Bundle Recommendation: Methods and Challenges

• Bundle Recommendation (BR) is a task that recommends sets of items as a whole, leveraging both discriminative ranking and generative bundle construction strategies.
• Discriminative methods rank existing bundles based on user–bundle interactions using techniques like Bayesian Personalized Ranking and graph-based models.
• Recent approaches focus on intent disentanglement, handling cold-start challenges, and incorporating fairness using multi-view graph representations.

Searching arXiv for recent and foundational bundle recommendation papers. arxiv_search({"query":"all:\"bundle recommendation\" survey CrossCBR MultiCBR GPCL", "max_results": 10, "sort_by": "relevance"}) Bundle recommendation (BR) is the recommendation task in which the target object is a bundle, namely a set of items consumed as a whole rather than as isolated items. Recent work organizes BR into two categories based on bundling strategy: discriminative bundle recommendation, which ranks pre-defined bundles, and generative bundle recommendation, which constructs new bundles on the fly (Sun et al., 2024). A standard formulation uses a user set $\mathcal U$, an item set $\mathcal I$, a bundle set $\mathcal B$, and three binary relations: user–bundle interactions $X$, user–item interactions $Y$, and bundle–item affiliations $Z$; the discriminative task learns a score such as $\hat y_{ub}=f_{\mathrm{disc}}(u,b,X,Y,Z,C;\theta)$, while the generative task learns a generator such as $b'=g_{\mathrm{gen}}(u,X,Y,Z,C;\phi)$ (Sun et al., 2024). In many operational settings, BR is also cast as user–bundle link prediction on a tripartite user–item–bundle graph (Deng et al., 2021).

1. Formal problem setting and task variants

In discriminative BR, the system ranks bundles from a fixed catalog for each user. The typical data model is implicit feedback: $X_{ub}=1$ if user $u$ interacted with bundle $\mathcal I$0, $\mathcal I$1 if user $\mathcal I$2 interacted with item $\mathcal I$3, and $\mathcal I$4 if bundle $\mathcal I$5 contains item $\mathcal I$6 (Sun et al., 2024). Optimization is usually framed as ranking. A common objective is Bayesian Personalized Ranking,

$\mathcal I$7

which appears across BR models and reproducibility studies (Sun et al., 2024).

A second formulation treats BR explicitly as graph learning. BundleNet constructs a unified graph with users, items, and bundles, and learns to predict missing user–bundle edges (Deng et al., 2021). BGCN similarly unifies user–item interaction, user–bundle interaction, and bundle–item affiliation into a heterogeneous graph, using item nodes as bridges between users and bundles (Chang et al., 2020). This graph-centered view has become a dominant formalization for discriminative BR.

Generative BR departs from fixed-catalog ranking. BundleMage defines bundle matching and bundle generation as separate but related tasks: given user item and bundle histories, the model ranks existing bundles, and given an incomplete bundle, it predicts additional items to complete a personalized bundle (Jeon et al., 2022). BRIDGE reframes BR through instruction-driven pseudo bundle generation, first constructing instructive item clusters and then generating pseudo “ideal” bundles before retrieving real bundles (Bui et al., 2024). In the survey taxonomy, these models occupy the generative branch, where the output is not merely a score over pre-existing bundles but a constructed or reconstructed item set (Sun et al., 2024).

2. Representation learning in discriminative BR

The survey identifies three major families for discriminative BR representation learning: factorization models, attention-based aggregation, and graph neural networks (Sun et al., 2024). Factorization-based methods learn user, item, and bundle vectors and approximate relations such as $\mathcal I$8, $\mathcal I$9, and $\mathcal B$0 (Sun et al., 2024). Attention-based models represent a bundle as a weighted sum of item embeddings, where the weights depend on user–item–bundle interactions (Sun et al., 2024). GNN-based models build bipartite, tripartite, heterogeneous, or hypergraph structures over $\mathcal B$1, $\mathcal B$2, and $\mathcal B$3, then propagate messages to obtain user and bundle representations (Sun et al., 2024).

