Counterfactual Reciprocal Recommender Systems

• CFRR is a reciprocal recommendation framework that models user–user interactions with counterfactual risk minimization to address exposure bias.
• It employs self-normalized IPS and doubly robust extensions to reduce variance and improve fairness in mutual matching.
• The approach is applied in domains like dating, gaming, and talent platforms where both parties’ acceptance is critical for success.

Counterfactual Reciprocal Recommender Systems (CFRR) are reciprocal recommender systems formulated as a causal learning and evaluation problem. In a reciprocal recommender system, users become the item being recommended to other users, and successful performance requires that both the end user and the user being recommended accept the matching recommendation rather than only one side reacting to it (Palomares et al., 2020). CFRR was introduced for user-to-user matching in dating, gaming, and talent platforms to address the fact that logged data over-represents popular profiles because historical exposure policies display only a small subset of all possible pairs, thereby creating feedback loops that distort learning, offline evaluation, and fairness (Kawamura et al., 3 Aug 2025).

1. Reciprocal recommendation as the substrate of CFRR

Reciprocal recommender systems differ from conventional user-item recommenders because they are inherently two-sided. The underlying object is not a user–item interaction but a user–user pair $(u,v)$, often drawn from two sets $U$ and $V$, which may or may not be identical. Reciprocal recommendation therefore requires modeling both initiator-side and receiver-side preferences, along with the probability that both sides accept. The general reciprocal objective is not merely to estimate unilateral preference but to calculate mutual compatibility between pairs of users, typically by applying fusion processes on unilateral user-to-user preference information (Palomares et al., 2020).

CFRR begins from the observation that this two-sided structure amplifies the standard logged-feedback problem. Let $\mathcal{P} = U \times V$ denote the full pair space. For each pair $(u,v)$, $O(u,v) \in \{0,1\}$ denotes whether the pair was displayed, while $r(u,v) \in [0,1]$ denotes the reciprocal outcome observed only when $O(u,v)=1$. The historical exposure policy induces a pair-level display probability

$\theta(u,v) \equiv P[O(u,v)=1 \mid u,v].$

In practice, popular or high-visibility users have high $\theta(u,v)$, whereas low-visibility or long-tail users have very low $U$0. The consequence is not only popularity bias but also skewed learning, distorted offline metrics, and fairness problems. This is particularly severe in reciprocal recommendation because success depends on two sides being exposed to each other and both accepting, while propensity can depend on both users’ historical popularity and platform routing on both sides (Kawamura et al., 3 Aug 2025).

A central implication is that naïve empirical optimization on displayed pairs does not answer the operational question of interest: what would happen under a different, typically more uniform, exposure policy? CFRR recasts this question as counterfactual risk minimization over user pairs rather than over user-item impressions (Kawamura et al., 3 Aug 2025).

2. Causal formulation and identification assumptions

CFRR adopts an explicit causal interpretation of logged pair exposure. For each pair $U$1, $U$2 denotes the true potential outcome if the pair were shown, while $U$3 is observed only when $U$4. The recommender learns a compatibility function

$U$5

and optimizes a loss $U$6 against a target exposure distribution that is taken to be uniform over the pair space. The resulting counterfactual objective is

$U$7

This objective is counterfactual because the historical log is generated under the logging policy $U$8, not under the target distribution (Kawamura et al., 3 Aug 2025).

The causal assumptions are standard for IPS- and SNIPS-based learning from logged feedback. CFRR requires positivity, expressed as $U$9 on the relevant subset of pairs; otherwise inverse propensity weighting is undefined. It also relies on an ignorability or unconfoundedness condition in the informal sense that the display decision can be modeled as a function of observed variables used in the propensity model. The framework further assumes SUTVA, so that outcomes for one pair do not depend on which other pairs are displayed, and stationarity, so that user preferences and the logging policy remain relatively stable over the logging window (Kawamura et al., 3 Aug 2025).

These assumptions delimit the scope of identification. They justify the use of pair-level propensity correction, but they also expose the main failure modes of CFRR: zero-exposure regions, propensity misspecification, and unmodeled interference. The same issues appear more generally in reciprocal recommendation, where the survey literature has already emphasized sparse reciprocal events, exposure bias, policy bias in offline evaluation, and the need to reason about recommendation as treatment and reciprocal match as outcome (Palomares et al., 2020).

