4.36 $\pm$ 0.8
PGPR0 | 1.78 $\pm$ 0.3 | 3.83 $\pm$ 0.7 | 0.31 $\pm$ 0.1 | 0.86 $\pm$ 0.3 | 1.85 $\pm$ 0.3 | 4.18 $\pm$ 0.6 | 0.51 $\pm$ 0.0 | 1.32 $\pm$ 0.1 | 3.07 $\pm$ 0.2 |  6.83 $\pm$ 0.3
UPGPRa | 2.26 $\pm$ 0.5 | 5.01 $\pm$ 1.3 | 1.05 $\pm$ 0.1 | 1.68 $\pm$ 0.2 | 1.74 $\pm$ 0.4 | 4.32 $\pm$ 0.8 |  1.76 $\pm$ 0.1 |  4.05 $\pm$ 0.2 |  3.49 $\pm$ 0.2 | 4.71 $\pm$ 0.1
UPGPR0 |  3.07 $\pm$ 0.2 |  6.75 $\pm$ 0.7 |  1.06 $\pm$ 0.2 |  2.61 $\pm$ 0.4 |  3.61 $\pm$ 0.1 |  7.97 $\pm$ 0.2 | 1.05 $\pm$ 0.1 | 2.64 $\pm$ 0.2 | 1.86 $\pm$ 0.2 | 3.56 $\pm$ 0.5

Table 1: Performance of GRECS compared to the baselines for strict cold start
users. The best results are highlighted in bold and the best baseline is
underlined.

To further explore performance differences between PGPR and UPGPR, we analyzed
the proportion of paths the agents followed on each dataset. Table 2 shows the
proportion of paths on the Beauty test set. The symbol
(${}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$) represents paths used for
warm users and the symbol
(${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$)
for cold users. UPGPR selects patterns more evenly than PGPR and frequently
uses those suitable for cold start users even in warm start scenarios.
Specifically, PGPR uses cold start-compatible patterns (marked in blue in
Table 2) on warm users $19.03\%$ of the time, whereas UPGPR does so $52.70\%$
of the time. This likely contributes to UPGPR’s superior performance in cold
start situations compared to PGPR since UPGPR’s agents are more familiar with
patterns that can be used for cold start users. Similarly, on the COCO dataset
(see Table 3), GRECS applies cold start-compatible patterns to warm users over
$90\%$ of the time for both PGPR and UPGPR, explaining their close
performances. This trend is consistent across all datasets, with detailed
proportions listed in Tables 8, 9, 10, 11, and 12 in Appendix C.

| PGPR${}_{a}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | UPGPR${}_{a}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | PGPR${}_{a}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | UPGPR${}_{a}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$
---|---|---|---|---
User $\xrightarrow{\text{mentioned}}$ Word $\xrightarrow{\text{described}}$ Product | 71.58% | 46.72% | 0% | 0%
User $\xrightarrow{\text{interested\\_in}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Category $\xrightarrow{\text{belong\\_to}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Product | 16.78% | 29.18% | 65.18% | 64.95%
User $\xrightarrow{\text{like}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Brand $\xrightarrow{\text{produced\\_by}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Product | 2.26% | 23.52% | 31.3% | 35.0%

Table 2: Proportion of the three most frequent patterns used by the agents on
the test set of the Beauty dataset for warm users
(${}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$) and cold users
(${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$).
Rows highlighted in blue denote cold start-compatible patterns that can be
used for recommending an item to a strict cold user.

| PGPR${}_{a}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | UPGPR${}_{a}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | PGPR${}_{a}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | UPGPR${}_{a}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$
---|---|---|---|---
User $\xrightarrow{\text{know}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Skill $\xrightarrow{\text{know}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ User $\xrightarrow{\text{enroll}}$ Course | 59.0% | 9.86% | 65.45% | 6.5%
User $\xrightarrow{\text{know}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Skill $\xrightarrow{\text{cover}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Course | 40.18% | 83.84% | 34.55% | 93.5%
User $\xrightarrow{\text{enroll}}$ Course $\xrightarrow{\text{enroll}}$ User $\xrightarrow{\text{enroll}}$ Course | 0.0% | 5.61% | 0% | 0%

Table 3: Proportion of the three most frequent patterns used by the agents on
the test set of the COCO dataset for warm users
(${}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$) and cold users
(${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$).
Rows highlighted in blue denote patterns that can be used for recommending an
item to a strict cold user.

