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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>JoLA: Job Landscape Aware Job Recommendation</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Solal Nathan</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Guillaume Bied</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Elia Perennes</string-name>
          <email>r@10</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Philippe Caillou</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Bruno Crepon</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Christophe Gaillac</string-name>
          <email>HR@10</email>
          <email>hr@10</email>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Michèle Sebag</string-name>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Centre de Recherche en Économie et de Statistiques (CREST), CNRS, École polytechnique, GENES, ENSAE Paris, Institut Polytechnique de Paris</institution>
          ,
          <addr-line>91120 Palaiseau</addr-line>
          ,
          <country country="FR">France</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>France Travail</institution>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Ghent University</institution>
          ,
          <addr-line>IDLab</addr-line>
          ,
          <institution>Department of Electronics and Information Systems</institution>
        </aff>
        <aff id="aff3">
          <label>3</label>
          <institution>University of Geneva</institution>
          ,
          <addr-line>GSEM</addr-line>
        </aff>
      </contrib-group>
      <abstract>
        <p>Job recommendation (JR), among the most critical challenges of AI, aims to alleviate frictional unemployment with major potential impacts on society and economy at large. However, Job Recommender Systems (JRS) might become counter-productive and create a congestion phenomenon, if job seekers are mostly recommended the most popular job ads. This paper proposes a novel perspective on JRS, observing that the job market tends to involve a number of so-called “orphan" job ads, that receive very few or no applications. The orphan-job phenomenon is detrimental to the job market as it mechanically decreases the number of jobs efectively considered, worsening the market imbalance and increasing the congestion; in the long term, it also tends to prevent companies from publishing other ads, de facto creating a sleeping job market that is not revealed to the job seekers. This paper introduces new JRS losses, aimed to prevent both the congestion and the orphan-jobs phenomenon, based on a diferentiable approximation of the market share attributed to a job ad. The resulting so-called Job Landscape Aware recommender system (JoLA) is experimentally assessed and compared with the state of the art on public datasets, showing new trade-ofs that exist between standard recommendation metrics and congestion, while enforcing the desired exposure for most ads. The JoLA code is publicly available at https://codeberg.org/solal/jola.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Job recommender system</kwd>
        <kwd>Congestion avoidance</kwd>
        <kwd>Exposure in ranking</kwd>
        <kwd>Popularity bias</kwd>
        <kwd>Matching</kwd>
        <kwd>Labor market</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Job Recommender Systems (JRSs), at the forefront of AI for
good, are viewed as a promise to reduce frictional
unemployment [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. In the perspective of job seekers, JRSs can
potentially alleviate the burden of finding a job best suited
to them, among the many job ads available through diverse
canals, ranging from e.g. LinkedIn [
        <xref ref-type="bibr" rid="ref2 ref3">2, 3</xref>
        ] or CareerBuilder to
Public Employment Services (PES) [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. In the perspective of
recruiters, JRSs can symmetrically help finding job seekers
best suited to a job ad [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ].
      </p>
      <p>
        JRSs build upon the massive development of recommender
systems [
        <xref ref-type="bibr" rid="ref6 ref7">6, 7</xref>
        ], prompted by the deployment of e-commerce
and entertainment platforms since the mid 1990s [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. Yet,
unlocking the full potential of these systems in the
context of job platforms or PES requires taking into account
specificities of the labor market [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ], the more so given the
high-risk nature of this AI application [
        <xref ref-type="bibr" rid="ref8 ref9">8, 9</xref>
        ].
      </p>
      <p>
        Among these specificities is the fact that job
recommendation is a multi-stakeholder, reciprocal problem [
        <xref ref-type="bibr" rid="ref10 ref11 ref12">10, 11, 12</xref>
        ].
Enforcing an appropriate distribution of the
recommendations, as detailed below, is achieved by intervening in an
in-processing or post-processing manner on the
recommendation policy [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ] beyond the standard probability ranking
principle.
      </p>
      <p>
        This paper focuses on enforcing two desired properties of
the recommendation distribution.1 The first one is to avoid
the so-called congestion phenomenon. As job ads are rival
RecSys in HR’25: The 5th Workshop on Recommender Systems for Human
Resources, in conjunction with the 19th ACM Conference on Recommender
Systems, September 22–26, 2025, Prague, Czech Republic.
