Beyond Match Maximization and Fairness: Retention-Optimized Two-Sided Matching
Authors: Ren Kishimoto
Rikiya Takehi
Koichi Tanaka
Yoji Tomita
Masahiro Nomura
Riku Togashi
Yuta Saito
Venue: ICLR 2026 Poster (2026)
Keywords: Two-Sided Matching
User Retention
Learning-to-Rank
Primary area: optimization

Abstract: On two-sided matching platforms such as online dating and recruiting, recommendation algorithms often aim to maximize the total number of matches. However, this objective creates an imbalance, where some users receive far too many matches while many others receive very few and eventually abandon the platform. Retaining users is crucial for many platforms, such as those that depend heavily on subscriptions. Some may use fairness objectives to solve the problem of match maximization. However, fairness in itself is not the ultimate objective for many platforms, as users do not suddenly reward the platform simply because exposure is equalized. In practice, where user retention is often the ultimate goal, casually relying on fairness will leave the optimization of retention up to luck.

In this work, instead of maximizing matches or axiomatically defining fairness, we formally define the new problem setting of maximizing user retention in two-sided matching platforms. To this end, we introduce a dynamic learning-to-rank (LTR) algorithm called Matching for Retention (MRet). Unlike conventional algorithms for two-sided matching, our approach models user retention by learning personalized retention curves from each user’s profile and interaction history. Based on these curves, MRet dynamically adapts recommendations by jointly considering the retention gains of both the user receiving recommendations and those who are being recommended, so that limited matching opportunities can be allocated where they most improve overall retention. Naturally but importantly, empirical evaluations on synthetic and real-world datasets from a major online dating platform show that MRet achieves higher user retention, since conventional methods optimize matches or fairness rather than retention.

Published as a conference paper at ICLR 2026
BEYOND MATCH MAXIMIZATION AND FAIRNESS: INTENTION-OPTIMIZE TWO-SIDED MATCHING
Ren Kishimoto"
Rikiya Takehi"
Institute of Science Tokyo
Waseda University
Tokyo. Japan
Tokyo. Japan r
kishimoto. r. www..aateeee.................... ac.
waseea...wwddd........ jp
Koichi Tanaka
Masahiro Nomura
Riku Togashi
Keio University
Institute of Science Tokyo
CyberAgent
Tokyo. Japan
Tokyo, Japan
Tokyo, Japan
kouichi 12070keio. ip
nomura@comp. ac.
rt rtogashi@acm org
Yoji Tomita
Yuta Saito
CyberAgent
Hanuku-kaso, Co., Ltd.
Tokyo, Japan
Tokyo, Japan
saito@hang juku- com
ABSTRACT
On two-sided matching platforms such as online dating and recruiting, recom- mendation algorithms often aim to maximize the total number of matches. How- ever, this objective creates an imbalance, where some users receive far too many matches while many others receive very few and eventually abandon the platform. Retaining users is crucial for many platforms, such as those that depend heavily subscriptions. Some may fairness objectives to solve the problem of match maximization. However, fairness in itself not the ultimate objective for many platforms, users do not suddenly reward the platform simply because exposure is equalized. In practice, where user retention is often the ultimate goal, casually relying fairness will leave the optimization of retention up to luck.
In this work, instead of maximizing matches or axiomatically defining fairness, we formally define the new problem setting of maximizing user retention in two-sided matching platforms. To this end, we introduce a dynamic learning-to-ran (LTR) algorithm called Matching for Retention (MRet). Unlike conventional algorithms for two-sided matching, our approach models user retention by learning person- alized retention curves from each user's profile and interaction history. Based on these curves, MRet dynamically adapts recommendations by jointly considering the retention gains of both the receiving recommendations and those who are being recommended, so that limited matching opportunities can be allocated where they most improve overall retention. Naturally but importantly, empirical evaluations on synthetic and real-world datasets from a major online dating plat- form show that MRet achieves higher user retention, since conventional methods optimize matches or fairness rather than retention.
INTRODUCTION
Predominantly, recommendations for two-sided matching platforms like online dating (Neve & Palo-
mares 2019 Pizzato et al. 2010b; Xia et al., (015a) and recruitment (Jiang al.] 2020 et al., Yang al. (2022) aim maximize the overall number of matches between the two sides of
2019
users
Mine et al. 2013 Pizzato et al. 2010a Palomares et al. 202 Pizzato et al, 2010b Qu et al.)
2018
However, this objective leads to significant matching imbalances, where users receive
Equual contribution.

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login continutiio rate (narmalizae)
females
males
login continuation rate (narmalizzo
number of usere ( sormallzzed
number of Usere Ancormann
login continustion rate
login continustion
number of users
number of users
number matches
number matches
Figure 1: The relationship between retention and the number of matches collected on a large-scale
online dating platform, showing females (left) and males (right). Details of the data in Appendix B
many matches, while many others rarely receive matches (Chen et al. 2023 Celdir et al. 2024) Consequently, users who get insufficient matches can be prompted to leave the platform PProk & Denissen 2020 dos Reis Alba 2020 Dechant al. 2019).
Figure T shows the probability of a user staying on the platform in the next month given the number of matches they had, collected on large-scale online dating platform (details of the data setup in Appendix B). We observe that the users with smaller numbers of matches have much higher chances of leaving the platform in the next month.
problematic for many two-sided platforms to have users leaving the platform, particularly since many of these platforms rely on models where user retention directly determines platform success. An illustrative example an online dating application that is mostly based on a subscription model, where user retention directly corresponds to profit. When the system focuses only on maximizing the number of matches, recommendations become concentrated on small group of already popular users. This leaves many others with very few opportunitics, even though those users are the most likely to leave they do not get matches. As result, the overall number of matches may increase, but the imbalance inevitably causes more users to churn (Chen et al.) 2023 Celdir et al., 2024).
To account for the problem of match maximization. one might consider fairness potential solu- tion (Tomita & Yokoyama| 2024; Chen et al.) [2033] | Celddi et al.) 2024 Morik et al. (220)). Fairness objectives, such as fairness of exposure (Singh & Joachims) 2018), 8), typically aim ensure that every user receives the amount of exposure in proportion to their potential utility. However, while fairness might, in rare cases, be the ultimate goal of platform, this is not true for the majority. Users do not suddenly change their behavior or reward the platform simply because they receive the amount of exposure specified by a fairness objective. In contrast, user retention is the ultimate goal for the majority of platforms, as it is directly tied to long-term sustainability and revenue generation in vari- ous business models (e.g., subscription- based services). In real-world practice, where user retention is the ultimate goal, casually choosing fairness formulations or methods leaves the optimization of retention up to chance. Specifically, fairness objectives are only effective if popular users require high exposure to stay the platform, and less popular users need less exposure stay. Such pattern is not promised, as different users would have different satisfaction levels, often regardless of their popularity.