GRECS provides the most relevant recommendations for strict cold start users
across all 5 datasets.

###  5.2 Exp. 2: GRECS achieves high coverage of cold start items

| Beauty | CDs | Cellphones | Clothing | COCO
---|---|---|---|---|---
Measures (%) | Cov.${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | Prop.${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | Cov.${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | Prop.${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | Cov.${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | Prop.${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | Cov.${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | Prop.${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | Cov.${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | Prop.${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$
Pop | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0
ItemKNN | 0.21 $\pm$ 0.0 |  5.74 $\pm$ 0.0 | 0.08 $\pm$ 0.0 |  11.34 $\pm$ 0.0 | 0.48 $\pm$ 0.0 |  11.54 $\pm$ 0.0 |  0.22 $\pm$ 0.0 |  11.51 $\pm$ 0.0 | 0.25 $\pm$ 0.0 |  11.42 $\pm$ 0.0
BPR | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0
NeuMF | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0
CFKG |  5.00 $\pm$ 0.2 | 0.20 $\pm$ 0.0 |  9.96 $\pm$ 0.9 | 1.23 $\pm$ 0.1 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.27 $\pm$ 0.2 | 0.18 $\pm$ 0.1
KGCN | 0.34 $\pm$ 0.3 | 0.01 $\pm$ 0.0 | 0.15 $\pm$ 0.1 | 0.00 $\pm$ 0.0 |  1.02 $\pm$ 1.3 | 0.02 $\pm$ 0.0 | 0.20 $\pm$ 0.1 | 0.01 $\pm$ 0.0 |  0.40 $\pm$ 0.3 | 0.01 $\pm$ 0.0
MKR${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0
SpectralCF${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0 | 0.00 $\pm$ 0.0
PGPRa |  46.03 $\pm$ 1.2 | 10.27 $\pm$ 0.3 |  28.98 $\pm$ 0.9 | 7.35 $\pm$ 0.4 |  39.79 $\pm$ 1.3 | 11.18 $\pm$ 0.3 |  40.66 $\pm$ 1.7 | 9.59 $\pm$ 0.3 | 21.88 $\pm$ 1.8 | 0.88 $\pm$ 0.0
PGPR0 | 2.85 $\pm$ 0.2 | 0.05 $\pm$ 0.0 | 0.08 $\pm$ 0.1 | 0.00 $\pm$ 0.0 | 1.58 $\pm$ 0.1 | 0.02 $\pm$ 0.0 | 0.97 $\pm$ 0.3 | 0.03 $\pm$ 0.0 | 10.86 $\pm$ 0.7 | 0.25 $\pm$ 0.0
UPGPRa | 33.10 $\pm$ 3.1 |  11.46 $\pm$ 1.2 | 23.96 $\pm$ 3.0 | 5.70 $\pm$ 0.5 | 35.83 $\pm$ 4.2 |  11.97 $\pm$ 2.2 | 31.72 $\pm$ 5.2 | 8.34 $\pm$ 0.4 |  27.72 $\pm$ 2.8 | 3.52 $\pm$ 0.2
UPGPR0 | 21.05 $\pm$ 1.1 | 2.96 $\pm$ 0.1 | 2.31 $\pm$ 0.0 | 0.34 $\pm$ 0.0 | 14.41 $\pm$ 1.6 | 2.07 $\pm$ 0.0 | 11.09 $\pm$ 1.0 | 1.47 $\pm$ 0.1 | 19.15 $\pm$ 0.6 | 2.86 $\pm$ 0.3

Table 4: Perfomance of GRECS compared to the baselines for strict cold start
items on all datasets. The best results are highlighted in bold and the best
baseline is underlined.