$ solal.nathan@inria.fr (S. Nathan)
0000-0002-5800-1271 (S. Nathan)
© 2025 Copyright for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0).
1Another most desired property concerns the fairness of the
recommendation policy [
        <xref ref-type="bibr" rid="ref14 ref5">5, 14</xref>
        ], as the recommender system can amplify the
biases and discriminations observed in the data. Fairness aspects are
outside the scope of this paper.
goods − an item (job ad) can most generally be attributed
to a single user − recommending a small subset of popular
job ads to most users can create severe congestions, where
many job seekers compete for the same job ads. The second
one is that many job ads − referred to as orphan jobs in the
following − actually receive few or no applications, de facto
worsening the job market imbalance, and discouraging the
afected companies from publishing more job ads on job
platforms or at the PES.
      </p>
      <p>
        How to avoid congestion and resist the bias toward
popular items has been extensively investigated in the general
recommender systems literature [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ] and in the context of
Job Recommender systems [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ] (more in Section 4). How to
ensure a fair share of users’ attention to every item has also
been extensively considered in the literature [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ], although
much less so in the JRS context [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ] to our best knowledge.
Still, the point of attracting job seekers to every job ad
appears a strategic issue, in both perspectives of job seekers
and recruiters. On the one hand, recommending orphan
jobs to job seekers contributes to alleviate the congestion
and the competition on the job market. On the other hand,
the fact that companies receive more (or at least some)
applications on every job ad might incentivize them to publish
more and possibly more diverse job ads. Actually, some
practitioners suggest that a significant part of the jobs to be
fulfilled are sleeping ones: they are not published on the PES
platforms as the recruiters feel that they would receive no
applications.2
      </p>
      <p>
        This paper focuses on the design and assessment of a job
recommender system addressing both issues of congestion
and orphan jobs, with two main contributions. First, we
propose using a diferentiable approximation of the
mar2Indeed, part of the so-called sleeping job ads require skills that might
be missing among the job seekers. However, the indication that some
people are willing to apply to such job ads might still unlock the
situation, e.g. by pointing at the need to ofer specific training and the
existing motivation to follow these.
ket share associated with each job ad (the number of
applications received after recommending the top- items
corresponding to each job seeker) to design loss functions
targeting the distribution of exposure among job ads. Such
loss functions may be added to standard pointwise losses in
JRSs to minimize the number of orphan jobs, or to reduce
congestion, as an in-processing strategy. Secondly, a JRS
trained using these compound training losses, called Job
Landscape Aware recommender system (JoLA) is assessed
on public job recommendation datasets, and compared with
the state of the art, chiefly the ReCon approach [
        <xref ref-type="bibr" rid="ref16 ref4">16, 4</xref>
        ]. Most
interestingly, in the considered settings the number of
orphan jobs appears to be significantly more informative than
the entropy of the market shares, classically used to train a
congestion-avoiding JRS [
        <xref ref-type="bibr" rid="ref16 ref19">16, 19</xref>
        ].
      </p>
      <p>The paper is organized as follows. Section 2 presents an
overview of the proposed JoLA. The experimental setting
used to comparatively assess JoLA, and the empirical results
are respectively detailed in Sections 3 and 4. Section 5
discusses the position of the proposed approach with respect
to related work. We last conclude and present the research
perspectives opened by the proposed approach.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Overview of JoLA</title>
      <p>This section presents the proposed JoLA approach and
details its components.</p>
      <p>
        Notations. The recommendation dataset consists of the
interaction matrix  (, ) between  users (job seekers)
and  items (job ads). Binary interactions are considered:
 [, ] = 1 if the -th user applies on the -th job ad, and
0 otherwise. Following [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] the feature-based description
of users and items is not considered, as the focus is on the
recommendation policy in a warm-start recommendation
setting [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ].
      </p>
      <p>It is worth noting however that the proposed approach
extends to the feature-based recommendation setting in
a straightforward manner.</p>
      <sec id="sec-2-1">
        <title>2.1. Position of the warm-start recommendation problem</title>
        <p>Recommender systems classically proceed by learning from
the interaction matrix a real-valued score function (, ).
The recommendation policy   recommends to each -th
user a list of items, ordered by decreasing value of (, ).