To deal with the problem that existing methods do not account for user retention, we propose a new problem setting, where the objective is to maximize retention for users both sides of the matching platform. Instead of axiomatically defining fairness as in existing methods, we build data-driven algorithms based on formulations aligned with the real-world motivation, where user retention is the ultimate goal. Specifically, we introduce a novel dynamic Learning-to-Rant (LTR) algorithm, called Matching for Retention (MRet), which provides recommendations that lead the highest rate of user retention. MRet first learns personalized retention curve for each user based on profile and interaction history (like Figure I but for each user). Then, for each arriving user, MRet jointly considers two perspectives: the retention probability gains of the user receiving the recom- mendations, as well as the retention probability gains of the users who are being recommended. This means that the recommended users are chosen not only because they increase the likelihood of the receiver retaining, but also because their own retention can be impacted by the interaction. By explicitly modeling retention probability gains from both sides, algorithm strategically deter- mines the ideal recommendations that best maximize user retention across the entire platform. MRet adapts time and naturally directs scarce matches where they have the biggest retention gain
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at each time step. As expected yet crucial, empirical evaluations synthetic and real-world datasets from a major online dating platform demonstrate that our algorithm maximizes user retention, while traditional methods focus match counts or fairesss heuristics instead. The code is provided in the supplementary material.
2 PRELIMINARIES
In this section, we formally define the ranking problem in a two-sided matching setting, clearly highlighting the limitations of current matching algorithms.
Consider two distinct sets of users, denoted by and V representing the two sides of a matching platform (e.g., men and women arrives from one of the two sides: either X ~ p(r), where x E X, or y ~ p(y), where y E V. The arrival distributions p(x:) and p(y) are unknown. Note that and y also contain user context (user profile + interaction history) that we can fully use for recommendation.
online dating platform). At each time step т, single user
Upon arrival, the platform generates ranking/sequence of K recommendations from the pool of users in the opposite group. The recommendations may be shown in any format: either as a ranked list sequentially one by one. Specifically, when user X' arrives time т, we select an ordered list of candidates
(1) with Jr E y for all k. Conversely, if the arriving user is y y, then Fr.6 E X. We follow common setting used online matching platforms (Bapna et al.] 2023 Pizzato et al. 2010c Xia et al. 2015b; Tyson et al. 2016). where the arriving user sees two blocks: (i) all users who have already liked them, and (ii) the fresh top-K recommendations o,. After viewing the list, the visitor may like or skip each profile.
of 10,,1. Tr.K],
Since any one-sided like is always shown to the recipient at their next login, the match probability r(x,y) [0, specifically represents the likelihood that both users and y liked each other, result- ing in a match. Although the second user's 's response can arrive with a delay in practice, the like is guaranteed be shown, and the result is fully determined. Thus, following most online bandit and LTR models (Li et al. 2010: Joachims et al. 2017). we suppose that we observe the binary match indicators immediately after the recommendation for simplicity. In this work, we take r(z, y) as given (either available or estimated upstream), since our focus is on user retention rather than on estimating match probabilities.
Finally, we may let rank position & receive visibility weight ag with 1 = a1 2 02 ... 2 ag 2 0. Then the expected number of matches for the receiver time T, given a ranking d,, is
my (v)
Σ On (x,
2.1 MAXIMIZATION OF MATCHES
Typically, existing recommendation algorithms aim maximize the immediate expected number of matches. Given a user æ, a conventional matching maximization method generates the recommen- dation set by sorting in the order of match probability
mmax match = arg max
Σ as (xT arg nort sort r(x, 8).
(3)
Cy
MEY
However, optimizing solely for the highest match probabilities leads imbalanced matches among users. Some users consistently appear in the recommendations, thereby having many matches. Con- versely, other users rarely appear high enough in rankings, resulting in limited matches, frustration, and eventually abandonment from the platform (Tomita & Yokoyama 2024). We observe clear pattern in Figure [ that users are more likely to leave the platform with fewer matches. Especially, observe special pattern that the first few matches impact retention probabilities much more than increased match counts. Consequently, recommendations based purely on maximizing matches can lead to user abandonment, which is the ultimate objective of the platform.
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2.2 FAIRNESS IN RANKINGS
Fairness objectives are often used to ensure that even unpopular users receive exposure, which seem- ingly addresses this problem. The most common fairness objective the fairness of exposure in ranking (Morik et al. 2020; Singh & Joachims 2018).
Specifically, Morik et al. (2020) has introduced a dynamic LTR algorithm that can effectively ensure that each user receives exposure in proportion to their merit. If the arriving user is r E X, we aim achieve fair exposure for any candidate user y E y.
Let the exposure of candidate y at time step T be
K
Exp, (v) = Σ on 1( = y)-
(4)
Then, for any two candidates yo. V. the disparity
D+ U5) = + E Exp,(y)
1
E Exp,(1)) EpG (26))r(2,10 Uj)]
(5)
Bp(x) (r vs)
measures how far amortized exposure over т time steps was fulfilled. When the disparity is zero, it means that all users exposed fairly in relative to their expected utility Ep( v)J, which denotes the expected match probability of user y over the population of users x.
Now, convert the current faireess disparity into adjustment term, for every candidate y E V, we set
err, (g) (r 1) max D (v/, y). y'Ey
(6)
This term is zero for users who already have the highest exposure- merit ratio, and grows linearly in for under-exposed users, ensuring stronger corrections when unfairness persists.
With a trade-off parameter >> 0, at time step т, FairCo builds the rankings by solving
Fairroo arg sort [r(z,,)) v) Aerr, (v)],
yey
where the first term prioritizes estimated relevance, and the second lifts candidates from underserved groups.
However, while such fairness objectives can prevent extreme imbalances, they do directly align with the true objectives of most platforms. Users do not necessarily remain active or reward the system simply because exposure meets the fair target. In practice, user retention is often the more fundamental goal, as it determines both long-term sustainability and revenue. Relying only on fairness, therefore. makes improvements in retention a matter of luck. Specifically, fairness helps only when the required exposure happens to match the retention needs of both popular and less popular users. Since retention behavior varies widely across individuals, such alignment cannot be assumed. As result, fairness serves as, at best, heuristic proxy for retention rather than reliable optimization target.
OPTIMIZING USER RETENTION
Despite many two-sided platforms having their revenue dependent on user retention, existing meth- ods do not account for user abandonment. To solve the issue, we define new problem setting of explicitly optimizing user retention. User retention is often the ultimate platform objective, many two-sided matching platforms are reliant subscriptions. Thus, rather than maximizing matches or targeting match maximization or some heuristic fairness objective, we align the formu- lation with the real-world motivation, where user retention is the ultimate objective.
To solve this new problem, we come up with a novel dynamic LTR framework that updates the recommendations dynamically given the observed rewards. The framework not only considers the retention users receiving the recommendations, but also considers the retention of users being recommended.
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We first consider a retention function f(z, m) that represents the likelihood that stays on the platform (i.e., retention probability) given m matches. We can similarly write f m) to represent the reward function of user y E V. The reward function f is estimated by simply performing reward regression, using the user context. Now, to derive the optimal ranking, denote the number of matches user received until time step
E X
mi: (z) - Σ mz(a).
(8)
At the end of step т, user x stays with probability (1, (1:((x) + mz(x)) and never return.