Table 4 details the performance of GRECS compared to baselines for strictly
cold items. We observe that: (1) GRECS outperforms all baselines in cold item
coverage across all five datasets, indicating that GRECS is capable of
identifying a wider variety of relevant cold items across different users than
baseline approaches. (2) ItemKNN shows high
Prop.${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char
94\relax}}}$, matching or exceeding GRECS on four out of the five datasets.
ItemKNN recommends on average one cold item in the top 10 for each user.
However, the low coverage of ItemKNN (less than $1\%$ on all datasets)
indicates that the method tends to recommend the same cold items to all users,
revealing a lack of personalization. (3) UPGPRa/PGPRa significantly outperform
UPGPR0/PGPR0 in terms of coverage and proportion, suggesting that agents avoid
recommending items with zero-initialized cold embeddings. Despite this
observation, the null embedding strategy still manages to recommend relevant
items to cold users (see Table 1), as the agents have to start from these
users to provide a recommendation (regardless of their embedding values).
Combining the results from Tables 1 and 4, the average translation strategy
for cold embeddings is the most effective for covering both cold user and cold
item scenarios. GRECS archives the highest cold item coverage, indicating its
ability to recommend cold items.

###  5.3 Exp. 3: GRECS mitigates the popularity bias

| Beauty | CDs | Cellphones | Clothing | COCO
---|---|---|---|---|---
Pop | 1.00 $\pm$ 0.0 | 1.00 $\pm$ 0.0 | 1.00 $\pm$ 0.0 | 1.00 $\pm$ 0.0 | 1.00 $\pm$ 0.0
ItemKNN |  0.06 $\pm$ 0.0 |  0.05 $\pm$ 0.0 |  0.03 $\pm$ 0.0 |  0.02 $\pm$ 0.0 |  0.13 $\pm$ 0.0
BPR | 0.32 $\pm$ 0.0 | 0.21 $\pm$ 0.0 | 0.33 $\pm$ 0.0 | 0.26 $\pm$ 0.0 | 0.23 $\pm$ 0.0
NeuMF | 0.36 $\pm$ 0.0 | 0.21 $\pm$ 0.0 | 0.37 $\pm$ 0.0 | 0.39 $\pm$ 0.0 | 0.25 $\pm$ 0.0
CFKG | 0.39 $\pm$ 0.0 | 0.28 $\pm$ 0.0 | 0.26 $\pm$ 0.0 | 0.22 $\pm$ 0.0 | 0.47 $\pm$ 0.1
KGCN | 0.34 $\pm$ 0.0 | 0.16 $\pm$ 0.0 | 0.38 $\pm$ 0.1 | 0.31 $\pm$ 0.0 | 0.25 $\pm$ 0.0
MKR${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | 0.42 $\pm$ 0.1 | 0.31 $\pm$ 0.1 | 0.52 $\pm$ 0.0 | 0.43 $\pm$ 0.1 | 0.36 $\pm$ 0.1
SpectralCF${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | 0.75 $\pm$ 0.2 | 0.25 $\pm$ 0.0 | 0.96 $\pm$ 0.0 | 0.83 $\pm$ 0.1 | 0.90 $\pm$ 0.0
PGPRa | 0.27 $\pm$ 0.0 | 0.37 $\pm$ 0.0 | 0.36 $\pm$ 0.0 | 0.27 $\pm$ 0.0 | 0.24 $\pm$ 0.0
PGPR0 | 0.32 $\pm$ 0.0 | 0.41 $\pm$ 0.0 | 0.51 $\pm$ 0.0 | 0.46 $\pm$ 0.0 | 0.27 $\pm$ 0.0
UPGPRa | 0.12 $\pm$ 0.0 | 0.10 $\pm$ 0.0 | 0.09 $\pm$ 0.0 | 0.12 $\pm$ 0.0 |  0.05 $\pm$ 0.0
UPGPR0 | 0.15 $\pm$ 0.0 | 0.11 $\pm$ 0.0 | 0.11 $\pm$ 0.0 | 0.14 $\pm$ 0.0 |  0.05 $\pm$ 0.0

Table 5: Popularity Bias (POPB) of GRECS compared to the baselines on all
datasets. The best results (lowest) are highlighted in bold and the best
baseline is underlined.

Table 5 shows the popularity bias of GRECS compared to the baselines across
all datasets. Interestingly, ItemKNN exhibits the lowest bias because it
relies only on items each user has interacted with, it is less sensitive to
the popularity bias than supervised methods optimized on the entire dataset.
Despite this low bias, ItemKNN performs poorly in scenarios with cold users
(as shown in Table 1). UPGPR is the second-best method, consistently
outperforming all other baselines as well as PGPR. These results suggest that
GRECS is better suited to handle popularity bias than the baseline approaches,
due to its exploration of the KG, which restricts the set of recommendable
items. The large difference between PGPR and UPGPR indicates that the reward
mechanism greatly impacts mitigating popularity bias in RL-based GR methods.
PGPR relies on embedding-similarity-based rewards, while UPGPR relies solely
on the relevance of the recommendation, leading to less biased outcomes.
Finally, PGPR0/UPGPR0 are more bias towards popular items than PGPRa/UPGPRa.
This finding highlights the importance of embedding initialization in
mitigating the popularity bias, showing that using neighboring embeddings
instead of null embeddings makes recommendations less biased.