Most generally, the set of recommendations to the -th user
is the set of top- job ads after (, · ) with  a positive
integer (1 ≤  ≤ ). Let us denote ,, the -th item
recommended to the -th user after policy  .</p>
        <p>A scoring function is first assessed from its Recall at ,
measuring the fraction of true interactions present in the
top- recommendations, averaged over all users:
{︃ ∑︀</p>
        <p>=1  (, ,,) }︃
∑︀
=1  (, ,,)
A more relaxed performance metrics is the Hit-rate at ,
measuring the fraction of users for whom at least one
interaction appears in the top- recommendations:
@() = ∈[]
{︁
1∑︀=1 (,,,)
}︁
where indicator function 1 is 1 if A is positive, and 0
otherwise.</p>
        <p>
          Following the standard methodology for warm-start
collaborative filtering [
          <xref ref-type="bibr" rid="ref20">20</xref>
          ], the scoring function is learned from
the training part of the interaction matrix, and assessed from
its performance on the rest of the interaction matrix.
        </p>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. A multi-stakeholder recommendation problem</title>
        <p>
          As said, the domain of job recommendation involves rival
goods, i.e. a given item can be attributed to at most one
user. Two more performance metrics are thus considered to
assess the global impact of the recommendation policy. The
ifrst one is the congestion score [
          <xref ref-type="bibr" rid="ref16">16</xref>
          ], defined as follows.
        </p>
        <p>Let us first define the market share of an item, noted
 (), as the number of job seekers who are recommended
this item according to   :</p>
        <p>
          () = #{ ∈ [] .. (, ) &gt;= (, ,,)}
The normalized market share noted  () is  ()
divided by ; the normalized market shares thus sum to 1.
The congestion is then classically defined as the entropy of
the normalized market shares:
() = −
∑︁  () log  ()
∈[]
Another performance metrics, noted , and
generalizing the coverage [
          <xref ref-type="bibr" rid="ref21">21</xref>
          ], is also considered. , counts the
number of job ads that are involved in less than 
recommendations, with  a positive integer.3 Formally, a job ad is
said to be a (, )-orphan if its number of applicants after
  is less than , when each user receives 
recommendations. The proportion of (, )-orphans noted , is then
defined as:
,() =
1

∑︁ 1()&lt;
∈[]
Note that for  = 1, the , metrics is but the
complementary of the coverage metrics.
        </p>
      </sec>
      <sec id="sec-2-3">
        <title>2.3. The JoLA algorithm</title>
        <p>
          JoLA is built by training two neural embeddings respectively
associated with users and items and referred to as  and
 . The recommendation score (, ) associated to the pair
made of the -th user and -th item is defined as:
(, ) = (⟨(),  ()⟩ + )
The use of the sigmoid enforces (, ) in [
          <xref ref-type="bibr" rid="ref1">0, 1</xref>
          ] for a better
training stability; constant  is trained and adjusts the range
of recommendation scores amenable to optimization (with
non vanishing gradients) [
          <xref ref-type="bibr" rid="ref22">22</xref>
          ].
        </p>
        <p>
          Embeddings are learned by minimizing a compound loss.
The first term of the learning loss classically is the binary
3Note that by design, the maximal value of  such that there exists no
(, )-orphan is
 =
︂⌊  ⌋︂

(1)
For  &gt; , the recommendation policy can but create (,
)orphans. Note that [
          <xref ref-type="bibr" rid="ref18">18</xref>
          ] minimizes the number of orphan jobs for
 = .
 (, ) ((, ))
+ (1 −  (, )) (1 − (, ))
ℒ () = ∑︀
        </p>
        <p>∈[],∈[]</p>
        <p>A first JoLA mode, referred to as JoLA-Congestion
(JoLAc), is trained by minimizing the loss defined as:</p>
        <p>ℒ() = ℒ () +   ()
with  &gt;</p>
        <p>0 the weight of the congestion term; the
congestion term relies on a diferentiable approximation of the
market shares, detailed below.</p>
        <p>Likewise, a second JoLA mode, referred to as JoLA-Orphan
(JoLA-o), is trained by minimizing:</p>
        <p>ℒℎ() = ℒ () +  ℒ,()
with  &gt;</p>
        <p>0 the weight of the orphan loss defined as:
ℒ,() =</p>
        <p>1
 ·  ,()</p>
        <p>∑︁
 / ()&lt;
( −  ())2
 .