We aim recommend set of users that would maximize the retention probability gain for both the receiving user x E X' and the recommended users a E )ik Specifically, given some receiving user X, we propose that the optimal ranking time step is
o arg max
f(r, m1: (2) + Σk our(2,0r,x)) Ma, (10,mirr(0)) (x))
Gain For receiver
Mar,ks (ax(( our (ar()))))) Mares Mares
(ix(
Gain for recommended users
Eq. (9) explicitly chooses ranking where both the receiver and the recommended users increase their retention probabilities the most.
Figure demonstrates a toy example of how we select the top-1 ranking for Receiver E. Here, Candidate A has the most gain on the reward function f from the candidate's point of view, and Receiver will gain the most by selecting Candi- date B However, since we seek to maximize the total gain in the reward function, the best op- tion is Candidate C with total gain of 60%, instead of Candidates of 50%.
Candidate Users
Candidate's Gain +400%
+100%
+300%
Receiver's Gain +10%
+40%
+30%
largest total gain
or with the gains
Toy example of how top-1 rank- ing would be selected for Receiver & In this case, the optimal recommendation is Candidate because it raises the total retention proba- bility the most.
Figure 2:
However, directly solving the optimization prob- lem Eq. (9 is ha-hard. Thus, its direct optimiza- tion is not practical.
3.1 THE MRET RANKER
To overcome this NP-hard optimization, we introduce our Matching for Retention (MRet) ranker. MRet quickly approximates Eq. ( with theoretical grounding.
To demonstrate MRet, we introduce a realistic assumption: the reward function is concave.
Assumption 1 (Concavity of the Reward Function). For every user & E X, the reward function fzz -) is concave the number of matches m 2 0. Formally, for all mı, m2 2 and every 0 1].
fm 0m1 (1-0))2) 2 fxx mn) + (1 0) (xx,
(10)
We assume similarly for y E y and f(y.
Intuitively, this assumption implies that as users receive more matches, their retention gain is decel- erated. This may lead to peak retention probability at an optimal number of matches, beyond which additional matches no longer help the retention probability. For example, user who gets their first match gains more incremental retention probability than when they get the 10th match. This is
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very realistic assumption, actual online dating application. We also provide experimental results where this assumption does not hold.
also observe this pattern in Figure I which is collected
Under Assumption ! the receiver-side term in Eq. 9 admits a lensen-type lower bound. Writing A = Σ j=1 aj. concavity of f(x,) :) gives the following lemma.
Lemma (Jensen lower bound). Under the Assumption 1 for ranking T,,
1, (,)):(() + Σ aurls, 0...))
0Kk
A I [x, mir Ar(a,
(11)
On the candidate side, the contribution a user y depends on the position-specific visibility weight ak- Concavity again provides way to bound this dependence using a linear factor based on the maximum weight Omax-
Lemma 2 (Concavity-baad based linear bound). Under Assumption 1 for any candidate E y and any 0 S ag S amax
fl. m1-(() + cxr(1, u)) fly, m1:((1)
(flymmi. (y) + Qmax7 v)) fyy mi)(
Qmax
Using Lemma | and 2 we reformu- late the original optimization problem Eq. ( into tractable lower bound maximization problem. In particular, Lemma [ provides decomposition of the receiver side, and by further applying concavity-based linear lower bound to each candidate user, the objective can be expressed as
We prove the Lemmas [ and 2 in Appendix and C.2
max
ag Score(ar,k):
(12)
where, with Qmax maxę agg, the per-item score is defined
1
Score(y)
fxx m1: (I) + Ar(x,
1
[f mi. (v) + @max7(x, v))
fly mi:r())))
(13)
O'yax
By the rearrangement inequality, assigning higher-score candidates to positions with larger visibility weights 04 maximizes this lower bound. Therefore, the MRet ranking is obtained as
MMRe arg sort Score(y).
(14)
DEy
This allows to solve the problem using argsort, significantly redueing computational complexity. Specifically, instead of an NP-hard problem, is transformed into one where we compute an individ- ual score for each potential candidate user from the opposing set. Assuming constant-time function evaluations and lookups, the operation takes O(N log N) time. This is a substantial improvement over the complexity of Eq. (9). We now provide its empirical performance through extensive exper- iments.
4 EXPERIMENTS
In this section, report the experimental results with synthetic data and real-world data from a Japanese online dating platform. Our experiment code available at https: //q1
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4.1 SYNTHETIC EXPERIMENTS
To generate synthetic data, we consider two user groups, X' and y. We sample 10-dimensional context vectors I E X. y E y from the standard normal distribution. We synthesize the match probability between user x and user y as
r(a, y) = (1 (1-k) Toase y) + K TTpop (2, y),
where Pbase 1/ =
Z-9 | represents the base reward using cosine similarity, which captures T
the compatibility between user x and user y. The second term introduces a popularity skew, where T (2) pop= popy and pops: popy are sampled from uniform distribution with range [0, 1]. pop, and popy represent the popularity levels of user x and user y, respectively. The parameter [0, 1] controls the strength of the popularity skew, and larger value of x leads to a stronger bias. We assume that r(z, y) is known in advance when selecting a ranking. Next, the user retention label {0, 1} is sampled from a Bernoulli distribution with the user retention probability determined by f(r m1:7 (x)), where mi. (I) denotes the cumulative number of matches until time step T for user æ. We define the user retention probability f as
f(z, (1r,)))))))) - {
0r (mi:r (z) by)² 0.95 1 0.05 exp (2(b, m.)())))
0 S (1) S by) (mir (x) > bz)
(15)
where ag Ma Ma aad by My are scalar values determined by the user feature vector z. We refer to by as the satisfactory match count, since it represents the number of matches at which the user retention probability substantially levels off. The probability increases quadratically with the cumulative number of matches mı (2) until reaching bz, after which the growth becomes gradual.
We simulate the dynamics of user retention over time. Let Khuum denote the set of users who have left the platform by time т, and retention denote the set of users who remain on the platform. At each time step, we randomly select user group (X' or ))) according a proportion parameter p E [0, 1]. From the selected group. we then sample a user uniformly at random from those who remain on the platform (c.g., if X is selected, we sample user x E X According the algorithm recommends a ranked list of users from the opposite group (c.g., y E ) )etemtion) and the cumulative number of matches mi:r is updated based on the ranking and r(x:, y). After the recommendation phase, we perform a retention phase in which we independently select every user (including those not involved in the ranking process) with probability of 0.2% to undergo churn evaluation. For each selected user, we sample a user retention label E {0, 1} from Bernoulli distribution parameterized by [(- (-). If u O, the user is removed from the platform and X retention and D Deeeeniion updated accordingly. We repeat this process from time step 0 to T.
each method,
T
Compared methods. We compare MRet with Max Match, Uniform, and FairCo (Morik et al.
2020). FairCo's fairness weight À is set to 100, but we ablate and confirm in Appendix D that different hyperparameters do not change the conclusion. Uniform selects random rankings without considering matches. MRet trains a regression model f using XGBoost Chen & Guestrin (2016) on a dataset {x, m, / We synthesize this dataset by generating n samples, each consisting of a user feature vector x, a match count m drawn from an exponential distribution with mean 2.0, and a retention label u determined according to the retention function f. For reference, we also report the result of MRet (best), which has access to the ground-truth function f and thus serves as an oracle upper bound of MRet. We clarify here that TTomita& & Yokoyamal (2024) cannot be compared as baseline, because they calculate a doubly-stochase matrix which takes exponential time when done in dynamic LTR setting.
