Long-Term Fairness-Aware Recommendation via Adaptive Fairness Metric Selection

1. Introduction

Recommender systems have become indispensable in modern online platforms, shaping user experiences across e-commerce, social media, and content streaming [1]. However, mounting evidence shows that these systems can inadvertently reinforce or amplify societal biases, leading to unfair treatment of certain demographic groups [2,3]. For instance, job recommendation systems might favor male candidates for technical roles, while product recommenders may under-expose fashion items to male users. Such biases erode user trust and raise serious ethical and legal concerns.

To mitigate these issues, a large body of fairness-aware recommendation methods has been developed. The majority focus on removing or obfuscating information related to sensitive attributes (e.g., gender, age) from user representations  [4,5,6,7]. More recent approaches employ causal reasoning to separate fair from unfair information paths [13,14,15,16,17,73]. Nevertheless, a critical and often overlooked limitation persists: these methods almost uniformly adopt a fixed fairness metric, most commonly Demographic Parity (DP), for both evaluation and optimization. DP demands that the probability of receiving a positive recommendation be identical across groups. While seemingly impartial, this requirement becomes problematic when a sensitive attribute genuinely influences user preferences—for example, when gender causally affects interest in certain product categories. In such cases, enforcing DP forces the system to ignore legitimate taste differences, inevitably hurting recommendation accuracy. Conversely, if the observed correlation is purely spurious (e.g., driven by historical exposure bias), DP is indeed appropriate, whereas Equal Opportunity (EO), which only equalizes true positive rates, may fail to rectify the underlying injustice.

This observation reveals a fundamental tension: a single fairness metric cannot serve all scenarios well. We argue that the choice of fairness criterion should be guided by the causal role of the sensitive attribute. When the attribute has a genuine causal effect on user preferences, it is reasonable to tolerate outcome disparities as long as qualified users from different groups enjoy equal access to relevant items; hence, Equal Opportunity is the more suitable metric. When the association is spurious, the system must pursue complete statistical independence from the attribute, i.e., Demographic Parity. This adaptive principle avoids the unnecessary accuracy degradation caused by blindly applying DP where it is not needed, while also providing stronger fairness guarantees than EO when bias is purely artifactual.

Figure 1 illustrates the contradictions inherent in existing approaches and how our adaptive strategy resolves them. Existing work typically tries to simultaneously satisfy both DP and EO, but this joint pursuit ignores three critical aspects: (1) the intrinsic tension between the two metrics, (2) the causal nature of the sensitive attribute, and (3) the dynamic amplification of bias over time. Depending on whether the attribute is truly causal or spurious, enforcing the wrong metric leads to either accuracy collapse (when DP is forced on a causal attribute) or residual bias (when EO is applied to a spurious association). Moreover, static one-shot evaluations miss the gradual accumulation of unfairness through feedback loops. Our LFR-via-AFMS framework addresses all three issues by first diagnosing the causal status, then adaptively selecting EO (for causal) or DP (for spurious), and finally embedding this choice into a reinforcement learning agent that optimizes long-term fairness.

Guided by this principle, we propose LFR-via-AFMS (Long-term Fairness-aware Recommendation via Adaptive Fairness Metric Selection). LFR-via-AFMS consists of three integrated stages: (1) Causal Structure Identification to determine whether the sensitive attribute operates through a genuine causal pathway or a spurious back-door path; (2) Disentangled Representation Learning that preserves legitimate causal information or removes bias factors accordingly; and (3) Actor-Critic Reinforcement Learning with Adaptive Fairness Penalty, where the reward function dynamically selects EO or DP penalty based on the causal diagnosis, thereby optimizing long-term fairness without compromising accuracy.

Our main contributions are:

• Principle of Adaptive Fairness Metric Selection: We formally analyze why simultaneously satisfying DP and EO is contradictory under genuine causality, and propose a causal diagnosis-based strategy that applies EO for true causal attributes and DP for spurious ones, fundamentally avoiding the accuracy-fairness dilemma.
• Integrated LFR-via-AFMS Framework: We combine causal discovery, path-specific/VAE debiasing, and an actor-critic RL agent with an adaptive fairness reward, achieving long-term group fairness with minimal accuracy loss.
• Empirical Validation: Extensive experiments on MovieLens and Alibaba datasets show that LFR-via-AFMS outperforms fixed-metric and non-causal baselines in both fairness and recommendation quality, and confirm the indispensability of adaptive metric selection.

