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Beyond Observed Auxiliary Relations: Environment-Conditioned Modeling for Multi-Behavior Recommendation

Seunghan Lee, Hyunsik Yoo, Jian Kang, Susik Yoon, SeongKu Kang

arXiv:2608.22920v1cs.AIcs.LG

TL;DR

MBR must handle missing auxiliary observations that limit generalization and unreliable signals that may misalign with target behavior. BOAR uses two observability-conditioned modules for densification and refinement, and experiments show particularly strong gains for hidden target items without auxiliary behaviors.

  • Problem

    MBR faces missing auxiliary signals that do not necessarily indicate absent interest and unreliable signals that do not necessarily indicate target intent.

  • Method

    BOAR conditions two complementary rewiring modules on auxiliary observability, using densification for hidden preferences and refinement for unreliable auxiliary relations.

  • Results

    BOAR achieves consistent gains, particularly on hidden target items without auxiliary behaviors, validating its ability to capture preferences beyond observed auxiliary relations.

  • Takeaways & Limitations

    Environment-conditioned modular modeling addresses missing and unreliable auxiliary signals through complementary strategies tailored to auxiliary observability.

  • Takeaways & Limitations

    The evaluation uses hidden-preference discovery and noise suppression as proxy tests because ground-truth purchase labels are unavailable for every interaction edge.

Abstract

from arXiv · show

Multi-behavior recommendation (MBR) leverages auxiliary behavioral signals, such as clicks and add-to-cart, to enhance target behavior prediction like purchases. While recent graph neural network-based approaches have achieved strong performance by systematically propagating auxiliary behavior signals, they still suffer from two fundamental challenges inherent to auxiliary behaviors: (1) missing auxiliary signals, which hinder generalization to items without auxiliary observations, and (2) unreliable auxiliary signals, which amplify noise misaligned with the target behavior. To address these challenges in a unified manner, we propose BOAR, an environment-conditioned MBR framework that addresses missing and unreliable auxiliary signals through two complementary modules conditioned on auxiliary observability. Extensive experiments demonstrate that BOAR consistently outperforms state-of-the-art baselines, achieving up to 7.82% gains in HR@10 overall and up to 44.2% gains for target items without auxiliary observations, highlighting its ability to capture hidden preferences beyond observed auxiliary relations. Our code is available at: https://github.com/LSH0411/BOAR.

1 Introduction

MBR combines auxiliary behaviors with target behavior signals, but missing and unreliable auxiliary observations challenge generalization and target alignment. BOAR addresses these challenges with environment-conditioned complementary modules.

  • Auxiliary behaviors such as clicks, cart additions, and wishlists provide complementary signals for predicting target behaviors such as purchases.
  • GNN-based MBR methods propagate auxiliary behavior signals through behavior-specific graph relations to enhance target prediction.
  • Missing auxiliary signals are observation-biased and do not necessarily indicate absent user interest.
  • MBR must recommend target-positive items without auxiliary behaviors because observed interactions cover only part of the inference space.
  • BOAR rewires auxiliary relations using observability-dependent strategies for hidden-preference recovery and unreliable-signal filtering.

2 Related Works

MBR research has progressed from matrix factorization and neural models to graph-based methods, but existing approaches do not jointly resolve missing and unreliable auxiliary signals. BOAR is motivated by observability-conditioned graph rewiring tailored to these imperfections.

  • Multi-Behavior Recommendation (MBR): MBR methods span matrix factorization, deep neural networks, attention mechanisms, and increasingly dominant GNN-based approaches.
  • Multi-Behavior Recommendation (MBR): Existing methods encode behaviors through unified graphs, behavioral sequences, parallel behavior graphs, self-supervised learning, and multi-task learning.
  • Limitations of Existing Methods: MEMBER addresses missing auxiliary signals, while MuLe and related methods address unreliable signals, but prior methods do not jointly address both challenges.
  • Graph Rewiring for Imperfect Graphs: Graph rewiring reconstructs graph connections by adding potential edges and pruning unreliable ones, but generic similarity-based rewiring can amplify observability-related imperfections in MBR.

3 Preliminaries

The formulation represents target prediction over user-item behavior graphs and conditions prediction on whether auxiliary interactions are observed. BOAR uses two sub-modules whose outputs are softly aggregated according to auxiliary observability.