Results. We use default parameters of | 1000, | 1000, K 5, 5000, T 2000, x = 0.5, p 0.5 and ou 1/k. Each experiment is repeated 10 times with different random seeds, and we report the average results. We show cumulative number of matches per user Enex mx)r()) Eyey mir(y)) and user retention rate
| |
x++
+++
Note that a is scaled take negative values so that the user retention function f hecomes concave.
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How does MRet perform as the time step increases? Figure how the cumulative number of matches per user and user retention rate change as the time step T increases. As T increases, the cumulative number of matches per user grows approximately proportionally across all methods. Max Match achieves the highest number of matches by a significant margin, whereas Uniform results in the lowest. Despite the substantial gap in total matches, Uniform and MaxMatch achieve almost the same user retention rate. This indicates that simply maximizing the number of matches does not necessarily help reduce user drop-off. MRet achieves a higher user retention rate than all baselines, including FairCo, Max Match, and Uniform, with only about 70% of the matches obtained by Max Match. While MRet does not reach the performance of MRet (best), it maintains a high level of user retention by effectively allocating matches.
Natch
FairCo
Uniform
MRat
Miat (best)
300
1290 trocstog
1500
2000
1255
3550
2002
02
2.4 US5 popuenity
0.5
0.4
Bmicstop
populanity
Figure 3: Comparison of cumulative number of matches and user retention rate across different time steps (r).
Figure 4: Comparison of cumulative number of matches and user retention rate (normalized by Uniform) under varying levels of user popular- ity (k).
How does MRet perform when user popularity varies? Next, we evaluate how MRet performs under varying levels of user popularity k, as shown in Figure We adjust the parameter to control the degree of popularity imbalance across users. When popularity is highly skewed, it becomes difficult for any method to allocate matches to less popular users. As a result, the gap user retention rate between each method and Uniform tends to narrow. Max Match tends to achieve higher match counts as popularity skew increases. However, user retention decreases significantly because popular users receive an even greater share of the matches. FairCo, which emphasizes fairness, often ends up allocating more matches to already popular users under skewed settings. This leads to increased disparity and ultimately results in performance that is comparable to that of Uniform. MRet maintains a high user retention rate across varying levels of popularity and is particularly effective in preventing retention loss under severe popularity imbalance.
Why does Fairco underperform in user re- tention? Here, we clarify the reason why FairCo performs worse in terms of user re- tention, although the cumulative number of matches it achieves is not substantially differ- ent from that achieved by MRet (best). Fig- ure Pa] shows the histogram of actual match counts among users who remain on the plat- form at time T. While FairCo and MRet (best) differ slightly in the total number of matches, their distributional shapes are similar. Never- theless, Figure 55 reveals a critical difference between FairCo and MRet (best). This figure shows a histogram of the differences between each user's actual match counts and their satis- factory match counts (m1:r b). Since b repre- sents the threshold at which the retention func- tion levels off, the quantity m7.7 b directly indicates whether a user has obtained fewer or more matches than this satisfactory level. FairCo allocates matches without considering user tention, resulting in a distribution of match counts that is spread out like a normal distribution, regardless of each user's satisfactory match counts. In contrast, MRet yields mostly non-negative
FairCo
MRet (best]
250
200
150
100
20
0
-2.5
0.0
25
5.0
75
number matches
number matches
(a) Histogram of actual match counts mI.7.
(b) Histogram of devia- tions between actual and satisfactory match counts mI.r b.
Figure 5: Comparison of match allocation strate- gies between FairCo and MRet for remaining users at time step T.
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differences, indicating that it successfully identifies and allocates matches according to each user's necessary amount. These results suggest that fair methods are not sufficient to prevent user churn.
Appendix D further reports and discusses (i) the performance with varying numbers of users, (ii) the performance on different FairCo hyperparams, (iii) the performance under varying noise levels in the match probabilities, (iv) the performance when popularity drifts over time, (v) the performance when FairCo uses the equal-exposure fairness criterion, and (vi) comparison of MRet with the optimal NP- hard recommendations.
4.2 REAL-WORLE EXPERIMENTS
To assess the real-world applicability of MRet, we report the results of real-world experiments. We use interaction data from a large-scale Japanese online dating platform with millions of registered users. On this platform, male users receive recommendation lists of female users and can either send "like" or skip each recommendation. When male sends a "like," the female a notification and either matches with him or declines the interaction. Once they form a match, the users can initiate conversation. Female users follow similar mechanism in the reverse direction.
receives
To construct the dataset, we first select 1,000 male users and 1,000 female users with relatively many interactions. and create a 1000 x 1000 matching matrix. Each element of this matrix represents the matching probability, denoted r r(z, y). which takes the value I if user æ and user y have matched and 0 otherwise. For user pairs with unobserved interactions, we apply the Alternating Least Squares (ALS) Hu et al. (2008) algorithm to impute missing values. We also define user retention as whether the user logs in again in the following month. Specifically, among users who logged in during February 2025, we label those who also log in March 2025 retained, and those who do not as churned. We aggregate the cumulative match counts for the user retention probability function from matches obtained in February 2025. Since we cannot obtain user retention labels for arbitrary numbers of matches for the users included in the matching matrix, we construct the user retention probability function using separate dataset of 60,000 records containing user features, cumulative match counts, and corresponding user retention labels.
To create the user retention probability f, we first apply k-means clustering partition male and female users separately into five clusters based on their user features. For each cluster, we calculate the average user retention label each level of cumulative match count. We assume that users within the same cluster share similar retention behavior, and define the function I by assigning the corresponding average retention label to each combination of cluster and match count. This enables us to assign the retention probability for any user based on their cluster and the cumulative number of matches. Using these definitions derived from real data, the simulation follows the same procedure as the synthetic data experiments. The detailed experimental settings are provided in Appendix F
Results We evaluate MRet against Max Match, FairCo, and Uniform varying time steps T on the real-world data in Figure [ In con- trast to the synthetic experiments, most ele- ments in the matching matrix are zero in the
Mac Match
FairCo
Unilorm
Hilet
Nhu (bws))
real-world data setting, indicating that matches rarely occur. Under such sparse conditions, fairness-oriented methods such as FairCo and Uniform fail to perform effective matching,
of 1 3.
100
3000
500 1000
1500
resulting in significantly lower user retention. Max Match turns out to be relatively effective, achieving higher retention than the fairness- based baselines. Notably, MRet achieves the highest user retention with extremely sparse match data. Moreover, although MRet is origi- nally designed under the assumption I that the user retention function f is concave in the number of matches, it still performs well even when applied to non-concave functions in the real-world data ex- periments. This demonstrates that MRet is not only effective but also robust and broadly applicable in practical scenarios.
Figure 6: Comparison of cumulative number of matches and user retention rate across different time steps (7) on real-world data.

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Appendix E further reports and discusses the performance (i) with different training data sizes, (ii) under different exposure probabilities, (iii) under different group recommendation ratios and (iv) under large-scale user setting.