with ,() the proportion of (, )-orphans after policy</p>
      </sec>
      <sec id="sec-2-4">
        <title>2.4. Diferentiable Market Share</title>
        <p>For simplicity and computational frugality, an approximate
computation of the market share is used:4
(2)
(3)
(4)
(5)
 () =</p>
        <p>∈[]

1 ∑︁ ((, ) − (, ,,))+
where + = (0, ) and  set to the diference
between (, ) and (, ,,) when the diference is positive,
averaged over all recommendations:
 =
1</p>
        <p>∑︁
∈[],∈[]</p>
        <p>((, ) − (, ,,))+
Informally,  () considers all users  who will be
recommended the -th job ad after   (i.e., (, ) &gt;= (, ,,)).
The sum of these scalar diferences is approximated into a
count by the division by  .</p>
      </sec>
      <sec id="sec-2-5">
        <title>2.5. The case of invisible job ads</title>
        <p>A main weakness of the orphan loss (Eq. 5) is that its
gradient does not involve any -th job ad whose market share is
0, referred to as invisible job ad, as</p>
        <p>∀ ∈ [], (, ) &lt; (, ,,)
better market share.</p>
        <p>For such invisible job ads , the loss gradient can only flow
through ℒ , hampering the evolution of  toward any</p>
        <p>Several options have been considered to take into
account the case of invisible job ads. We eventually define a
third JoLA mode, referred to as JoLA-Orphan-compound
(JoLA-oc), where the recommendation score is trained by
minimizing:</p>
        <p>
          ℒℎ() = ℒ () +  ℒ,() +  ℒ,() (6)
4An alternative left for further work is to use diferentiable sorting
and ranking [
          <xref ref-type="bibr" rid="ref23 ref24 ref25">23, 24, 25</xref>
          ]. We opted for the approximate estimation
for the sake of computational frugality, after preliminary experiments
showing a good accuracy of the approximation for  ≥ 10.
teraction matrix and defined as:
cross-entropy loss ℒ (), meant to approximate the
inwhere the third term with weight  &gt;
0 aims to decrease
the market share of non-orphan job ads, thereby increasing
the market share of orphan job ads (including the invisible
ones).
        </p>
        <p>ℒ,() =</p>
        <p>1
 · (1 −  ,())</p>
        <p>∑︁
∈[]/ ()&gt;
( ()− )
(7)</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Experimental Setting</title>
      <p>This section details the goals of experiments and the
methodology followed to experimentally validate JoLA.</p>
      <sec id="sec-3-1">
        <title>3.1. Goals of experiments</title>
        <p>Our main goal is to comparatively assess the respective
merits of the diverse JoLA modes in terms of the trade-of
among the diferent performance indicators. The
tradevs the user metrics (congestion) vs the recruiter metrics
(number of (, )-orphans).</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Baselines and Benchmarks</title>
        <p>
          The first baseline is the policy based on the optimization of
the only BCE loss (Eq. 2). The second baseline is the ReCon
JRS [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ], also aimed at alleviating the congestion through an
in-processing method (more in Section 5); as said, ReCon is
the approach most related to ours.
        </p>
        <p>
          For the sake of comparison and reproducibility, we thus
consider the same public datasets as those used to assess
ReCon, i.e. the small and large CareerBuilder datasets
described in Table 1, abbreviated as CB-S and CB-L. Both are
extracted from the whole anonymized CareerBuilder dataset,
released for the 2012 Kaggle competition.5 CB-S and CB-L
respectively retain interactions from the last 10 and 90 days.
The training/validation/test split of the interaction matrix,
the training interaction matrix noted , the validation
interaction matrix noted  and the batch sampling
process are set after [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ] for the sake of a fair comparison. 
is used to determine the early stopping (see section 3.6) of
the BCE phase.