GRECS archives the best trade-off between unbiased and relevant
recommendations.

###  5.4 Exp. 4: GRECS requires few relations to provide accurate
recommendations

Lastly, we evaluated the effectiveness of GRECS for sparse cold start
scenarios with few interactions and explored the impact of the number of known
relations on performance for strict cold start users.

(a) Beauty

(b) CDs

(c) Cellphones

(d) Clothing

(e) COCO

Figure 2: Evolution of the HR against the number of training interactions. The
shaded area represents the standard deviation across 3 runs.

Figure 2 shows the HR against the number of interactions in the training set,
ranging from 0 (strict cold start) to 3. We only display the Pop and BPR
baselines, as they perform the best for strict cold start and warm users
respectively. As expected, the performance of the Pop baseline does not
improve with the number of interactions, since it recommends the most popular
items regardless of the user’s profile. Conversely, all other approaches show
improvement, even from minimal interaction data. The results show that even a
single known interaction in the training set can significantly enhance model
performance. Fianlly, we see that UPGPRa surpasses PGPRa in performance on the
E-commerce datasets, while both methods exhibit comparable results on the COCO
dataset.

(a) Beauty

(b) CDs

(c) Cellphones

(d) Clothing

(e) COCO

Figure 3: Evolution of the HR against the number of relations for strict cold
start users. The shaded area represents the standard deviation across 3 runs.

Figure 3 shows the HR relative to the number of known relations for strict
cold start users. For instance, in an E-Commerce dataset, a strict cold start
user without any purchase interactions still has relations such as like or
interested_in, indicating preferences for categories or brands. Generally,
GRECS benefits from an increase in known relations for strict cold start
users, with HRs improving initially with the addition of a few relations.
however, HR declines and its variance increases with too many known relations
and no interactions. This is expected: recommending items to a cold user who
likes a variety of brands is more difficult than recommending items to a user
with specific preferences.

GRECS is best suited for strict cold start recommendations when a small number
of relations are known, and knowing a few interactions increases the relevance
of recommendations even further.

##  6 Discussion & Conclusion

In this paper, we proposed GRECS, a framework for adapting GR-based
recommendations to cold start scenarios while keeping recommendations
explainable. By explicitly using relationships in the KG to connect users to
items, GRECS can find items matching users’ preferences even with limited
information about users. Our experiments across five datasets show that GRECS
provides to better and less biased recommendations for new users than state-
of-the-art baselines. GRECS is also able to recommend cold items, requiring
only few relations to make relevant recommendations. Furthermore, we show that
both the strategy for initializing the embeddings of cold-start users and
items as well as the choice of reward are crucial for recommending cold items
and mitigating the popularity bias.

Limitations and future work. GRECS relies on KGs and can therefore make
recommendations without pre-existing relational data about cold users or
items. It can for example not take advantage of attributes with real values
such as the item’s price. Furthermore, the GR methods at the basis of GRECS
exhibit an inherent recall bias [17]. Specifically, their recall is limited by
the existence of user-item pairs that cannot be connected through paths of
length $k$, restricting their ability to recommend certain relevant items.
Finally, our cold embedding assignment method is specific to PGPR and UPGPR.
Future work should extend GRECS to other GR approaches, namely LLM-based
approaches that are not subject to the recall bias.