2. Related Work

2.1. Fairness in Recommendation

Research on fairness in recommender systems has flourished, covering pre-processing, in-processing, and post-processing techniques. Ekstrand et al. [70] provided a comprehensive survey categorizing fairness approaches along dimensions including consumer versus provider fairness [2,18,22,23], individual versus group fairness [19,20], and static versus dynamic settings. Most existing approaches follow one of three intervention strategies: pre-processing, in-processing, or post-processing.

Pre-processing methods modify the training data before model learning to remove or mitigate bias [29,30]. Common techniques include reweighting samples from underrepresented groups [62], obfuscating sensitive attributes through feature transformation [63], and generating counterfactual data augmentations [64]. While straightforward, pre-processing approaches often fail to eliminate bias that emerges through complex interactions during model training.

In-processing methods incorporate fairness constraints directly into the optimization objective or learning algorithm [18,31]. Regularization-based approaches add penalty terms that encourage prediction parity across groups [32,33,65,76], while adversarial methods learn representations invariant to sensitive attributes [69]. More recent approaches integrate fairness constraints into graph neural network architectures [66,67]. However, these methods typically treat all variation related to sensitive attributes as undesirable, failing to distinguish between legitimate preference differences and discriminatory bias.

Post-processing methods adjust model outputs after training to satisfy fairness constraints [34,35,68]. These approaches are model-agnostic and computationally efficient but may substantially degrade recommendation quality when the underlying model is severely biased.

Most existing methods optimize fairness constraint by Demographic Parity, regardless of the data generation process. While some works have incorporated Equal Opportunity, they treat fairness metrics as fixed and universally desirable, ignoring the fact that their appropriateness depends on the causal nature of the sensitive attribute. Our work departs from this static view by making the fairness metric itself adaptive.

2.2. Causal Inference for Fairness

Causal inference provides a powerful language for reasoning about fairness [36]. Counterfactual fairness [37] requires that a model’s prediction remain unchanged under counterfactual interventions on the sensitive attribute. Path-specific fairness allows certain causal pathways while blocking others. Wang et al. [28,38] used a causal graph to debias click data. PSF-RS preserves the fair influence of sensitive features by identifying fair and unfair latent mediators [73], but it only focuses on the immediate fairness of a single model’s prediction. Nevertheless, most existing causal fair recommenders do not consider long-term fairness under the loop effect of the recommender system over time, nor do they employ a predetermined fairness evaluation metric without considering that the definition of fairness should adapt according to the causal status of the attribute. LFR-via-AFMS fills this gap by using causal discovery to also decide which metric to optimize.

2.3. Disentangled Representation Learning and RL

Disentangled representation learning aims to separate independent generative factors in data. Variational autoencoders (VAEs) with modified loss functions (e.g., $\beta$-VAE [39], FactorVAE [40]) have been widely used. In recommendation, disentanglement can separate user preferences from confounding factors like popularity bias [41,42,60,61,71]. In fairness applications, disentanglement has been employed to separate variation related to sensitive attributes from task-relevant information. The CAD-VAE framework [59] introduces correlation-aware regularization to separate sensitive attributes from other factors. Existing fairness-aware RL methods add a static fairness penalty to the reward. In contrast, we design an adaptive penalty that switches between EO and DP based on causal identification, leading to a more intelligent long-term policy.

2.4. Reinforcement Learning for Recommendation

Reinforcement learning (RL) is well-suited for recommendation as a sequential interaction process [43,44]. Actor-Critic methods have been applied to optimize long-term user engagement [45]. Recently, fairness-aware RL approaches incorporate fairness metrics into the reward function [46,47,61]. However, existing RL-based fairness methods do not consider causal structure, and causal-based reinforcement learning recommendation algorithms typically consider only features with causal effects while neglecting features without causal influence [48,49]. Our work builds upon these RL foundations but differs in the state representation: rather than using raw user histories or biased embeddings, our RL agent operates on the debiased representations produced by our causal disentanglement module, providing a cleaner signal for fairness-accuracy trade-off optimization.

3. Preliminaries

In this section, we first recall standard fairness definitions and causal graph notations. Then, we present a detailed analysis of the dilemmas that arise when simultaneously applying DP and EO in recommendation, which directly motivates our adaptive fairness metric selection strategy.