        </p>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Training/test split and batch sampling</title>
        <p>Following ReCon’s experimental setting, each batch ℬ
includes i)  positive interactions (, ) uniformly sampled
in the positive interactions in ; ii) negative
interactions sampled as follows. For each positive interaction (, ),
two user indices ′, ” (respectively two item indices ′, ”)
are additionally uniformly sampled without replacement
in [] (resp. []) such that (, ′), (, ”), (′, ), (”, ) are
negative interactions according to .</p>
        <p>The BCE loss is computed after Eq. 2, and divided by 5
for the sake of normalization.
the number of (, )-orphans in ℬ.</p>
        <p>Congestion and orphan losses are computed from the
market shares estimated on the batch. Formally, all (unique)
job ads involved in ℬ are considered and the associated
market share is computed by approximating how many (unique)
users involved in ℬ are recommended this job ad. The value
of () involved in the losses (Eqs. 5 - 6) corresponds to
5https://www.kaggle.com/competitions/job-recommendation/data.</p>
      </sec>
      <sec id="sec-3-4">
        <title>3.4. Performance indicators</title>
        <p>The reported HR@k and Recall@k metrics are computed
on the test interaction matrix . The fraction of
orphan and invisible jobs are computed on the whole dataset
( ∪  ∪ ), as their estimation on a small
dataset (e.g.  only) is irrelevant (Fig. 1). For the sake of
readability, all tables report the proportion of non-orphans
(to be maximized) instead of the number of orphans denoted
8,10. All performance metrics thus follow the “higher is
better” principle.</p>
      </sec>
      <sec id="sec-3-5">
        <title>3.5. Hyper-parameter configurations</title>
        <p>
          Following ReCon again, the dimension  of the user
embedding  (resp. item embedding  ) varies in [256, 512]. Each
coordinate of  and  is initialized to  − 4 with  randomly
drawn after  (0, .01) in ReCon [
          <xref ref-type="bibr" rid="ref16">16</xref>
          ].
        </p>
        <p>In early experiments, the initialization of  and  in JoLA
was based on the singular value decomposition (SVD)
decomposition of , significantly speeding up the
optimization of the BCE loss term. In counterpart however, this
initialization resulted in a large number of invisible job ads
in the first optimization epochs, increasing from circa 0 with
a random initialization to circa 20% with SVD initialization,
all the more so with small batch sizes:</p>
        <p>
          The hyper-parameters of ReCon are taken from [
          <xref ref-type="bibr" rid="ref16">16</xref>
          ]
(parameters of the Sinkhorn algorithm:  = 10.0,  = 1× 10− 2
and _ = 100). The dimension  of embeddings
 and  ranges in [256, 512]; their initialization is random
(see above).
        </p>
        <p>
          The hyper-parameters of JoLA include: i) the type of
loss (BCE only; JoLA-c; JoLA-o and JoLA-oc); ii) the loss
weights  and  ; iii) the size of the batch, controlled after
the number  of positive interactions; iv) the initial
learning rate adapted using AdamW [
          <xref ref-type="bibr" rid="ref26">26</xref>
          ]; v) the dimension  of
the embeddings. In all experiments,  = 10 and the
threshold  on the market shares is set to 8 (= , Eq. 1). The
selected hyper-parameter configuration is determined by
optimizing loss BCE: the learning rate is 10− 2; the batch
size is  = 1024 for CB-S and  = 4096 for CB-L; the
embedding dimension  = 512. The value of hyper-parameter
 (respectively  ) varies in {10− ℓ, ..10+ℓ} for ℓ = 2.
        </p>
      </sec>
      <sec id="sec-3-6">
        <title>3.6. Computational resources</title>
        <p>The runtimes are measured on consumer grade GPU.
• CPU: 12th Gen Intel i3-12100 (8) @ 5.500GHz
• GPU: NVIDIA GeForce RTX 2070 SUPER [8 GiB</p>
        <p>VRAM]
• Memory: 32 GiB
All experiments consider 50 epochs, amounting to circa 10
minutes on CB-S and circa 4 hours and 20mn on CB-L.</p>
        <p>The overall computational cost of JoLA is reduced by
using a schedule. A first warm-start phase relies on the
optimization of the BCE loss (Eq. 2) during the first epochs.