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##  Appendix A Datasets Statistics

E-commerce | Education
---|---
| CDs | Cloth. | Cell. | Beauty | COCO
#Entities |  |  |  |  | #Entities |
User | 75k | 39k | 27k | 22k | User | 25k
Product | 64k | 23k | 10k | 12k | Course | 23k
Word | 202k | 21k | 22k | 22k | Category | 132
Brand | 1.4k | 1.1k | 955 | 2k | Teacher | 4.1k
Category | 770 | 1.1k | 206 | 248 | Skill | 5.5k
#Relations |  |  |  |  | #Relations |
User $\xrightarrow{\text{purchase}}$ Product | 1.1M | 278k | 194k | 198k | User $\xrightarrow{\text{enroll}}$ Course | 428k
User $\xrightarrow{\text{mention}}$ Word | 191M | 17M | 18M | 18M | User $\xrightarrow{\text{know}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}}$ Skill | 278k
User $\xrightarrow{\text{like}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}}$ Brand | 192k | 60k | 90k | 132k | Course $\xrightarrow{\text{belong\\_to}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}}$ Category | 23k
User $\xrightarrow{\text{interested\\_in}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}}$ Category | 2.0M | 949k | 288k | 354k | Course $\xrightarrow{\text{cover}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}}$ Skill | 47k
Product $\xrightarrow{\text{described\\_by}}$ Word | 191M | 17M | 18M | 18M | Course $\xrightarrow{\text{taught\\_by}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}}$ Teacher | 23k
Product $\xrightarrow{\text{belong\\_to}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}}$ Category | 466k | 154k | 36k | 49k |  |
Product $\xrightarrow{\text{produced\\_by}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}}$ Brand | 64k | 23k | 10k | 12k |  |
Product $\xrightarrow{\text{also\\_bought}}$ Product | 3.6M | 1.4M | 590k | 891k |  |
Product $\xrightarrow{\text{also\\_viewed}}$ Product | 78k | 147k | 22k | 155k |  |
Product $\xrightarrow{\text{bought\\_together}}$ Product | 78k | 28k | 12k | 14k |  |

Table 6: Statistics of the e-commerce and education datasets. Relations
indicated with ${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char
94\relax}}}$ are used to integrate cold users or cold items into the KG.

##  Appendix B Results on all users

Graph Reasoning approaches match or outperform all the baselines on 4 out of
the 5 datasets for warm users whose interactions are available in the training
set. These results confirm the findings of Xian et al. [36] and Frej et al.
[15]: Graph Reasoning methods can make explainable and relevant
recommendations competitively even against non-interpretable baselines. It
should be noted that the results reported here are different than the ones
reported in the PGPR [36] and UPGPR [15] papers because our method for
splitting the datasets is different than theirs. We adopted a different
splitting method (user level splitting, and removing users and items from the
training set) to study the recommendations under cold start scenarios.