3. Learning objectives: pair-level propensities, SNIPS, clipping, and doubly robust augmentation

The defining mechanism of CFRR is pair-level propensity correction. The framework assumes a parametric propensity model

$V$0

where $V$1 and $V$2 are feature vectors for the two users, $V$3 is a predictor such as logistic regression or a small neural net, and $V$4 is the sigmoid. The propensity model is trained on exposure logs $V$5 using cross-entropy, and the experiments instantiate this step with LightGBM on user-level popularity and activity features (Kawamura et al., 3 Aug 2025).

Given displayed pairs with observed outcomes, CFRR assigns inverse propensity weights

$V$6

The Horvitz–Thompson IPS risk estimator is

$V$7

but CFRR uses self-normalized IPS as its core training objective: $V$8 SNIPS is slightly biased in finite samples, but the bias vanishes asymptotically, while the variance reduction is substantial when some pair propensities are very small (Kawamura et al., 3 Aug 2025).

Mutual acceptance is encoded in the outcome variable rather than in the weighting scheme. The observed $V$9 is defined as a mutual event such as both users liking each other, reciprocal trust, or co-authorship. The model score $\mathcal{P} = U \times V$0 therefore directly predicts compatibility or the probability of mutual acceptance from both users’ features, while $\mathcal{P} = U \times V$1 captures only the probability that the pair is exposed under the logging policy (Kawamura et al., 3 Aug 2025).

Variance control is essential. CFRR therefore adds two stabilizers. First, it uses weight truncation: $\mathcal{P} = U \times V$2 with clipping threshold $\mathcal{P} = U \times V$3 in the reported experiments. Second, it optionally uses a doubly robust extension with an auxiliary outcome model $\mathcal{P} = U \times V$4. The resulting SNIPS-DR estimator is

$\mathcal{P} = U \times V$5

This estimator is consistent if either the propensity model or the outcome model is correctly specified (Kawamura et al., 3 Aug 2025).

The framework is model-agnostic with respect to $\mathcal{P} = U \times V$6. The scoring model may be a latent-factor model, a neural network over user features, or a graph-based model. What changes is the training objective: plain empirical loss is replaced by SNIPS- or SNIPS-DR-weighted loss over displayed pairs (Kawamura et al., 3 Aug 2025). Closely related counterfactual risk minimization work in user-item recommendation reaches the same conclusion for IPS-weighted BPR and self-normalized evaluation, and explicitly positions variance regularization as crucial when exposure probabilities are extreme (Raja et al., 30 Aug 2025).

4. Fairness, exposure inequality, and graph-based counterfactual variants

Although CFRR is primarily a bias-correction framework, its empirical motivation is tightly coupled to fairness. The paper evaluates two exposure-side measures in addition to ranking accuracy. Coverage@$\mathcal{P} = U \times V$7 is defined as the fraction of users who appear at least once in any other user’s top-$\mathcal{P} = U \times V$8 recommendation list. Gini-Exposure is the Gini coefficient of the exposure distribution across users, computed from the number of times each user appears in others’ top-$\mathcal{P} = U \times V$9 lists. Higher Coverage@$(u,v)$0 and lower Gini-Exposure correspond, respectively, to broader long-tail visibility and less concentrated exposure (Kawamura et al., 3 Aug 2025).

The mechanism is straightforward. Reweighting by inverse exposure propensity makes popular, high-propensity pairs contribute less effective mass during training, while rare, low-propensity pairs receive larger weights subject to clipping and normalization. This pushes the model toward the full pair distribution rather than toward the historically overexposed head, which in turn increases long-tail user coverage and reduces exposure inequality (Kawamura et al., 3 Aug 2025).

CFRR sits within a larger counterfactual recommendation literature that is not inherently reciprocal but is structurally adjacent. A graph-based unfairness mitigation method adds a minimal set of user-item edges to an interaction graph so that a fixed GNN recommender yields fairer outcomes, formalized by

$(u,v)$1

with fairness defined as demographic parity of utility measured by approximate NDCG differences across groups and minimality enforced by a graph-distance penalty (Boratto et al., 2023). The same work explicitly notes that the pattern is reusable for a user–user or user–provider graph, suggesting a graph-augmentation route to CFRR in which candidate counterfactual matches are added for disadvantaged groups on one or both sides.