3.1. Fairness Definitions

We consider a binary sensitive attribute $A\in \{0,1\}$. Let $Y\in \{0,1\}$ be the true user preference (e.g., click) and $\widehat{Y}\in \{0,1\}$ be the recommendation decision. Two widely used group fairness metrics are:

• Demographic Parity (DP): $P(\widehat{Y}=1\mid A=0)=P(\widehat{Y}=1\mid A=1)$. It requires equal positive prediction rates across groups.
• Equal Opportunity (EO): $P(\widehat{Y}=1\mid Y=1,A=0)=P(\widehat{Y}=1\mid Y=1,A=1)$. It requires equal true positive rates across groups.

DP focuses on outcome distribution, while EO focuses on equitable access for those truly interested.

3.2. Causal Graphs and Path-Specific Fairness

We model the recommendation environment with variables: sensitive attribute A, user intrinsic preference U, item features X, exposure E, and interaction Y. The causal role of A determines not only how bias arises but also which fairness intervention is appropriate. In this work we distinguish two fundamental structures, as illustrated in Figure 2.

Genuine causal effect.

Figure 2(a) depicts the case where the sensitive attribute has a genuine causal influence on user preference. The path $A\to U\to Y$ captures how inherent group characteristics (e.g., gender differences in movie genre affinity) legitimately shape interests. At the same time, $A\to E\to Y$ may represent an unfair exposure mechanism (e.g., historical under-representation of certain groups in recommendations), which introduces bias. In this scenario, it would be incorrect to remove all influence of A on Y—doing so would discard the authentic preference signal carried by $A\to U\to Y$ and degrade recommendation accuracy. Path-specific fairness [73] provides the right tool: we should preserve the fair causal path $A\to U\to Y$ while blocking the unfair mediation through E. Consequently, enforcing Demographic Parity (which forces total independence between A and $\widehat{Y}$) is too restrictive: it eliminates even the legitimate variation, leading to unnecessary accuracy loss. Instead, Equal Opportunity is the natural metric, as it allows group-level differences in base rates while requiring equal true positive rates for those truly interested. This aligns with the idea that we only constrain the unfair pathway, not the causal one.

Spurious association.

Figure 2(b) illustrates the spurious case, where A and Y share a common confounder C (e.g., societal stereotypes that affect both group identity and perceived preferences). There is no causal path from A to Y; the statistical association is entirely artificial. In this setting, any dependence between $\widehat{Y}$ and A arises purely from bias. The system should therefore aim for complete independence, making Demographic Parity the appropriate fairness criterion. Removing the sensitive attribute’s influence is both safe and necessary, as it does not sacrifice any genuine preference signal. Using only Equal Opportunity would be insufficient because it could still leave the spurious correlation untouched.

Based on this causal diagnosis, we learn the causal graph and perform conditional independence tests to distinguish between the two cases, yielding a flag $c_{\mathrm{spurious}}\in \{0,1\}$ ($c_{\mathrm{spurious}}=0$ for genuine causal, $c_{\mathrm{spurious}}=1$ for spurious).

3.3. The Dilemma of Simultaneous DP-EO Evaluation and Our Adaptive Principle

Most prior studies simultaneously report DP and EO, and often try to improve both. However, this joint pursuit is fundamentally problematic when the sensitive attribute has a genuine causal effect on user preferences, which is the primary motivation behind our work. We elaborate the issues below.

1. Mathematical impossibility under true causality. Suppose gender (A) causally influences movie genre preference (Y). Then the base rate $P(Y=1|A=1)$ may naturally differ from $P(Y=1|A=0)$. DP requires $P(\widehat{Y}=1|A=0)=P(\widehat{Y}=1|A=1)$. Since the optimal prediction should approximate the true preference Y, achieving DP forces the system to over-recommend to the group with lower true interest or under-recommend to the group with higher interest, thereby introducing systematic distortion. EO only requires $P(\widehat{Y}=1|Y=1,A=0)=P(\widehat{Y}=1|Y=1,A=1)$, which can be satisfied without altering the overall recommendation rates; it respects genuine base rate differences. Thus, when A is causal, strict DP and EO cannot be simultaneously satisfied unless base rates are equal—a condition rarely met in reality.

2. Conflicting optimization objectives. Many fairness-aware models add penalty terms for both DP violation and EO violation to the loss function. Under genuine causality, these two penalties push the model in opposite directions: DP penalty discourages any dependence on A, while EO penalty only discourages unequal error rates. The model is forced to reach a suboptimal compromise that satisfies neither perfectly and degrades recommendation accuracy. This “waterbed effect” leads to unstable training and unpredictable fairness-accuracy trade-offs.