| Beauty | CDs | Cellphones | Clothing | COCO
---|---|---|---|---|---
Measures (%) | nDCG | HR | nDCG | HR | nDCG | HR | nDCG | HR | nDCG | HR
Pop | 1.00 $\pm$ 0.0 | 1.97 $\pm$ 0.0 | 0.29 $\pm$ 0.0 | 0.71 $\pm$ 0.0 | 1.60 $\pm$ 0.0 | 3.18 $\pm$ 0.0 | 0.40 $\pm$ 0.0 | 0.78 $\pm$ 0.0 | 0.98 $\pm$ 0.0 | 2.30 $\pm$ 0.0
ItemKNN | 3.02 $\pm$ 0.0 | 5.58 $\pm$ 0.0 |  3.15 $\pm$ 0.0 |  6.28 $\pm$ 0.0 | 2.19 $\pm$ 0.0 | 4.10 $\pm$ 0.0 | 0.75 $\pm$ 0.0 | 1.33 $\pm$ 0.0 |  2.90 $\pm$ 0.0 |  6.03 $\pm$ 0.0
BPR |  3.13 $\pm$ 0.1 |  6.02 $\pm$ 0.2 | 2.45 $\pm$ 0.0 | 5.37 $\pm$ 0.0 |  3.32 $\pm$ 0.0 |  6.10 $\pm$ 0.1 |  0.84 $\pm$ 0.0 |  1.54 $\pm$ 0.0 | 2.54 $\pm$ 0.0 | 5.37 $\pm$ 0.1
NeuMF | 2.28 $\pm$ 0.0 | 4.55 $\pm$ 0.1 | 1.67 $\pm$ 0.0 | 3.75 $\pm$ 0.0 | 2.24 $\pm$ 0.1 | 4.18 $\pm$ 0.1 | 0.35 $\pm$ 0.0 | 0.68 $\pm$ 0.0 | 0.93 $\pm$ 0.1 | 2.17 $\pm$ 0.0
CFKG | 2.54 $\pm$ 0.1 | 5.08 $\pm$ 0.2 | 1.88 $\pm$ 0.0 | 4.33 $\pm$ 0.0 | 1.35 $\pm$ 0.1 | 2.68 $\pm$ 0.1 | 0.27 $\pm$ 0.0 | 0.53 $\pm$ 0.0 | 1.31 $\pm$ 0.2 | 2.87 $\pm$ 0.5
KGCN | 1.90 $\pm$ 0.1 | 3.93 $\pm$ 0.1 | 1.40 $\pm$ 0.0 | 3.36 $\pm$ 0.0 | 2.07 $\pm$ 0.2 | 3.94 $\pm$ 0.4 | 0.35 $\pm$ 0.0 | 0.70 $\pm$ 0.1 | 0.78 $\pm$ 0.5 | 1.81 $\pm$ 1.0
MKR${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | 0.75 $\pm$ 0.0 | 1.58 $\pm$ 0.1 | 1.27 $\pm$ 0.0 | 2.98 $\pm$ 0.0 | 0.93 $\pm$ 0.1 | 2.02 $\pm$ 0.1 | 0.19 $\pm$ 0.0 | 0.41 $\pm$ 0.0 | 0.35 $\pm$ 0.1 | 0.89 $\pm$ 0.2
SpectralCF${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | 0.91 $\pm$ 0.1 | 1.95 $\pm$ 0.1 | 0.55 $\pm$ 0.0 | 1.50 $\pm$ 0.0 | 1.51 $\pm$ 0.0 | 3.10 $\pm$ 0.1 | 0.35 $\pm$ 0.0 | 0.70 $\pm$ 0.1 | 0.67 $\pm$ 0.2 | 1.53 $\pm$ 0.4
PGPRa | 3.08 $\pm$ 0.1 | 5.77 $\pm$ 0.0 | 1.20 $\pm$ 0.1 | 2.76 $\pm$ 0.3 | 2.53 $\pm$ 0.2 | 4.86 $\pm$ 0.4 | 1.35 $\pm$ 0.1 | 2.58 $\pm$ 0.2 | 4.21 $\pm$ 0.3 | 9.40 $\pm$ 0.6
PGPR0 | 3.07 $\pm$ 0.1 | 5.81 $\pm$ 0.0 | 1.17 $\pm$ 0.1 | 2.75 $\pm$ 0.3 | 1.95 $\pm$ 0.1 | 3.87 $\pm$ 0.2 | 0.65 $\pm$ 0.0 | 1.29 $\pm$ 0.0 | 4.22 $\pm$ 0.2 | 10.30 $\pm$ 0.1
UPGPRa | 4.15 $\pm$ 0.2 | 8.16 $\pm$ 0.5 | 2.17 $\pm$ 0.0 | 4.26 $\pm$ 0.1 | 3.86 $\pm$ 0.1 | 7.42 $\pm$ 0.2 |  1.75 $\pm$ 0.0 |  3.85 $\pm$ 0.2 |  7.29 $\pm$ 0.2 |  12.25 $\pm$ 0.4
UPGPR0 |  4.30 $\pm$ 0.2 |  8.61 $\pm$ 0.3 | 2.19 $\pm$ 0.1 | 4.41 $\pm$ 0.1 |  4.07 $\pm$ 0.1 |  7.90 $\pm$ 0.3 | 1.68 $\pm$ 0.1 | 3.73 $\pm$ 0.2 | 7.26 $\pm$ 0.2 | 12.15 $\pm$ 0.3

Table 7: Perfomance of Graph reasoning approaches compared to the baselines
across all users on all datasets. The best results are highlighted in bold and
the best results for the baselines are underlined.