RELATED WORK
Two-sided matching platforms, such as online dating Neve & Palomares 2019 Pizzato et al. 20106 Xia et al. 2015a) and recruitment (Jiang al.) 2020 Le et al. 2019 Yang et al. [022]] differ from conventional recommender systems in that they recommend users from one side of the platform to those on the other, rather than recommending items users. This reciprocal nature has motivated the development of Reciprocal Recommender Systems (RRS). which typically focus on maximizing the total number of matches (Mine et al. 2013; Pizzato et al., 2010a| Palomares
et al. 2021] Pozzato Pizzato et al., 2010b Qu et al. [018] Su et al. [202]] Hayashi et al. (025). However,
this objective often results in severe imbalances, where popular users accumulate large number of
matches, whereas many others receive very few (Chen et al., 2023] /023]/Celdir et al.) 2024). Such dis-
parities can drive under-served users to leave the platform (Pronk & Denissen, 2020 dos Reis Alba
2020 Dechant et al. 2019), ultimately threatening platform sustainability.
To address these imbalances, fairness-oriented approaches have been widely studied (Singh & Joachims 2018 Tomita & Yokoyama| 2024 Tomita et al. [023 Celdir et al. 2024 Morik al.)
2020 Devic et al., [2023] Saito & Joachims [2022). Several works explicitly integrate fairness into two-sided matching (Tomita & Yokoyama 2024 Do al. 2021 Xia al. 2019). In ad- dition, fairness-aware dynamic Learning-to-Rann
(LTR) algorithms have been developed, where past feedback influences future rankings to ensure that
receive exposure proportional their merit (Yang & Ai 2021 Morik et al., 22200] Wang et al. 2024: Biswas et al., (202I). Although these approaches mitigate disparities, fairness serves only as a heuristic principle rather than direct objective, and it does not necessarily align with maximizing user satisfaction or retention.
Beyond short-term optimization, recommender systems research has increasingly emphasized long- term user engagement. Several studies have proposed models that optimize return visits or sub- 7ou
scription renewals (Wu et al. 2017, Zou al. 2019: McDonald al., 2023) Hohnhold et al. 2015] Takehi et al.) 2025)] Saito et al. (2024) highlighted the necessity of incorporating long-term satisfac- tion into search and recommendation models. These works underscore the importance long-term
user engagement, which constitutes primary objective for platforms.
We propose a new problem setting, where the objective is to maximize user retention on both sides of the platform. Most prior approaches in two-sided matching optimize probabilistic recommen- dation lists represented as doubly stochastic matrices (Su et al. 2022; Tomita & Yokoyama, 2024] Tomita al. 2023). This formulation becomes computationally prohibitive the number of users grows. In contrast, we introduce a different problem setting that extends dynamic LTR (Morik et al.) 2020) to two-sided matching. This framework more realistically captures sequential user arrivals, significantly reduces computational complexity, and enables direct optimization of user retention.
6 CONCLUSIONS
This paper introduces new problem of optimizing user retention in a two-sided matching platform. While existing studies on two-sided platforms typically aim to maximize the number of success- ful matches between the two user sides, this makes some users receive more matches than others, prompting unpopular users to leave the platform. A high user abandonment rate is often unaccept- able for many two-sided matching platforms, as long-term sustainability and revenue depend on retaining users. Fairness objectives have been explored as a way to mitigate imbalance, but they are not the ultimate goal for most platforms and do not reliably ensure retention. Therefore, instead of axiomatically defining fairness, we formulate user retention the main objective, directly reflecting the real-world motivation. We provide a theoretically grounded dynamic learning-to to-kkkk algorithm synthetic data and real-world data collected on ma-
called MRet, with empirical evaluations jor online-dating platform. As naturally expected but important, our results demonstrate that MRet methods.
retains significantly more users than match maxim maximization and
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A LIMITATIONS & FUTURE WORK
While our work introduces a novel problem setting that directly maximizes user retention in two- sided matching, several limitations remain. Our model assumes that the matching matrix, which encodes the preferences of both sides, is given in advance. In practice, such preferences need to be estimated either offline or online, and an important extension our framework is to incorporate this estimation process directly into the model. We also learn user retention functions from offline data, whereas in real-world platforms, would be valuable to adaptively update them online, potentially leading to models that balance exploration and exploitation. Moreover, current formulation treats both sides of the platform as cqually important, while in practice the platform' 's business model may prioritize one side the other. For instance, in online dating, male users are often the paying side and retention that group may be more critical, whereas in job matching, where employer demand often exceeds job seeker supply, it may be desirable place greater weight on the retention of job seekers.
B DETAILED DESCRIPTION OF FIGURE
We provide a detailed description of the data aggregation procedure in Figure 1 The figure shows the relationship between the number of matches obtained by users and their login continuation rate based data collected from large-scale online dating platform in Japan. We focus users who logged in during February 2025, where login continuation is defined as whether the user logged in again March 2025, For each user, we calculate the total number of matches obtained in February 2025. Male and female users are binned separately according to their total number of matches, and for each bin, we report both the average login continuation rate and the number of users it contains. All values are normalized by the bin with the smallest number of matches.
C
PROOF
Here, we provide the derivations and proofs that omitted in the main text.
C.1 PROOF OF LEMMAT
x, 1. (2)
aurlz, 0r,4)
K
K
K v == Σ 0r > 0
f
Ok
mi:r (x) + Σ
(ur(I,07,5)
A
1=1
k=1
1=1
(mirr (x) + Ar( onik)
A
k=
Ok
0
(z, (1)(x) + Ar(x,
Jensen's inequality under Assumption
1
1
A
A
C.2 PROOF OF 2
My mi:(())) (v) + oxr(y,x)) - My. ml=(v))
(m1:r (b) + aman)) fly (y.mi:110) (v)) amaz max az
m1:
amax
Omax
1 O'ma
f(y, (0. (v)) +
O:k
-fy,, mi. (v) + (mmax) (1.mm.)))) Assumption!
Omax
+ Omaxr(y, xx) Hy m1. (v))
amax
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C.3 PROOF THAT MRET MAXIMIZES A LOWER BOUND OF THE OPTIMIZATION PROBLEM
We show that the original optimization problem Eq. (9) can be reformulated as a tractable lower bound maximization problem Eq. (4).
[x, 2, mar (x) + Ex= our(e (ur(e, ona)) - Mx, (1)
(or (ar((rn)) aur (or(o)))))) (or
K
fa, mir (2) + Ar(z, - (1)m))(()) ak
A
K
M (or() our aur(or))))) (ora
Lemma
Ok
far Ar(z,rr)))))) (1x))1-(x))
K
ak (HOTTA mi: + amaxx (max)((r, f(o7,K. mir(ora)))
Lemma
Quax
K
or Score(ar,,) (1))
where
Score(ar,))) = A
f(z m1:(x)) + Ar(z,
f( (1:((Tr.)) + amaxF((r x)) f(r))) mi=(orr,)))
amax
Since on 02 ox 0, follows that Eq. 14 ensures that MRet maximizes lower bound of the original optimization problem.
