[Paper Review] Beyond Match Maximization and Fairness: Retention-Optimized Two-Sided Matching

Ren Kishimoto, Rikiya Takehi+5 more|arXiv (Cornell University)|Feb 17, 2026

Evolutionary Psychology and Human Behavior0 citations

TL;DR

The paper defines retention-optimized two-sided matching and introduces MRet, a dynamic learning-to-rank algorithm that maximizes user retention on both sides of a platform, validated on synthetic and real dating data.

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.

Motivation & Objective

• Address the problem that maximizing matches on two-sided platforms creates imbalances and churn.
• Propose retention as the primary objective rather than fairness or match count.
• Learn personalized retention curves from user profiles and history.
• Develop MRet that allocates scarce matching opportunities to maximize overall retention.
• Demonstrate superior retention performance on synthetic and real-world dating data.

Proposed method

• Formally define a retention function f(x,m) for each user side and model retention probability as a function of cumulative matches m.
• Derive a retention-maximizing ranking objective (Eq. 9) that sums receiver and recommended-user retention gains.
• Introduce the MRet ranker that approximates the NP-hard objective using a concavity-based lower bound and a Score(y) function (Eq. 13) to enable O(N log N) ranking.
• Leverage Jensen-type bounds (Lemmas 1 and 2) to decompose and bound the objective for tractable optimization.
• Train a regression model to estimate f from context (XGBoost) and use observed interactions to learn retention dynamics.
• Validate the approach with synthetic data and a real Japanese online dating dataset, with code provided in supplementary material.

Experimental results

Research questions

• RQ1 Can retention, not matches or fairness, be directly optimized in two-sided matching?
• RQ2 Does a dynamic LTR approach (MRet) improve long-term user retention compared to baselines like Max Match or FairCo?
• RQ3 Can the NP-hard retention optimization be efficiently approximated without sacrificing performance?
• RQ4 How does MRet perform on synthetic data and real-world dating platform data under varying conditions?
• RQ5 Is MRet robust to deviations from the concavity assumption in retention functions?

Key findings

• MRet achieves higher user retention than baselines such as Max Match, Uniform, and FairCo, while using about 70% of the matches achieved by Max Match.
• In synthetic experiments, MRet outperforms baselines in retention under varying popularity skew (kappa).
• On real-world data, MRet yields the highest retention in extremely sparse matching scenarios where fairness methods fail.
• FairCo can underperform retention optimization due to misalignment between exposure fairness and actual retention needs.
• MRet remains effective even when the concavity assumption is violated in real data, indicating robustness.