##  Appendix C Pattern proportion on all datasets

| PGPR${}_{a}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | PGPR${}_{0}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | UPGPR${}_{a}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | UPGPR${}_{0}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | PGPR${}_{a}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | PGPR${}_{0}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | UPGPR${}_{a}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | UPGPR${}_{0}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$
---|---|---|---|---|---|---|---|---
User $\xrightarrow{\text{mentioned}}$ Word $\xrightarrow{\text{described}}$ Product | 71.58% | 70.17% | 46.72% | 44.21% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{interested\\_in}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Category $\xrightarrow{\text{belong\\_to}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Product | 16.78% | 18.7% | 29.18% | 30.52% | 65.18% | 73.58% | 64.95% | 61.99%
User $\xrightarrow{\text{purchase}}$ Product $\xrightarrow{\text{also\\_bought}}$ Product $\xrightarrow{\text{also\\_bought}}$ Product | 4.12% | 3.38% | 0.51% | 0.48% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{purchase}}$ Product $\xrightarrow{\text{described}}$ Word $\xrightarrow{\text{described}}$ Product | 3.98% | 4.1% | 0.05% | 0.05% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{like}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Brand $\xrightarrow{\text{produced\\_by}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Product | 2.26% | 2.31% | 23.52% | 24.73% | 31.3% | 25.07% | 35.0% | 38.01%

Table 8: Proportion of the most frequent patterns used by the agents on the
test set of the Beauty dataset for warm users
(${}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$) and cold users
(${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$).
Rows highlighted in blue denote cold start-compatible patterns that can be
used for recommending an item to a strict cold user.

| PGPR${}_{a}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | PGPR${}_{0}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | UPGPR${}_{a}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | UPGPR${}_{0}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | PGPR${}_{a}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | PGPR${}_{0}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | UPGPR${}_{a}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | UPGPR${}_{0}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$
---|---|---|---|---|---|---|---|---
User $\xrightarrow{\text{mentioned}}$ Word $\xrightarrow{\text{described}}$ Product | 49.09% | 48.74% | 63.54% | 61.31% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{interested\\_in}^{\text{{\char 94\relax}}}}$ Category $\xrightarrow{\text{belong\\_to}^{\text{{\char 94\relax}}}}$ Product | 30.35% | 30.56% | 23.24% | 24.77% | 85.01% | 80.6% | 80.3% | 75.4%
User $\xrightarrow{\text{mentioned}}$ Word $\xrightarrow{\text{mentioned}}$ User $\xrightarrow{\text{purchase}}$ Product | 6.81% | 6.76% | 0.0% | 0.0% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{purchase}}$ Product $\xrightarrow{\text{described}}$ Word $\xrightarrow{\text{described}}$ Product | 6.26% | 6.22% | 1.55% | 1.5% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{purchase}}$ Product $\xrightarrow{\text{also\\_bought}}$ Product $\xrightarrow{\text{also\\_bought}}$ Product | 4.51% | 4.47% | 6.78% | 6.53% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{like}^{\text{{\char 94\relax}}}}$ Brand $\xrightarrow{\text{produced\\_by}^{\text{{\char 94\relax}}}}$ Product | 2.28% | 2.54% | 4.59% | 5.59% | 14.25% | 18.32% | 19.59% | 24.49%

Table 9: Proportion of the most frequent patterns used by the agents on the
test set of the CDs dataset for warm users
(${}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$) and cold users
(${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$).
Rows highlighted in blue denote cold start-compatible patterns that can be
used for recommending an item to a strict cold user.

| PGPR${}_{a}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | PGPR${}_{0}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | UPGPR${}_{a}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | UPGPR${}_{0}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | PGPR${}_{a}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | PGPR${}_{0}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | UPGPR${}_{a}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | UPGPR${}_{0}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$
---|---|---|---|---|---|---|---|---
User $\xrightarrow{\text{mentioned}}$ Word $\xrightarrow{\text{described}}$ Product | 65.4% | 61.2% | 49.6% | 49.18% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{interested\\_in}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Category $\xrightarrow{\text{belong\\_to}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Product | 30.19% | 31.14% | 29.18% | 28.03% | 78.96% | 77.22% | 70.46% | 57.42%
User $\xrightarrow{\text{like}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Brand $\xrightarrow{\text{produced\\_by}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Product | 3.88% | 4.22% | 19.87% | 21.45% | 20.99% | 22.75% | 29.49% | 42.53%
User $\xrightarrow{\text{purchase}}$ Product $\xrightarrow{\text{also\\_bought}}$ Product $\xrightarrow{\text{also\\_bought}}$ Product | 0.36% | 1.3% | 1.18% | 1.16% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{purchase}}$ Product $\xrightarrow{\text{described}}$ Word $\xrightarrow{\text{described}}$ Product | 0.08% | 1.89% | 0.13% | 0.13% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{purchase}}$ Product $\xrightarrow{\text{also\\_viewed}}$ Product $\xrightarrow{\text{also\\_bought}}$ Product | 0.03% | 0.06% | 0.01% | 0.02% | 0% | 0% | 0% | 0%