D SYNTHETIC EXPERIMENTS
Additional Results. We report and discuss additional synthetic experiment results.
Natch
ParCo
Uniform
Milet
Hileet (best)
2.35
3.0
230
300
2200
2000
600
2.30
1.0
23.00
102.00
001
0.10
2.00
12.00 100.00
LSD'S
Figure 7: of matches and user retention rate (normalized by Uniform) under varying the number of users (|x' + [)]).
Comparison of cumulative number
Figure 8: Comparison of cumulative number of matches and user retention rate (normalized by Uniform) under varying the hyperparameter of FairCo (X).
How does the proposed method perform when varying the number of users? Figure 7 shows the results when increasing the number of users + with each value normalized by the result of Uniform. As the number users increases, the number of possible recommendation candidates also increases, and thus all methods show improvements in both the cumulative number of matches
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and user retention rate compared to Uniform. Max Match slightly outperforms Uniform only when the number of users is large. In contrast, MRet consistently exhibits superior performance across all user sizes, with significant margin.
How does the hyperparameter of FairCo affect its performance? Figure shows the experi- mental results when varying the hyperparameter of FairCo À in Equation 7 A smaller value of places more emphasis maximizing the number of matches, while larger value emphasizes fair- ness. As expected, increasing À results decrease in the number of matches, which aligns with the theoretical perspective. Regarding rate at À = 0.1, but still performs worse than MRet. This shows that even with careful tuning, fair metries cannot outperform MRet. In contrast, MRet requires no parameter tuning, making it easier to apply in real-world scenarios.
retention rate, FairCo achieves the best user retention
Natch
(best)
3,10
68
10
027
1,05
044
1,00
80
362
2000
Smesiop
Binsstop
Figure 9: Comparison of cumulative number of matches and user retention rate (normalized by Uniform) under varying noise levels in the match probabilities (8).
Figure 10: Comparison of cumulative number of
matches and user retention rate (normalized by Uniform) when popularity drifts over time.
How does MRet perform under varying noise levels the match probabilities? To empirically assess the robustness of MRet to match probabilities, conducted experiment in which noise was injected into the match probabilities, as shown in Figure [5 Specifically, we perturb the true probabilities according to
7(x,y) r Ex,y
Eg.y u[-8, 6].
where 8 controls the noise level. The results show that as the noise level increases and the accuracy of the match probabilities deteriorates, the number of matches decreases for MaxMatch, MRet, and MRet (best). Moreover, both MRet and MRet (best) exhibit lower user retention rates the noise increases. However, across all noise levels, MRet consistently outperforms all baseline methods, demonstrating that it remains robust even when the match probabilities are substantially perturbed.
How does MRet perform when popularity drifts over time? We conducted an experiment to test how MRet adapts when popularity drifts over time, shown in Figure 10 In this experiment, we introduce time-dependent popularity skew, defining the match probability at time step f.
re (r 3) = (1 x) These (2, 3) + x pop:(x) pop)(y).
We assign each user æ E X and y E y one of three popularity trajectories: constant, increasing, decreasing. For each user we sample initial popularity e; Uniform(0, 1) and set fixed slope Letting т, E [] denote the normalized time step index, we define the time-varying popularity
Ci: (1))(1) = 0; + 0.5mz increasing,
constant,
0.5m decreasing.
We then clip the resulting pop, (i) to the range [0. 1] to ensure remains within a valid bound. Figure 10 shows that MRet outperforms all baselines in terms of user retention rate, demonstrating its effective adaptation to popularity drifts. This confirms that MRet successfully adapts to popularity drifts, expected from its dynamic design.
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Nax Natch
FainCo
FairCo (equal exposure)
Uniferm
Mict
Nitee (best)
30
US0: 8t0- Mcth 627
Brncstop
Emestop
Figure 11: Comparison of cumulative number of matches and user retention rate when FairCo uses the equal-exposure fairness criterion.
How does FairCo perform under the equal-exposure fairness criterion? Figure IT shows the results from an experiment where we modify FairCo's fairness definition to require equal exposure across all users, using the same experimental setting as Figure g We implement this variant by removing the "merit" component from FairCo's original objective. Now, the disparity function for FairCo (equal exposure) given by
Dj (yt, 34)
(x1)
Expx(uy)
FairCo (equal exposure) achieves slightly better performance than the original FairCo, but it follows the same overall trend and still performs worse than MRet.
Mileet (best)
Optime
2.18
3:45
2.40
2.
2.65
Bmeettp
timestep
Comparison of cumulative number of matches and user retention rate between FairCo and MRet across different time steps (7).
Figure 12:
How accurate is MRet as an approximation to the Optimal method? Figure 8 compares the performance of MRet with that of the Optimal method, which directly maximizes the ranking objec- tive defined in Eq. | Since Optimal requires exhaustive search over all possible rankings to select the best one, cannot be applied to large-scale settings due to computational constraints. We there- fore conduct experiments in small-scale setting with | 20, | 20, K = 3, and T = 50. and compare the performance of the two methods as the time step progresses. As shown in the figure, the cumulative number of matches and the user retention rate almost identical. This indicates that although MRet maximizes a lower bound of the objective function rather than the objective itself, achieves sufficiently high approximation accuracy while drastically reducing computation by only requiring the sorting of item scores.
E WOAL-WORDD EXPERIMENTS
Detailed Setup. We describe the training procedure of and the data employed in this process. We compute the values of the true user retention probability function f using the cumulative match counts m from the real data and the user clusters e obtained by k-means. We then sample retention label u from Bernoulli distribution parameterized by f. Finally, we train the predictive model with XGBoost using the resulting triples (c. m, u). In practice, implementation with 200 trees, a maximum depth of 6, and a learning rate of 0.05.
the XGBClassifier
In the real-worlh world experiments, n = 5000, T 3000, 0.5, and aş = 1/k. Each experiment is repeated 10 times with different random seeds, and report the average results.
set the default parameters to | 1000, |/ 1000, K 5,
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Additional Results. We report and discuss additional real-world experiment results.
Natch
(best)
3.68
matthes
Vdee retention olte
3.03
2.50
3.55
3.3
training data 576
triiing deta 577
extmrnation function
esamination function
Figure 13: Comparison of cumulative number of matches and user retention rate under varying training data sizes (n) on real-world data.
Figure 14: Comparison of cumulative number of matches and user retention rate under varying examination probability functions (ag) real- world data.
How does the performance of MRet change as training data size increases? Figure 13 shows the results when varying the number of training data sizes 7. used to train the function f that predicts user retention probability. the amount of training data increases, the performance of MRet grad- ually improves, and when n 16000, it achieves performance level comparable to MRet (best), which uses the true function f. Even in the case where training data is limited (n = 2000), MRet significantly outperforms FairCo and Uniform, and performs at least par with Max Match. These results indicate that MRet effective even with relatively small amounts of training data.