3. Masking the true nature of unfairness. Reporting both metrics without causal context can obscure the source of bias. A low DP gap might be achieved by sacrificing EO (e.g., recommending fewer relevant items to a disadvantaged group to equalize exposure), while a low EO gap might coexist with a large DP gap that reflects legitimate preference variation. Without causal diagnosis, we cannot interpret whether a disparity is discriminatory or simply a reflection of diverse interests. The field lacks a principled guideline on when each metric is appropriate.

4. Our adaptive solution. To resolve these dilemmas, we propose a simple yet effective rule: the choice of fairness metric should align with the causal role of the sensitive attribute. Specifically:

• If the attribute has a genuine causal effect on preference ($c_{\mathrm{spurious}}=0$), we adopt Equal Opportunity. This allows natural base rate differences while ensuring that truly interested users from all groups receive fair access. DP is not enforced.
• If the attribute has only a spurious correlation ($c_{\mathrm{spurious}}=1$), we adopt Demographic Parity. Since the observed association is entirely due to bias, the system should aim for complete independence from the attribute, eradicating the illegitimate signal.

This adaptive strategy eliminates the contradictory objectives inherent in previous approaches and provides a causally grounded definition of fairness. It forms the foundation of the LFR-via-AFMS framework.

3.4. Actor-Critic Reinforcement Learning

We formulate sequential recommendation as a Markov Decision Process (MDP). At step t, the state $s_t$ includes user representation and history; action $a_t$ is a set of recommended items; reward $r_t$ combines accuracy and fairness. The goal is to learn a policy ${\pi }_{\theta }$ that maximizes expected cumulative reward $\mathbb{E}\left[{\sum }_t{\gamma }^t{r}_t\right]$. We adopt an Actor-Critic architecture, where the Critic estimates $Q(s,a)$ and the Actor updates the policy via PPO [52]. The fairness penalty in $r_t$ will be defined adaptively based on the causal flag, as detailed in Section 4.

4. Proposed Method: LFR-via-AFMS

In this section we detail the three core components of LFR-via-AFMS: causal structure identification, conditional representation learning, and actor-critic training with adaptive fairness penalties. An overview of the pipeline is shown in Figure 3.

4.1. Causal Structure Identification

The first stage diagnoses whether the sensitive attribute A has a genuine causal effect on user preference Y or merely exhibits a spurious correlation. We treat the observed variables $\{A,U,E,Y\}$ and aim to recover the underlying causal graph. A proxy for the latent intrinsic preference U is obtained from a pre-trained matrix factorization model, which provides low-dimensional user embeddings that capture genuine taste factors independent of exposure.

We apply the PC algorithm [50] with Fisher’s z-test for conditional independence. Starting from a fully connected graph, edges are iteratively removed when a conditional independence is detected. After orienting edges via collider detection and propagation rules, we obtain a partial ancestral graph. The critical question is whether A has any directed path to Y that does not go through U—that is, whether there exists a direct effect or a back-door path remaining after conditioning on U and E. If A and Y are independent given U and E, i.e. $A\perp \perp Y\mid U,E$, then the entire association is mediated by the fair path $A\to U\to Y$ and possibly the unfair path $A\to E\to Y$ (which we will later block). In this case the effect of A on Y is genuine and operates through known mediators; we set the spurious flag $c_{\mathrm{spurious}}=0$.

If, however, the conditional independence does not hold, the remaining dependence indicates an unblocked back-door path (e.g., a hidden confounder C affecting both A and Y, as in Figure 2(b)), or a direct causal link not captured by U or E. Such a residual association has no legitimate grounding in user preference and is therefore deemed spurious; we set $c_{\mathrm{spurious}}=1$. In practice, to be robust to finite-sample noise, we additionally train a simple classifier to predict Y from A given $U,E$; if the AUC exceeds $0.55$, we also decide $c_{\mathrm{spurious}}=1$. The outcome of this stage is a binary flag that determines both the representation learning strategy and the fairness metric to be used in the RL reward.

4.2. Conditional Representation Learning

Given the causal diagnosis, we adopt one of two debiasing approaches to learn a user representation that only retains fair information.