The embeddings  and  trained at the end of this first
phase are further optimized by JoLA-c, JoLA-o and JoLA-oc
during the last epochs, respectively considering Eq. 3, 4 and
6.</p>
        <p>For CB-S, the first phase lasts for 25 epochs. For CB-L,
the length of the first phase is set by early-stopping, based
on the HR@10 score on  (30 epochs on average).</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Experimental Validation</title>
      <p>This section reports on the comparative experimental
validation of JoLA on CB-S and CB-L. The JoLA code is
publicly available at https://codeberg.org/solal/jola. In all tables
and figures, 8,10 corresponds to the number of non-(,
)orphans for  = 10,  = 8.</p>
      <sec id="sec-4-1">
        <title>4.1. CareerBuilder-Small</title>
        <p>Table 2 displays the comparative performances obtained on
CB-S for  = 512 and batch size  = 1, 024, selecting the
non-dominated configurations. ReCon improves on BCE
in terms of congestion (from .92 to .94) and (, )-orphans
(from .35 to .38), with same HR@10, at the expense of a
slight loss in Recall@10 (from .32 to .31).</p>
        <p>JoLA-c achieves a quasi optimal congestion (.99) and an
excellent performance in terms of non-(, )-orphans (.68)
at the expense of a significant loss in HR@10 (from .55 to
.45) and in Recall@10 (from .32 to .24). JoLA-o achieves a
more balanced trade-of than JoLA-c: for a slightly lesser
congestion (.98) and number of non-(, )-orphans (.64) it
reaches a better HR@10 and Recall@10 (.49 and .28). Finally,
JoLA-oc can be finely controlled using weight  to either
favor the congestion and the number of non-(, )-orphans
(.99 and .70) or the accuracy metrics (.49 and .27).</p>
        <p>All in all, Table 2 presents a set of non-dominated
configurations, enabling the designer to select their preferred
tradeofs among the diferent performance metrics. Schematically,
BCE is the best approach for Recall@10 and HR@10;
JoLAoc is the best one for congestion and non-(, )-orphans.
ReCon is non-dominated w.r.t. congestion and HR@10.</p>
        <p>It is noteworthy that the reduction of non-(, )-orphans
goes with a better congestion: indeed, if all or most market
shares are above  (all the more so as  = , Eq. 1) then
the market shares can only be balanced. In other words, the
metrics suited to job seekers and to recruiters do not seem
to be antagonistic.</p>
        <p>Another remark is that the congestion value appears to be
less finer-grained (varying from .92 to .99) than the number
of non-(, )-orphans (varying from .35 to .70). More
specifically, the number of orphans and the congestion value are
informative for diferent modes of the market share
distribution, after complementary experiments (not shown in the
paper): for a high number of non-(, )-orphans (≥
the congestion widely varies in [.4, .8]. Quite the contrary,
80%),
for high values of congestion (&gt; .9), the number of
non(, )-orphans widely varies. In other words, the number
of non-(, )-orphans appears to be more detailed in the
interesting region, where the market shares are not too
CareerBuilder-Small: Comparative performances of the baselines
BCE and ReCon, versus JoLA-congestion, JoLA-orphan and
JoLAimbalanced.
0.92
0.94
0.99
0.98
0.98
0.99</p>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. CareerBuilder-Large</title>
        <p>as well on CB-L in terms of congestion and number of
non(, )-orphans, as on CB-S. Both diferences suggest that</p>
        <sec id="sec-4-2-1">
          <title>CB-L is less diversified than CB-S.</title>
          <p>On CB-L, the best approach in terms of HR@10 and
Recall@10 still is BCE (respectively .60 and .41), at the expense
of a low congestion (.90) and number of non-(, )-orphans
(.31). ReCon improves on BCE in both terms of congestion
and non-(, )-orphans (respectively .97 and .49) with no
(from .41 to .40). JoLA-c significantly improves on ReCon in
terms of congestion (.98) and non-(, )-orphans (.64) with
to .38).