How does MRet perform under variations in examination probability? Next, Figure 14 shows the results under varying examination probability functions. We consider four types of examination functions: "exp' corresponds a' 1/ exp(k). 'inv' to ar 1/k: 'log' ag 1/ 1oga (2 + k), and 'uniform" to 0% 1. The figure is arranged so that values on the right correspond to more uniform examination probabilities across positions, while values on the left indicate stronger position bias, where rankeer positions receive substantially more attention. MRet consistently outperforms existing baseline methods across all examination probability patterns. This confirms that MRet exhibits high robustness to variations in the examination probability.
Match
FairCo
MRet
MRat
8.00
3.
M0tenttonn 13
8.00
6.53
group recommended 1800
group recommended ratlo
Brocttop
Briestop
Figure 15: Comparison of cumulative number of matches and user retention rate under varying the ratio of male and female users receiving recom- mendations (p) real-world data.
Figure 16: Comparison of cumulative number of
matches and user retention rate under large-scale user settings on real-world data.
How does MRet perform under variations in group recommendation ratio? Figure 15 shows the experimental results when varying the ratio p. which controls whether male or female users receive recommendations on the platform. When p 0, the system recommends only male users to female users, whereas when p = 1.0, it recommends only female users to male users. The results suggest that MRet performs well even under extreme settings where only one side (either male or female) receives recommendations. While this experiment is based on online dating data, it also implies that MRet is applicable to more general matching scenarios, such as job matching, where one side is always the recipient of recommendations (p 0 or = 1.0). This demonstrates that MRet is broadly applicable wide range of matching problems.
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How does MRet perform under large-scale user settings real-world data? To examine how MRet performs in large-scale user settings, we conduct an experiment on real data with ng By = 5000 in Figure T6 We observe that even in this substantially larger setting, MRet remains the best-perforning algorithm.
19


Reviews:
[{"review_id": "n9Pb0jUFic", "reviewer": "Reviewer_3G7d", "summary": "This manuscript proposes a novel problem setting focused on maximizing user retention in two-sided matching platforms, along with a dynamic learning-to-rank algorithm (MRet) that models personalized retention curves to optimize recommendations. The work addresses a critical gap in existing research—where match maximization causes user imbalance and fairness objectives fail to directly align with platform sustainability—and validates the approach through rigorous synthetic and real-world experiments on a large-scale online dating platform. The paper is well-structured, logically coherent, and its core contribution directly responds to practical needs of two-sided platforms dependent on user retention.", "questions": "Note: Here are some questions I have after reading the paper. Since I am not very familiar with this field, the authors may choose to answer selectively, focusing on issues related to the paper’s contributions. I will also take into account comments from other reviewers when forming my final evaluation.\n\n1. The retention function f(x,m) is assumed to be concave, but the paper notes MRet performs well on non-concave functions in real-world data. What specific properties of non-concave retention functions does MRet leverage to maintain effectiveness, and are there scenarios where non-concavity would significantly degrade performance?\n2. How does MRet handle users with limited interaction history (e.g., new users) who lack sufficient data to train personalized retention curves? Is a fallback strategy (e.g., cluster-based retention curves) used, and how does this affect overall retention?\n3. The paper mentions platform business models may prioritize one user side (e.g., paying male users in dating). How would MRet be modified to incorporate weighted retention objectives (e.g., 60% weight on male retention, 40% on female), and what trade-offs would arise from such prioritization?\n4. In the real-world experiment, missing match probabilities are imputed using ALS. How sensitive is MRet’s performance to imputation errors? Would alternative imputation methods (e.g., matrix factorization with side information) yield better retention results?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper breaks away from the dominant paradigms of match maximization and axiomatic fairness, instead centering on user retention as the core objective—an issue directly tied to platform revenue and sustainability (e.g., subscription-based models). This choice is well-justified by empirical evidence (Figure 1) showing that users with fewer matches have significantly higher churn rates, addressing a real pain point ignored by prior work.\n2. MRet’s focus on dual retention gains (both the recommending and recommended users) is a key innovation. Unlike conventional methods that optimize for one-sided utility, this two-sided consideration aligns with the reciprocal nature of matching platforms. The use of personalized retention curves, derived from user profiles and interaction history, ensures recommendations are tailored to individual retention needs rather than generic fairness or match probability.\n3. Experiments not only demonstrate higher retention rates but also explore edge cases (e.g., varying popularity skew, sparse match data, different exposure probabilities), proving MRet’s robustness. The analysis of match distribution (Figure 5) further clarifies why fairness-based methods fail—they ignore individual satisfactory match counts—strengthening the paper’s core argument.", "weaknesses": "1. The paper assumes match probabilities (r(x,y)) are either known or estimated upstream, but provides no guidance on how to integrate this estimation into the MRet framework. In practice, inaccurate match probability estimates could degrade retention performance, and the authors should discuss how MRet interacts with common estimation methods (e.g., collaborative filtering) or mitigate estimation errors.\n2. Although the paper mentions potential applications in recruitment, experiments are limited to online dating. Job matching has distinct characteristics (e.g., asymmetric priorities between employers and job seekers, longer decision cycles) that may affect retention dynamics. Validating MRet on a recruitment dataset would strengthen its generalizability.\n3. The paper focuses on retention rates as the key metric but does not address whether MRet impacts user satisfaction beyond continued login. For example, do users receiving \"retention-optimized\" matches report higher engagement quality (e.g., longer conversations, successful relationships in dating)? Supplementing with qualitative or secondary engagement metrics would enrich the evaluation.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "1jq12T4Eba", "reviewer": "Reviewer_ioZz", "summary": "This paper reframes online two-sided matching around user retention rather than match count or fairness. Under the assumption that per-user retention as a function of cumulative matches is monotone and concave, the authors apply a Jensen/linear lower bound to derive an additive, argsortable score that accounts for both receiver- and candidate-side marginal retention gains. Experiments on synthetic data and a small real dataset report retention improvements.", "questions": "1. In dating, a “successful match” often triggers intentional departure. Did you distinguish success-exit from disengagement churn?\n2. Do you model popularity as time-varying $p_u(t)$ (recency, seasonality, inactivity decay)? Please provide dynamics of popularity over time and test whether your method adapts when popularity drifts.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- Elevates long-term user retention over proxy objectives like match count or exposure parity.\n- An interesting setting that explicitly models both receiver and candidate utilities to enhance long-term retention.\n- Clean derivation and standard components make the method easy to code and to reproduce end-to-end.", "weaknesses": "1. **Motivation/positioning is unclear. Fairness appears as a “solution” without a precise link to retention.**\n\nThe paper treats fairness methods as peers to retention optimization, but never clarifies the key retention concepts (e.g., “satisfaction thresholds,” “marginal retention slope,” “early low-match churn”) nor how these relate to fairness (guardrail vs competing target).\n\n2. **Related work is late and under-covered, blurring the contribution boundary.**\n\nRetention optimization and reciprocal-fairness are direct neighbors; coverage is thin and appears too late. The following are some examples:\n> - Wang Y, Sun P, Ma W, et al. Intersectional two-sided fairness in recommendation[C]//Proceedings of the ACM Web Conference 2024. 2024: 3609-3620.