4.2.1. Path-Specific Fair Representation (Genuine Causality)

When $c_{\mathrm{spurious}}=0$, the attribute A is a genuine cause of Y through the preference U. To avoid unfair bias introduced by differential exposure E, we learn a representation $z^{\mathrm{genuine}}$ that satisfies path-specific fairness: it preserves the causal pathway $A\to U\to Y$ while blocking the unfair mediation $A\to E\to Y$. Concretely, we define an encoder $f_{\mathrm{gen}}:(U,A,E)\mapsto z^{\mathrm{genuine}}$ and optimize the following objective:

$${\mathcal{L}}_{\mathrm{gen}}={\mathcal{L}}_{\mathrm{BPR}}\left(z^{\mathrm{genuine}}\right)+\lambda {\mathcal{L}}_{\mathrm{adv}}(z^{\mathrm{genuine}},E\mid U).$$

(1)

The first term is the standard Bayesian Personalized Ranking loss that encourages the representation to be effective for preference prediction:

$${\mathcal{L}}_{\mathrm{BPR}}=-\sum _{(u,i,j)\in \mathcal{D}}log\sigma ({\widehat{y}}_{ui}-{\widehat{y}}_{uj}),$$

(2)

where ${\widehat{y}}_{ui}$ is the predicted score for user u and item i computed from $z^{\mathrm{genuine}}$.

The second term penalizes any direct dependence between $z^{\mathrm{genuine}}$ and exposure E that is not mediated by U. We implement this using an adversarial discriminator D that tries to recover E from $z^{\mathrm{genuine}}$ and U, while the encoder is trained to fool it. With a gradient reversal layer [74], the adversarial loss becomes

$${\mathcal{L}}_{\mathrm{adv}}=-\mathbb{E}\left[logD(z^{\mathrm{genuine}},U)\right],$$

(3)

which is minimized by the encoder to make E unpredictable. This encourages the representation to be conditionally independent of E given U, thereby removing the influence of the unfair exposure path while keeping the legitimate signal from A through U intact.

4.2.2. Disentangled VAE (Spurious Correlation)

When $c_{\mathrm{spurious}}=1$, the correlation between A and Y is entirely non-causal. In this case we must remove any influence of A from the user representation. We employ a variational autoencoder that factorizes each user interaction vector $x_u$ (e.g., a multi-hot encoding of items clicked) into two independent latent variables: a preference component $z^{\mathrm{pref}}$ and a bias component $z^{\mathrm{bias}}$. The generative model is defined as

$$\begin{array}{cc}\hfill p_{\theta }(x_u\mid z^{\mathrm{pref}},z^{\mathrm{bias}})& =\mathrm{Bernoulli}\left(\sigma \left(g_{\theta }(z^{\mathrm{pref}},z^{\mathrm{bias}})\right)\right),\hfill \end{array}$$

(4)

$$\begin{array}{cc}\hfill p\left(z^{\mathrm{pref}}\right)& =\mathcal{N}(0,I),p\left(z^{\mathrm{bias}}\right)=\mathcal{N}(0,I).\hfill \end{array}$$

(5)

The encoder $q_{\varphi }(z^{\mathrm{pref}},z^{\mathrm{bias}}\mid x_u)$ outputs the parameters of the approximate posterior.

To ensure that $z^{\mathrm{pref}}$ contains no information about the sensitive attribute, we add an independence regularization between $z^{\mathrm{pref}}$ and the attribute vector $a_u$ (one-hot encoding of A). We employ the Hilbert-Schmidt Independence Criterion (HSIC) [75], which measures the dependence between two random variables in reproducing kernel Hilbert spaces:

$$\mathrm{HSIC}(z^{\mathrm{pref}},a)=\parallel \mathbb{E}[\kappa (z^{\mathrm{pref}},·)\otimes \psi (a,·)]-{\mu }_z\otimes {\mu }_a{\parallel }^2.$$

(6)

The overall VAE loss becomes

$$\begin{array}{c}\hfill {\mathcal{L}}_{\mathrm{VAE}}=-{\mathbb{E}}_{q_{\varphi }}\left[log{p}_{\theta }(x_u\mid z^{\mathrm{pref}},z^{\mathrm{bias}})\right]+D_{\mathrm{KL}}(q_{\varphi }\parallel p\left(z\right))+\beta \mathrm{HSIC}(z^{\mathrm{pref}},a).\end{array}$$

(7)

The HSIC penalty drives $z^{\mathrm{pref}}$ towards statistical independence from the sensitive attribute, effectively discarding the spurious signal. After training, we discard $z^{\mathrm{bias}}$ and use only $z^{\mathrm{pref}}$ as the debiased representation for downstream recommendation.