.51).</p>
          <p>JoLA-o very slightly improves on JoLA-c in terms of HR
and Recall, at the expense of a significant loss in terms of
congestion (.98 to .95) and non-(, )-orphans (from .64 to</p>
          <p>Finally, JoLA-oc dominates JoLA-o in all respects; it is
slightly dominated by JoLA-c in terms of congestion and
non-(, )-orphans and slightly better in terms of HR@10
8,10
0.31
and number of non-(, )-orphans (top-right), Recall@10
of non-(, )-orphans (bottom-right). As said, HR@10 and
Recall@10 are computed on the test interaction matrix; the
number of (, )-orphans and congestion are computed on
the whole interaction matrix.</p>
          <p>On CB-S, all four Pareto fronts present a similar
structure: mostly ReCon appears on the right side (high accuracy
pear in the center (trade-of between accuracy metrics and
congestion/non-(, )-orphans); and JoLA-c dominates in
the left (best congestion or non-(, )-orphans).</p>
          <p>On CB-L, the four Pareto fronts are more diverse. A
significant diference with CB-S is that</p>
        </sec>
        <sec id="sec-4-2-2">
          <title>JoLA-o is generally</title>
          <p>dominated. Except for this diference, we still have ReCon
in the right, together with BCE (high accuracy metrics),</p>
        </sec>
        <sec id="sec-4-2-3">
          <title>JoLA-oc in the center, and JoLA-c in the left.</title>
        </sec>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Position w.r.t. Related</title>
    </sec>
    <sec id="sec-6">
      <title>Work</title>
      <p>
        The goals of preventing congestion and ensuring a fair
distribution of the recommendations among items, users, or
stakeholders, addressing both ethical and practical concerns
have been extensively considered in the general literature
devoted to recommender systems (RS) [
        <xref ref-type="bibr" rid="ref13 ref14 ref27 ref28 ref29">27, 14, 28, 29, 13</xref>
        ].
      </p>
      <p>
        After [
        <xref ref-type="bibr" rid="ref30">30</xref>
        ], the main three methods to deal with popularity
bias and exposure fairness in RS include i) pre-processing
methods (e.g. based on data sampling or item exclusion
[
        <xref ref-type="bibr" rid="ref31">31</xref>
        ]); ii) in-processing methods (based on regularization,
constraints and/or weighting of the training loss) [
        <xref ref-type="bibr" rid="ref32 ref33 ref34">32, 33,
34</xref>
        ], and iii) post-processing methods, where the scoring
function is perturbed using re-scaling, re-ranking and model
aggregation [
        <xref ref-type="bibr" rid="ref35 ref36 ref37">35, 36, 37</xref>
        ].
      </p>
      <p>
        In the domain of Job Recommender systems, the research
has long been slowed down by the absence of public datasets,
preventing the reproducible assessment of the algorithms.
Indeed, the anonymization of HR-related datasets raises
many privacy concerns, all the more severe as such datasets
may involve vulnerable users. The RecSys challenge in 2017,
based on the Xing benchmark [
        <xref ref-type="bibr" rid="ref38">38</xref>
        ], has been instrumental in
the field [
        <xref ref-type="bibr" rid="ref39 ref40">39, 40</xref>
        ] (note that the Xing dataset does not involve
precise indications as to the locations of the job ads and the
job seekers).
      </p>
      <p>
        As said, the most related approach to ours is ReCon [
        <xref ref-type="bibr" rid="ref16 ref4">16, 4</xref>
        ]
(see [
        <xref ref-type="bibr" rid="ref41">41</xref>
        ] for a survey). ReCon is an in-processing method
using entropy-based regularization similar to [
        <xref ref-type="bibr" rid="ref42">42</xref>
        ] (see also
[
        <xref ref-type="bibr" rid="ref43">43</xref>
        ], where the regularization is based on the Gini index) or
borrowing optimal transport ideas [
        <xref ref-type="bibr" rid="ref44 ref45">44, 45</xref>
        ] for [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ]. More
remotely related is [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ] using Optimal Transport and [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ]
using envy-freeness and exposure, both in a post-processing
manner.
      </p>
      <p>The main originality of the proposed JoLA lies in the
three proposed losses. All these losses aim to shape the
distribution of the market shares, though in diferent ways.