\n> - Biswas A, Patro G K, Ganguly N, et al. Toward fair recommendation in two-sided platforms[J]. ACM Transactions on the Web (TWEB), 2021, 16(2): 1-34.\n\n3. **Target misaligned. Examples/experiments focus on popularity bias, but the primary comparator optimizes disparity**\n\nMost setups reveal a ‘rich-get-richer’ dynamic, yet the fairness baseline optimizes exposure disparity rather than marginal retention for low-match users and does not directly address popularity bias. This misalignment structurally favors MRet.\n\n4. **Baselines are limited and their selection lacks rationale.**\n\nSeveral cited works are not used as baselines; Max Match/FairCo’s origin/implementation/tuning is under-specified.\n\n5. **Real-world setting is narrow and assumption-heavy**\n\nSmall sample sizes(1000 x 1000), heavy reliance on missing-value imputation, coarse retention labels (e.g., next-month login), and no off-policy or online evidence.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "PkABcQEQQR", "reviewer": "Reviewer_M3j6", "summary": "This paper departs from the classic goals of two-sided matching (e.g., stable matchings, utility or welfare maximization, fairness constraints) by proposing a new objective: user‐retention (or platform‐driven “stickiness”) in a two-sided matchmaking setting (e.g., online dating, ride-sharing, job matching). The authors argue that match count or immediate welfare may not correlate strongly with long‐term retention, and instead propose modeling a personalized retention curve for each match pair (or each agent × partner type) that estimates the probability of continued engagement over time. They then formulate a matching/allocating algorithm, MRet, which assigns scarce match opportunities not simply to maximize immediate matching or fairness but to maximize expected retention gain subject to capacity constraints. Empirically, they validate the retention‐curve learning (from observational data) and test MRet on a large real‐world dataset (from a dating-platform) plus synthetic simulations. The results suggest that MRet can increase overall retention by focusing matches where retention impact is large, and still provide acceptable fairness outcomes (e.g., representation across groups).", "questions": "1- Is the allocation problem solved as a linear assignment with weights = expected retention gains, or is it more complex (e.g., non-additive, dependent pairs)? If the latter, what solver is used, and what is the worst‐case runtime?\n\n2- What features are used to predict retention? How was the model validated (train/dev/test splits, cross‐validation, hold‐out platform cohort)? What is the typical prediction error (e.g., RMSE, calibration by bins)?\n\n3- How sensitive are results to the capacity constraint (e.g., limited matches per period)? Did you vary the quota regime and show retention gains scale?\n\n4- Given that retention predictions may correlate with demographic/time-on‐platform features, how do you ensure that optimizing retention doesn’t disproportionately disadvantage historically marginalised groups? Could you offer fairness constraints (min‐quota, parity) and show corresponding retention/representation curves?\n\n5- If user cohorts shift or retention distributions change over time (e.g., seasonality, platform evolution), how robust is the learned retention model? Did you evaluate transfer across time windows or hold‐back users?\n\n6- Have you applied MRet beyond the dating platform domain (e.g., job-matching, ride‐sharing) or simulated different domains to test generality?\n\n7- Did you compare to simpler heuristics (e.g., match first, then sort by predicted retention gain greedily) rather than full model + allocation? And what is the incremental benefit of the full pipeline?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1-  Many matching/recommender systems (dating, jobs, rides, tutors) care about retention, not just initial matching. Framing retention‐maximization in two‐sided matching is novel in the ML/optimization space.\n\n2- Learning per‐agent or per‐pair retention probability over time is a creative step that bridges predictive modeling with matching allocation.\n\n3- The shift from maximizing number of matches/fairness to maximizing expected retention under capacity constraints is clean and actionable.\n\n4- Real‐world data from a large-scale platform, showing retention lift and reasonably good fairness outcomes, is a strong edge for an applied paper.\n\n5- The authors do not ignore fairness; they include group‐level analyses and discuss retention trade-offs across demographic slices.", "weaknesses": "1- The paper lacks formal results on the complexity of the retention‐objective matching problem, or approximation bounds/algorithms for large‐scale graphs. If the objective is non-linear or non-additive, this becomes non-trivial. The submission would be stronger if it clearly stated whether the problem is polynomially solvable (e.g., weighted bipartite matching) or NP‐hard and if so, provided a provably efficient approximation.\n\n2- Learning retention curves is central. However, the paper provides limited diagnostics of how accurate those curves are (prediction error, cross‐validation, time‐shift evaluation). Also, the domain dependence (single platform dataset) raises questions: how does the method generalize to new user cohorts, or across platforms?\n\n3- While fairness is discussed, the core algorithm (MRet) optimizes retention. If certain groups inherently have lower retention predictions, the algorithm may preferentially allocate to higher‐retention groups, exacerbating representation/fairness issues. More explicit trade‐off analysis (worst‐group retention, disparity curves) would strengthen the fairness dimension.\n\n4- The evaluation would benefit from stronger comparative baselines beyond standard matching: for example, match‐volume maximization with fairness constraints, heuristic retention prioritization without modeling, and analyses of small vs. large capacity constraints. Also, ablation studies (e.g., retention modeling on/off, fairness constraints on/off) would help attribute gains.\n\n5- It is unclear how the approach scales to many‐to‐many matching or large quotas, or domains where retention is less measurable or delayed. Some simulation/transfer experiments would help.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "PNQiW5DtJp", "reviewer": "Reviewer_WdJu", "summary": "In this paper, the authors studied a new paradigm for two-sided matching platforms that optimizes user retention rather than traditional objectives like match maximization or fairness. The authors proposed MRet (Matching for Retention), a dynamic learning-to-rank algorithm that learns personalized retention functions for each user. MRet then dynamically recommends users by maximizing the total expected retention gains for both the receiving and recommended users. The authors conducted numerical experiments on both synthetic and real-world data from a major online dating platform, demonstrating the efficacy of their method.", "questions": "Related to the real-world experiments, I also have a conceptual question: on dating platforms, user retention and user satisfaction may not always align. For instance, if matching is highly effective, satisfied users may form lasting relationships and naturally stop using the platform. In such cases, is retention truly the right optimization objective? It would be valuable for the authors to discuss how platforms might balance retention with user success or satisfaction, and whether MRet can accommodate such trade-offs.", "limitations": "", "rating": 4, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- I think the model studied in this paper is fairly novel and has practical relevance, as user retention is indeed aligned with real-world business metrics.\n- The theoretical results appear sound, where the authors derive an nice relaxation of an NP-hard objective via concavity assumptions. \n- The authors conducted numerical experiments on both synthetic and real-world data and provided very comprehensive analysis. In particular, the discussion provided nice insights into how fairness-centric methods differ from retention-centric approaches.", "weaknesses": "- The framework assumes access to the match probability $r(x,y)$, whereas in practice this must be estimated online. Although the paper acknowledges this limitation, it does not empirically assess robustness to estimation errors. Such errors could substantially degrade performance, and their impact deserves further investigation.\n- The real-world validation is relatively limited, as the experiment uses a sampled subset of 1k × 1k users with imputed match probabilities rather than a fully deployed system. This setup demonstrates feasibility but does not provide evidence of live or large-scale performance.\n- In this paper, fairness is presented primarily as a comparison to retention, but in practice I think it remains an important consideration for many platforms. Could fairness be incorporated alongside retention as a secondary objective within this framework?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)