The final debiased representation, denoted $z^{\mathrm{debiased}}$, is set to $z^{\mathrm{genuine}}$ when $c_{\mathrm{spurious}}=0$ and to $z^{\mathrm{pref}}$ when $c_{\mathrm{spurious}}=1$.

4.3. Actor-Critic with Adaptive Fairness Penalty

The debiased representation $z^{\mathrm{debiased}}$ is fed into a reinforcement learning agent that interacts with users over time. We model the sequential recommendation process as an MDP with state $s_t=[z^{\mathrm{debiased}},h_t]$, where $h_t$ is the aggregated history of recent interactions. The action $a_t$ is a slate of K items chosen from the candidate pool; the agent receives an immediate reward $r_t$ defined below.

The reward is composed of an accuracy term and an adaptive fairness penalty:

$$r_t=r_t^{\mathrm{acc}}-\alpha ·{\Phi }_t.$$

(8)

$r_t^{\mathrm{acc}}$ is the standard feedback (e.g., 1 for a click, 0 otherwise). The penalty ${\Phi }_t$ dynamically selects the appropriate fairness metric based on the causal flag:

$${\Phi }_t=\left\{\begin{array}{cc}\max \left(0,{\mathrm{EO}\text{\_}\mathrm{diff}}_t-{\tau }_{\mathrm{EO}}\right),\hfill & \mathrm{if}{c}_{\mathrm{spurious}}=0\hfill \\ \max \left(0,{\mathrm{DP}\text{\_}\mathrm{diff}}_t-{\tau }_{\mathrm{DP}}\right),\hfill & \mathrm{if}{c}_{\mathrm{spurious}}=1.\hfill \end{array}\right.$$

(9)

Here ${\mathrm{EO}\text{\_}\mathrm{diff}}_t=|{\mathrm{TPR}}_t^{\left(1\right)}-{\mathrm{TPR}}_t^{\left(0\right)}|$ and ${\mathrm{DP}\text{\_}\mathrm{diff}}_t=|P(\widehat{Y}=1|A=1)-P(\widehat{Y}=1|A=0)|$, both computed over a sliding window of the most recent W interactions. ${\tau }_{\mathrm{EO}}$ and ${\tau }_{\mathrm{DP}}$ are small tolerance thresholds to prevent over-penalisation of minor fluctuations. This formulation directly enforces the adaptive principle: when causality is genuine, the agent is penalized only for unequal true positive rates; when the association is spurious, it must equalize overall recommendation rates.

We implement the policy using Proximal Policy Optimization (PPO) [52], with an actor network ${\pi }_{\theta }(a_t\mid s_t)$ and a critic network $V_{\psi }\left(s_t\right)$. In addition to the intrinsic reward penalty, we adopt a Lagrangian approach to enforce a long-term fairness budget. Let $\overline{\Phi }$ be the cumulative fairness penalty over the whole trajectory. We introduce a Lagrange multiplier $\lambda$ and augment the PPO objective with a constraint:

$$\underset{\theta }{\max }\underset{\lambda \ge 0}{min}{\mathbb{E}}_{\tau \sim {\pi }_{\theta }}\left[\sum _t{\gamma }^t{r}_t^{\mathrm{acc}}\right]-\lambda \left(\mathbb{E}\left[\overline{\Phi }\right]-ϵ\right),$$

(10)

where $ϵ$ is the maximum allowable long-term unfairness. During training, $\lambda$ is updated by dual gradient ascent: $\lambda \leftarrow \lambda +{\eta }_{\lambda }(\overline{\Phi }-ϵ)$. The actor and critic are updated via the standard PPO clipped objective:

$$\begin{array}{c}\hfill {\mathcal{L}}_{\mathrm{PPO}}\left(\theta \right)={\mathbb{E}}_t\left[min\left({\rho }_t\left(\theta \right){\widehat{A}}_t,\mathrm{clip}({\rho }_t\left(\theta \right),1-{ϵ}_c,1+{ϵ}_c){\widehat{A}}_t\right)\right],\end{array}$$

(11)

where ${\rho }_t\left(\theta \right)={\pi }_{\theta }(a_t|s_t)/{\pi }_{{\theta }_{\mathrm{old}}}(a_t|s_t)$ and ${\widehat{A}}_t$ is the generalized advantage estimate using the value function $V_{\psi }$. The value loss is the squared error

$${\mathcal{L}}_{\mathrm{V}}\left(\psi \right)={\mathbb{E}}_t\left[{(V_{\psi }\left(s_t\right)-R_t)}^2\right].$$

(12)

An entropy bonus $\mathcal{H}\left({\pi }_{\theta }\right)$ is added to encourage exploration.