A different but related direction uses a graph neural network plus a Graph-VAE to propose minimal, high-impact changes in a bipartite user–listing interaction graph so as to increase the predicted probability of transaction while keeping edge and feature edits sparse (Mousavi et al., 5 Feb 2026). That framework is not presented as reciprocal recommendation in the classical sense, because it optimizes transaction probability rather than explicit two-sided utility, yet it already operates on a two-sided graph with mutable behavior and price features. This suggests an architectural blueprint for graph-structured CFRR in which a base reciprocal model and a feasible counterfactual graph generator are optimized jointly, though such an extension remains an inference beyond the reported experiments (Mousavi et al., 5 Feb 2026).

5. Evaluation protocols and empirical evidence

CFRR is evaluated on one synthetic benchmark and two real reciprocal domains: Synthetic, DBLP-CoAuthor, and Epinions-Trust. For the real datasets, observed reciprocal links are treated as positive outcomes and an equal number of non-linked pairs are sampled as negatives. The reported baselines are LFRR, CausE adapted to user–user matching, IPW-MF, DICE, and StableDR. Accuracy is measured with NDCG@10 and MRR; fairness is measured with Coverage@10 and Gini-Exposure; experiments use ten random seeds, twenty epochs with early stopping, Adam, embedding dimension $(u,v)$2, $(u,v)$3, batch size $(u,v)$4, weight clipping threshold $(u,v)$5, and paired $(u,v)$6-tests with Bonferroni correction (Kawamura et al., 3 Aug 2025).

Dataset	NDCG@10	Coverage@10 / Gini-Exposure
Synthetic	$(u,v)$7	$(u,v)$8, $(u,v)$9
DBLP-CoAuthor	$O(u,v) \in \{0,1\}$0	$O(u,v) \in \{0,1\}$1, $O(u,v) \in \{0,1\}$2
Epinions-Trust	$O(u,v) \in \{0,1\}$3	$O(u,v) \in \{0,1\}$4, $O(u,v) \in \{0,1\}$5

On the Synthetic dataset, CFRR-SNIPS improves NDCG@10 from $O(u,v) \in \{0,1\}$6 to $O(u,v) \in \{0,1\}$7, increases Coverage@10 from $O(u,v) \in \{0,1\}$8 to $O(u,v) \in \{0,1\}$9, and reduces Gini-Exposure from $r(u,v) \in [0,1]$0 to $r(u,v) \in [0,1]$1. On DBLP-CoAuthor, NDCG@10 rises from $r(u,v) \in [0,1]$2 to $r(u,v) \in [0,1]$3 and Coverage@10 from $r(u,v) \in [0,1]$4 to $r(u,v) \in [0,1]$5, while Gini-Exposure remains close to the best baseline. On Epinions-Trust, NDCG@10 rises from $r(u,v) \in [0,1]$6 to $r(u,v) \in [0,1]$7, Coverage@10 from $r(u,v) \in [0,1]$8 to $r(u,v) \in [0,1]$9, and Gini-Exposure from $O(u,v)=1$0 to $O(u,v)=1$1. The synthetic study therefore shows the clearest fairness effect, while the real datasets show smaller but still positive changes in both ranking quality and exposure distribution (Kawamura et al., 3 Aug 2025).