  • Problem Formulation: Each behavior is represented as a bipartite user-item graph, with auxiliary interactions collected separately from the target behavior graph.
  • Problem Formulation: The model learns a function estimating the probability that a user exhibits the target behavior for an item.
  • Problem Formulation: The formulation targets missing auxiliary signals and unreliable auxiliary signals as distinct problems arising from auxiliary behaviors.
  • Environment-Conditioned Modeling: Target-graph densification recovers hidden target items when auxiliary evidence is absent, while auxiliary-graph pruning suppresses noise when evidence is abundant.
  • Environment-Conditioned Modeling: Auxiliary observability is defined from the presence or absence of observed auxiliary interactions, although unobserved pairs may become observable as activity continues.
  • Environment-Conditioned Modeling: Two environment-conditioned sub-modules separately handle auxiliary-unobserved and auxiliary-observed conditions, then combine their predictions using soft observability-based weights.

4 Proposed Method

BOAR constructs shared representations and applies two environment-conditioned modules: debiased densification for missing auxiliary evidence and target-guided refinement for unreliable evidence. The densification pathway suppresses popularity bias, mines hidden preferences, selectively augments target relations, and stabilizes the added signals through contrastive learning.

  • 4.1 Input Representation Construction: BOAR uses global-graph and target-behavior representations, splitting the initial embedding to support environment-conditioned modules without increasing model capacity.Global embeddings provide densification or refinement signals, while target embeddings support final prediction.
  • 4.2 Debiased Densification Module: The debiased densification module suppresses popularity-driven bias, mines hidden preferences, and injects the resulting knowledge into target prediction.Its three components are auxiliary popularity adversarial learning, target hidden preference mining, and debiased densification learning.
  • 4.2.2 Target Hidden Preference Miner: Angular LSH retrieves candidate items without exhaustive pairwise similarity computation, after which learnable edge selection retains candidates aligned with target behavior.The retrieval pipeline uses random angular projections, bucket assignment, top-n cosine-similarity retrieval, and differentiable add-or-skip decisions.
  • 4.2.2 Target Hidden Preference Miner: The densification graph retains original target edges and adds selected candidate edges with weights combining angular similarity and magnitude consistency.The weighted augmented graph is then used to propagate representations.
  • 4.2.3 Debiased Densification Learning: Contrastive densification learning aligns original and augmented target embeddings, encouraging signals supported by both graph views rather than treating augmented edges as ground truth.The overall densification objective combines user- and item-side losses with loss-balancing hyperparameters.
  • 4.2.3 Debiased Densification Learning: Theoretical results establish unbiasedness of the IPS-weighted loss, suppression of popularity-driven bias by GRL, and the joint necessity of both for hidden preference recovery.These claims are stated as Theorem A.1, Lemma A.2, and Corollary A.3.

4.3 Target-Guided Refinement Module

The target-guided refinement module uses target behavior signals to make auxiliary representations and graph structures more target-consistent. It adaptively gates auxiliary features, prunes unreliable edges, and learns refinement through contrastive alignment and target ranking.

  • 4.3 Target-Guided Refinement Module: The refinement module prunes and reweights auxiliary behavior graphs while using target-guided preference learning to optimize target behavior prediction.It contains a target-guided auxiliary graph refiner and target-guided preference learning.
  • 4.3.1 Target-Guided Auxiliary Graph Refiner: A feature-wise gate balances auxiliary representations against fixed target anchors separately at each feature dimension.The gate conditions on both representations and filters auxiliary features inconsistent with the target preference space.
  • 4.3.1 Target-Guided Auxiliary Graph Refiner: The module estimates auxiliary-observation propensity with binary cross-entropy and uses inverse propensity weighting to correct observation bias.Pairs with low auxiliary-observation propensity are up-weighted, while pairs with high propensity are down-weighted.
  • 4.3.1 Target-Guided Auxiliary Graph Refiner: Differentiable keep-or-drop decisions selectively prune auxiliary edges, and the retained edges form weighted refined adjacency matrices for behavior-specific propagation.The same refinement procedure is applied to each auxiliary behavior.
  • 4.3.2 Target-Guided Preference Learning: Contrastive refinement aligns auxiliary representations with fixed target embeddings, while attention aggregates behavior-specific embeddings according to target relevance.The resulting aggregated representations produce target preference scores optimized with a BPR loss.
  • 4.4 Modular Integration: Soft propensity-based assignment routes each target interaction to the two modules according to auxiliary-observation likelihood and allows complementary signals from both modules.Replacing this with a hard indicator would route each instance exclusively to one module.