This design allows the agent to learn a recommendation policy that simultaneously maximizes user satisfaction and maintains long-term fairness, with the definition of fairness adaptively chosen according to the causal nature of each sensitive attribute.

4.4. Training Procedure

The full training algorithm is summarized in Algorithm 1. Stage 1 determines $c_{\mathrm{spurious}}$ offline. Stage 2 pre-trains the appropriate debiasing model to obtain $z^{\mathrm{debiased}}$. Stage 3 then trains the RL agent using the adaptive reward. All components are trained jointly in an end-to-end manner after pre-training.

Algorithm 1: LFR-via-AFMS Training Procedure

5. Experiments

In this section we conduct extensive experiments to evaluate LFR-via-AFMS from multiple perspectives. We first describe the datasets and experimental setup, then present overall performance, followed by detailed ablation studies and parameter analyses.

5.1. Datasets and Settings

We adopt two widely used public recommendation datasets with distinct causal properties.

• MovieLens-1M1: This dataset contains 1,000,209 ratings from 6,040 users on 3,952 movies. User gender is used as the sensitive attribute. Prior studies and preliminary causal analysis show that gender has a genuine causal effect on movie genre preferences (e.g., males tend to prefer action, females romance), making it a representative case of $c_{\mathrm{spurious}}=0$.
• Alibaba display advertising dataset2: This dataset contains 1,140,000 interactions from 10,000 users on 800,000 items. Gender serves as the sensitive attribute. Due to heavy exposure bias (certain ads are historically shown disproportionately to one gender), the correlation between gender and clicks is largely spurious, i.e., $c_{\mathrm{spurious}}=1$.

For both datasets, we filter out users with fewer than 20 interactions to ensure sufficient history. Data is split chronologically: the earliest 80% interactions form the training set, the next 10% validation, and the most recent 10% testing. We report recommendation accuracy via NDCG@K and Recall@K for $K=10,20$. Fairness is measured by the absolute difference in demographic parity ($\Delta DP$) and equal opportunity ($\Delta EO$) across the two gender groups, with lower values indicating better fairness. Long-term fairness drift is measured as the increase in the target fairness metric after 10,000 interaction steps compared to the initial state.

5.1.1. Implementation Details

All models are implemented in PyTorch. The user preference proxy U is obtained from a matrix factorization model with 64 latent dimensions. For the PC algorithm, we use a significance level of 0.01 for conditional independence tests. The path-specific model uses a two-layer MLP encoder with hidden sizes [128, 64] and a discriminator with a single hidden layer of 32 units. The VAE employs symmetric 128-64-32 encoder and decoder architectures with 32-dim $z^{\mathrm{pref}}$ and 16-dim $z^{\mathrm{bias}}$. The HSIC penalty coefficient $\beta$ is set to 0.1.

In the RL stage, we use a PPO agent with a learning rate of $3\times {10}^{-4}$, discount factor $\gamma =0.99$, clipping parameter ${ϵ}_c=0.2$, and entropy coefficient 0.01. The sliding window size W for online fairness estimation is 500. The fairness penalty weight $\alpha$ is 0.1, and tolerance thresholds ${\tau }_{\mathrm{EO}}=0.05$, ${\tau }_{\mathrm{DP}}=0.02$. The Lagrangian multiplier starts at 0.1 with a learning rate of 0.05. All hyperparameters were tuned on the validation set.

5.2. Baselines

We compare LFR-via-AFMS against the following methods:

• BPR-MF [55]: Bayesian Personalized Ranking with matrix factorization, a classic non-fair baseline.
• RLFair: A fairness-aware RL recommender that adds a fixed DP penalty to the reward.
• FairDgcl: A graph contrastive learning method for fairness that uses adversarial debiasing.
• CausalDF [38]: A causal click-bias removal method that uses a causal graph to infer true preference.
• PSFRS [73]: Path-Specific Fair Recommender System that blocks unfair pathways using counterfactual reasoning.
• LFR-via-AFMS-FixedDP: A variant of LFR-via-AFMS that always enforces DP regardless of causal diagnosis.
• LFR-via-AFMS-FixedEO: A variant of LFR-via-AFMS that always enforces EO.
• LFR-via-AFMS-NoCausal: A variant that skips causal identification and always applies the disentangled VAE (spurious branch).