Table 10: Proportion of the most frequent patterns used by the agents on the
test set of the Cellphones dataset for warm users
(${}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$) and cold users
(${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$).
Rows highlighted in blue denote cold start-compatible patterns that can be
used for recommending an item to a strict cold user.

| PGPR${}_{a}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | PGPR${}_{0}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | UPGPR${}_{a}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | UPGPR${}_{0}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | PGPR${}_{a}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | PGPR${}_{0}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | UPGPR${}_{a}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | UPGPR${}_{0}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$
---|---|---|---|---|---|---|---|---
User $\xrightarrow{\text{mentioned}}$ Word $\xrightarrow{\text{described}}$ Product | 74.23% | 74.41% | 58.27% | 57.5% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{interested\\_in}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Category $\xrightarrow{\text{belong\\_to}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Product | 16.24% | 20.48% | 37.19% | 38.43% | 92.02% | 95.7% | 81.99% | 90.31%
User $\xrightarrow{\text{purchase}}$ Product $\xrightarrow{\text{also\\_bought}}$ Product $\xrightarrow{\text{also\\_bought}}$ Product | 4.49% | 2.04% | 0.73% | 0.73% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{purchase}}$ Product $\xrightarrow{\text{described}}$ Word $\xrightarrow{\text{described}}$ Product | 4.01% | 2.28% | 0.13% | 0.13% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{like}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Brand $\xrightarrow{\text{produced\\_by}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Product | 0.41% | 0.26% | 3.63% | 3.18% | 7.41% | 4.14% | 17.85% | 9.69%

Table 11: Proportion of the most frequent patterns used by the agents on the
test set of the Clothing dataset for warm users
(${}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$) and cold users
(${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$).
Rows highlighted in blue denote cold start-compatible patterns that can be
used for recommending an item to a strict cold user.

| PGPR${}_{a}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | PGPR${}_{0}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | UPGPR${}_{a}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | UPGPR${}_{0}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$ | PGPR${}_{a}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | PGPR${}_{0}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | UPGPR${}_{a}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$ | UPGPR${}_{0}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$
---|---|---|---|---|---|---|---|---
User $\xrightarrow{\text{know}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Skill $\xrightarrow{\text{know}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ User $\xrightarrow{\text{enroll}}$ Course | 59.0% | 24.11% | 9.86% | 10.58% | 65.45% | 16.31% | 6.5% | 4.24%
User $\xrightarrow{\text{know}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Skill $\xrightarrow{\text{cover}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Course | 40.18% | 72.36% | 83.84% | 82.34% | 34.55% | 83.69% | 93.5% | 95.76%
User $\xrightarrow{\text{enroll}}$ Course $\xrightarrow{\text{belong\\_to}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Category $\xrightarrow{\text{belong\\_to}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Course | 0.47% | 1.81% | 0.27% | 0.24% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{enroll}}$ Course $\xrightarrow{\text{taught\\_by}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Teacher $\xrightarrow{\text{taught\\_by}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Course | 0.29% | 0.9% | 0.3% | 0.31% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{enroll}}$ Course $\xrightarrow{\text{cover}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Skill $\xrightarrow{\text{cover}^{\text{\color[rgb]{0.0600000000000001,0.46,1}{\char 94\relax}}}}$ Course | 0.07% | 0.08% | 0.12% | 0.05% | 0% | 0% | 0% | 0%
User $\xrightarrow{\text{enroll}}$ Course $\xrightarrow{\text{enroll}}$ User $\xrightarrow{\text{enroll}}$ Course | 0.0% | 0.74% | 5.61% | 6.48% | 0% | 0% | 0% | 0%

Table 12: Proportion of all the patterns used by the agents on the test set of
the COCO dataset for warm users
(${}^{\text{\color[rgb]{1,0,0.5}\tiny\faHotjar}}$) and cold users
(${}^{\text{\color[rgb]{0.0600000000000001,0.46,1}\tiny{\char 94\relax}}}$).
Rows highlighted in blue denote patterns that can be used for recommending an
item to a strict cold user.