Ablations isolate the role of self-normalization. On Synthetic, moving from CFRR-IPS to CFRR-SNIPS increases Coverage@10 from $O(u,v)=1$2 to $O(u,v)=1$3, reduces Gini-Exposure from $O(u,v)=1$4 to $O(u,v)=1$5, and improves NDCG@10 from $O(u,v)=1$6 to $O(u,v)=1$7 and MRR from $O(u,v)=1$8 to $O(u,v)=1$9. Under deliberate propensity misspecification with AUC approximately $\theta(u,v) \equiv P[O(u,v)=1 \mid u,v].$0, the doubly robust variant outperforms plain SNIPS, with NDCG@10 around $\theta(u,v) \equiv P[O(u,v)=1 \mid u,v].$1 versus $\theta(u,v) \equiv P[O(u,v)=1 \mid u,v].$2 and Coverage@10 around $\theta(u,v) \equiv P[O(u,v)=1 \mid u,v].$3 versus $\theta(u,v) \equiv P[O(u,v)=1 \mid u,v].$4. The reported computational overhead is about $\theta(u,v) \equiv P[O(u,v)=1 \mid u,v].$5–$\theta(u,v) \equiv P[O(u,v)=1 \mid u,v].$6 for SNIPS weighting and about $\theta(u,v) \equiv P[O(u,v)=1 \mid u,v].$7 for the doubly robust variant due to outcome-model training (Kawamura et al., 3 Aug 2025).

These findings align with the broader counterfactual risk minimization literature in recommendation, where self-normalized evaluation and propensity-aware regularization are reported to reduce evaluation variance and improve robustness under biased exposure (Raja et al., 30 Aug 2025).

6. Explanations, deployment, limitations, and future directions

CFRR as introduced is a causal training and evaluation framework rather than an explanation mechanism, but counterfactual explanation methods in recommendation provide a natural interface layer. One approach learns a surrogate model that predicts the effect of deleting subsets of a user’s history on the recommendation outcome, thereby avoiding repeated retraining; the explanation is a subset of past interactions $\theta(u,v) \equiv P[O(u,v)=1 \mid u,v].$8 such that the recommended item would no longer appear in top-$\theta(u,v) \equiv P[O(u,v)=1 \mid u,v].$9 if those interactions were removed (Yao et al., 2022). Another line formulates counterfactual explanation as a mixed-integer optimization problem that minimally changes a user interaction vector while enforcing ranking constraints and plausibility under a generative model (Černý et al., 10 Jul 2025). Provider-side graph explanations likewise define an explanation as a minimum set of the user’s own actions that, if removed, changes the recommendation to a different item, and derive a polynomial-time optimal algorithm for Personalized PageRank recommenders (Ghazimatin et al., 2019). These methods are one-sided, but the reciprocal extension is explicitly suggested or is a plausible implication: the same logic can be applied to user–user matching by treating pairwise mutual outcomes as the recommendation target.

For deployment, the reported implications are domain-specific and concrete. In dating platforms, CFRR can mitigate popularity bias where a small fraction of users absorb most attention. In gaming and social platforms, partner matching becomes less skewed toward top players or creators. In talent and collaboration platforms, debiasing co-author or hiring recommendations can give less prominent but high-quality candidates more exposure. The proposed operational sequence is to log exposure decisions and outcomes with user features, train a propensity model on those logs, train the reciprocal recommender with CFRR-SNIPS, optionally add doubly robust augmentation if propensities are noisy, use the resulting debiased scores in downstream matching, and monitor Coverage and Gini alongside ranking accuracy (Kawamura et al., 3 Aug 2025).

The framework’s limitations are equally explicit. CFRR requires positivity over the relevant pair space, a correct or at least reasonable propensity model, relative stationarity of preferences and policy, and no interference between pairs. It remains sensitive to extreme propensities even with SNIPS and clipping, depends on feature quality for both propensity and outcome models, and introduces moderate pipeline complexity because industrial systems must integrate exposure logging, propensity estimation, weighting, and optional doubly robust training (Kawamura et al., 3 Aug 2025). More general neural causal models for interactive recommendation propose learnable structural causal models with Gumbel-max constraints to address survivor bias in sequential settings, which suggests a route toward dynamic CFRR with explicit state transitions and counterfactual consistency, although that extension remains broader than the CFRR formulation currently evaluated (Liu et al., 2023).

The stated future directions are positivity at scale, more expressive propensity and outcome models, online learning and exploration, multi-objective optimization, and network effects with dynamic treatments (Kawamura et al., 3 Aug 2025). Taken together, these directions indicate that CFRR is best understood not as a single estimator but as a research program: reciprocal recommendation augmented with counterfactual risk minimization, pair-level exposure modeling, variance-aware estimation, and—potentially—counterfactual explanation and graph intervention layers.