5.3. Overall Performance

Table 1 and Table 2 summarize the accuracy-fairness trade-off on the two datasets.

On MovieLens, LFR-via-AFMS correctly identifies genuine causality and selects EO as the optimization target. It achieves the highest NDCG and Recall, demonstrating that preserving the legitimate $A\to U\to Y$ pathway is crucial for accuracy. Most importantly, it attains the lowest $\Delta$EO (0.0723 at K=10), meaning that truly interested users receive equally accurate recommendations irrespective of gender. The fixed-DP variant, while reducing $\Delta$DP significantly, severely damages recommendation quality (NDCG drops from 0.2356 to 0.2052) and even worsens EO compared to LFR-via-AFMS-FixedEO, confirming that forcing DP under genuine causality leads to contradictory objectives.

For the Alibaba dataset, LFR-via-AFMS correctly switches to DP as the fairness metric. It obtains the best $\Delta$DP (0.0651) while preserving competitive accuracy, closely matching the fixed-EO variant in NDCG but with far superior DP control. The fixed-EO variant, designed for genuine causality, fails to mitigate the spurious DP gap (0.2210). These results strongly support our adaptive metric selection principle.

5.4. Ablation Studies

We conduct ablation experiments to isolate the contribution of each component. Results are summarized in Table 3.

We start from the vanilla BPR-MF (no fairness components). Adding causal diagnosis alone (using the correct metric but without debiased representation) already improves fairness, confirming the value of metric selection. Incorporating the conditional representation learning module further reduces the target unfairness metric significantly while boosting accuracy, as the RL agent operates on cleaner signals. Finally, the full model with adaptive penalty achieves the best trade-off on both datasets. These results verify that all three components are essential and complementary.

5.5. Parameter Sensitivity

We analyze the sensitivity of the fairness penalty weight $\alpha$ and the tolerance thresholds $\tau$ on both datasets. Figure 4 and Figure 5 illustrates the Pareto frontier between recommendation accuracy and the respective target fairness metric as $\alpha$ varies from 0.01 to 1.0.

On MovieLens (Figure 4), increasing $\alpha$ strengthens EO enforcement, steadily reducing $\Delta$EO at a modest cost in NDCG. The curve stays relatively flat for $\alpha \in [0.05,0.2]$, demonstrating robust behavior. On Alibaba (Figure 5), a similar trend is observed for DP: larger $\alpha$ consistently shrinks $\Delta$DP without drastic accuracy degradation until $\alpha >0.5$. The recommended value $\alpha =0.1$ lies in the stable region for both datasets, achieving a favorable balance. Sensitivity analyses for ${\tau }_{\mathrm{EO}}$ and ${\tau }_{\mathrm{DP}}$ yield analogous conclusions, with ${\tau }_{\mathrm{EO}}=0.05$ and ${\tau }_{\mathrm{DP}}=0.02$ providing sufficient noise tolerance without compromising fairness goals.

5.6. Long-Term Fairness Evolution

To assess long-term dynamics, we simulate 10,000 recommendation steps and record the fairness drift. As shown in Figure 6 and Figure 7, LFR-via-AFMS maintains the target fairness metric (EO difference on MovieLens, DP difference on Alibaba) consistently below the tolerance threshold, while fixed-metric variants gradually drift upward due to feedback loops. The Lagrangian multiplier effectively adjusts the penalty strength, preventing fairness violation accumulation.

Table 4 quantifies the fairness drift after the long interaction sequence. LFR-via-AFMS exhibits the smallest increase in unfairness, demonstrating superior stability.

Overall, the empirical evidence confirms that LFR-via-AFMS effectively balances accuracy and fairness across different causal regimes, and that its adaptive design is vital for achieving robust long-term performance.

6. Conclusions and Future Work

We introduced LFR-via-AFMS, a causal-driven fairness-aware recommendation framework that adaptively selects between Equal Opportunity and Demographic Parity based on whether the sensitive attribute’s effect is genuine or spurious. By embedding this adaptive metric into an RL-based long-term optimization, LFR-via-AFMS resolves the contradictions of fixed-metric approaches and achieves state-of-the-art fairness-accuracy balance. Future work will extend the adaptive principle to multiple intersecting sensitive attributes and online causal discovery from dynamic interactions.