5 Experiments

Experiments evaluate BOAR across benchmark datasets, comparison settings, stress tests, ablations, hyperparameters, and efficiency. BOAR performs especially strongly for target items without auxiliary observations while maintaining competitive efficiency.

  • Experimental Setup: Experiments use Tmall, Taobao, and JData, treating buy as the target behavior and comparing BOAR with 13 single- and multi-behavior baselines.The baselines include MF-BPR, LightGCN, and eleven multi-behavior methods.
  • Overall Performance: BOAR achieves the best performance in general and unobserved settings across all datasets and metrics.In the general setting, gains reach 7.82% in HR@10 and 15.00% in NDCG@10; in the unobserved setting, they reach 44.2% and 36.7%, respectively.
  • Overall Performance: In the observed setting, BOAR is best or second-best, trading some observed-environment capacity for substantially stronger unobserved-item performance and the best general performance.HGIB can lead on datasets where its capacity is focused exclusively on pruning-based rewiring.
  • Stress Testing: In controlled stress tests, BOAR shows the smallest performance degradation as hidden preferences or noisy auxiliary interactions increase.Debiased densification recovers removed target-related signals, while target-guided refinement suppresses noise propagation.
  • Ablation Study: Ablations show that hidden-preference mining, combined representation- and prediction-level debiasing, target-guided refinement, and soft modular assignment are important to BOAR’s performance.Removing Ldense or TAGR degrades results, while hard or learnable assignment also causes performance drops.
  • Complexity Analysis: BOAR has the fastest inference latency, fastest per-epoch training on Tmall and Taobao, and comparable training time to HGIB on JData.It adds only a small number of parameters, mainly lightweight linear layers, and applies densification only during training.

6 Conclusion

The paper identifies missing and unreliable auxiliary signals as central challenges in multi-behavior recommendation and proposes BOAR to address them conditionally. Experiments report particularly strong gains for hidden target items without auxiliary behaviors, while future work includes streaming settings.

  • Missing and unreliable auxiliary signals are identified as two fundamental challenges in multi-behavior recommendation.
  • BOAR uses two complementary modules conditioned on auxiliary observability to address these challenges.
  • Experiments show particularly strong gains on hidden target items without auxiliary behaviors, and future work may study continuously evolving interactions.

A.1.1 On the Validity of Debiasing in BOAR.

BOAR combines inverse propensity scoring and adversarial learning to address observation bias in auxiliary behaviors. The supplied analysis gives IPS an unbiasedness guarantee under correct propensities and links adversarial alignment to less popularity-driven bias in item representations.

  • IPS validity: Under correct propensities, IPS has zero bias relative to the ideal risk.The theorem assumes p_obs(u,i) > 0 and exact propensity estimates.
  • IPS validity: BOAR estimates pair-level auxiliary-observation propensities with a lightweight binary classifier and uses self-normalized inverse propensity weights.Low-propensity pairs are up-weighted, while high-propensity pairs are down-weighted to correct observation bias.
  • Adversarial debiasing: The adversarial component aligns item representations across above- and below-median auxiliary-popularity distributions.Its classifier distinguishes items by whether auxiliary interaction counts exceed or fall below the median.
  • Adversarial debiasing: Driving the optimal domain-classifier error toward 1/2 implies vanishing H-divergence between the two representation distributions.This is the theoretical condition used to interpret adversarial suppression of auxiliary-popularity information.
  • Complementarity: Removing either GRL or IPS leaves a distinct observation bias that hinders reliable recovery of hidden preferences.Without GRL, candidate quality suffers from popularity-driven representation bias; without IPS, ranking remains biased toward frequently auxiliary-observed items.

GenAI Usage Disclosure

The authors report limited LLM use for manuscript grammar polishing and code debugging, with all outputs verified and revised by the authors.

  • GenAI Usage Disclosure: LLM tools were used only for grammar polishing and code debugging, while the authors conducted the core research process without LLM assistance.The authors state that all LLM outputs were verified and revised.
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