Specifically, the congestion metrics is optimal when market
shares are equal, and it takes very similar values for
sufifciently flat distributions. Quite the contrary, the orphan
metrics mostly require that no market share be too small;
the over-popularity of some job ads is only penalized in the
orphan-compound loss (Eq. 6). The diverse approaches thus
pave the Pareto front defined from the users and
recruitersrelated metrics, enabling the designers to select the proper
loss depending on their context and priorities.</p>
      <p>A potential weakness of JoLA is that it involves several
hyper-parameters (type of loss, weight  and weight  in
Eq. 6). A key limitation of the main orphan loss (Eq. 4)
however is that the so-called invisible job ads are not taken into
account in the back-propagation. The compound orphan
loss aims to alleviate this limitation. Further work is
concerned with reconsidering the learning schedule, and using
gradient clipping as an alternative to the use of weights 
and  .</p>
    </sec>
    <sec id="sec-7">
      <title>6. Conclusion</title>
      <p>A main contribution of the presented JoLA approach is to
explore several losses, aimed at controlling the distribution
 of the market shares associated to the considered
job ads. The extensively studied congestion, that is the KL
distance of  and the uniform distribution, reaches its
optimum when all market shares are equal. Note that this
property is far from being satisfied in the whole interaction
matrix, where the distribution of the market shares presents
a majority of very unpopular job ads (with less than two
applications) and circa 30% very popular job ads. An
optimal recommendation policy in terms of congestion is thus
focused on reducing the popularity of the most popular jobs.</p>
      <p>In contrast, the orphan loss (Eq. 4) reaches its optimum
when every market share is greater than some minimum
. This property is very far from being satisfied in the
considered public datasets. Note that it is even less satisfied in
PES datasets where a very significant fraction of the job ads
are invisible (receiving no applications).</p>
      <p>Complementary results show that: i) for a same HR value,
the congestion and orphan metrics can significantly vary;
ii) for a same congestion, with decent HR value, the orphan
metrics can significantly vary. This observation is explained
as the orphan metrics defines a finer-grained assessment of
the market share distribution, than the congestion.
Specifically, if the orphan metrics reaches a good value, then the
congestion metrics reaches a good value too; but the
converse does not hold true.</p>
      <p>As said, the goal of decreasing the number of orphan
or invisible job ads aims to two benefits: decreasing the
competition in the short run; unlocking the sleeping job ad
market, in the long run.</p>
      <p>This approach opens several perspectives for further
research. A short term perspective is to prevent or decrease
the presence of invisible job seekers in the batch, through
enforcing that each item participates in at least one
positive interaction.. An on-going perspective is to confront an
orphan-avoidance policy to the context of PES, and assess
its robustness w.r.t. human and computational priorities,
noting that the orphan phenomenon is significantly more
severe in PES data then in the public CB-S and CB-L datasets,
that are engineered to enforce the presence of suficiently
many interactions in the whole matrix.</p>
      <sec id="sec-7-1">
        <title>Acknowledgements</title>
        <p>The research leading to these results has received funding
from the Special Research Fund (BOF) of Ghent
University (BOF20/IBF/117), from the Flemish Government
under the “Onderzoeksprogramma Artificiële Intelligentie (AI)
Vlaanderen” programme, and from the FWO (project no.
G073924N).</p>
      </sec>
    </sec>
    <sec id="sec-8">
      <title>Declaration on Generative AI</title>
      <p>The author(s) have not employed any Generative AI tools.
CareerBuilder-Small
Dataset Statistics:
Total unique users: 3876
Total unique items: 4337
Total interactions: 29944
CareerBuilder-Large
Dataset Statistics:
Total unique users: 42346
Total unique items: 40542
Total interactions: 469813
Train interactions: 450670
Validation interactions: 9453
Test interactions: 9690
Combined Test+Val interactions: 19143
Unique users in train: 42346
Unique items in train: 40542
Unique users in validation: 2701
Unique items in validation: 5227
Average interactions per user (total): 11.09
Train interactions: 450670
Average interactions per user (train): 10.64
Validation interactions: 9453
Average interactions per user (validation): 3.50
Test interactions: 9690
Average interactions per user (test): 3.63
Combined Test+Val interactions: 19143
Average interactions per user (test+val): 4.02
Unique users in train: 42346 (100.00%)
Unique items in train: 40542 (100.00%)
Unique users in validation: 2701 (6.38%)
Unique items in validation: 5227 (12.89%)
Unique users in test: 2672 (6.31%)
Unique items in test: 4847 (11.96%)
Overlapping users train+validation: 2701 (6.38%)
Overlapping items train+validation: 5227 (12.89%)
Overlapping users train+test: 2672 (6.31%)
Overlapping items train+test: 4847 (11.96%)
Overlapping users train+combined test+val: 4758</p>
    </sec>
  </body>
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