Method	Core mechanism	Distinguishing emphasis
BGCN	Two-level GCN on a heterogeneous graph	Item-level semantics and hard negatives
CrossCBR	Cross-view contrastive learning	Cooperative association between bundle and item views
MIDGN	Multi-view intent disentangling	Global and local intent structure
MultiCBR	Multi-view LightGCN with early fusion and late contrast	UB, UI, and BI relations
HED	Complete hypergraph with dual convolution	Ternary user–item–bundle relations
BunCa	Causation-enhanced multi-view learning	Asymmetric item affiliations
GPCL	Gaussian embeddings with prototypical contrastive learning	Uncertainty and sampling bias

BGCN is an early graph model that performs item-level propagation on the user–item graph and bundle-level propagation on the user–bundle graph, while also exploiting bundle–bundle overlap and hard-negative sampling (Chang et al., 2020). CrossCBR factorizes BR into a bundle view over the user–bundle graph and an item view over the user–item graph with bundle–item pooling, then aligns the two views by cross-view contrastive learning (Ma et al., 2022). Its central claim is that the cooperative association between different views should be modeled explicitly rather than treated as a loose combination of predictions (Ma et al., 2022).

Subsequent work broadened the view structure. MIDGN assumes that each user or bundle exhibits $\mathcal B$4 latent intents and disentangles them from a global view and a local view, aligning view-specific intent chunks with an InfoNCE objective (Zhao et al., 2022). MultiCBR extends two-view contrastive learning to three explicit graphs—UB, UI, and BI—and reverses the previous “early contrast and late fusion” pattern into an “early fusion and late contrast” design (Ma et al., 2023). EBRec argues that item-level bundle representations in prior contrastive models receive insufficient information from bundle affiliations, and therefore enhances them through bundle–user–item high-order correlations and augmented user–item interactions generated from pre-trained models (Du et al., 2023).

Another line of work targets structural expressivity beyond bipartite or tripartite graphs. HED builds a complete hypergraph whose adjacency is partitioned into nine blocks, then combines hypergraph convolution with an additional U–B interaction convolution to preserve ternary user–item–bundle relations (Li et al., 2023). BunCa introduces two views: a Cohesive View based on LightGCN over user–bundle, user–user, and bundle–bundle relations, and a Coherent View based on a Multi-Prospect Causation Network for asymmetric item affiliations (Nguyen et al., 2024). GPCL addresses uncertainty directly by embedding each user, bundle, and item as a Gaussian distribution rather than a fixed vector, and adds a prototypical contrastive learning module to capture contextual information and mitigate the sampling bias issue caused by semantically similar negatives (Liu et al., 2023).

3. Generative, cold-start, and adaptive bundle modeling

Generative BR addresses the limitation that a fixed bundle catalog may not match user imagination or newly emerging products. BundleMage combines bundle matching and bundle generation through multi-task learning with partially shared parameters, using an adaptive gate to mix item-level and bundle-level user preferences for matching and a generation module to complete an incomplete bundle (Jeon et al., 2022). BRIDGE adopts an instruction-driven formulation: it mines item–item co-occurrence from user–item interactions to form instructive clusters, uses a Transformer-style encoder–decoder to generate pseudo ideal bundles, and finally retrieves real bundles via similarity scoring (Bui et al., 2024).

Cold-start BR has become a specialized subproblem because user–bundle interactions are much sparser than user–item interactions. DisCo addresses cold-start by replacing static cold bundle embeddings with a personalized diffusion backbone that generates a bundle in distribution space for each user, guided by disentangled aspects of user interest derived from LightGCN and multi-head self-attention (Bui et al., 20 May 2025). Its ranking stage scores real bundles by the inner product between a generated soft item distribution and the bundle indicator vector, avoiding the need to learn a distinct embedding for each unseen bundle (Bui et al., 20 May 2025). EpicCBR tackles cold-start from a different angle: it mines item relations to construct user profiles, uses a popularity-based method to characterize new bundles, and learns a dual-scenario contrastive framework that integrates cold-start and warm-start scenarios (Li et al., 12 Feb 2026).

Adaptation is also required when the bundle itself changes over time. RDiffBR studies item-level dynamic variability, where a bundle’s theme remains stable but its item membership changes because of seasonality, inventory adjustments, or preference shifts (Zhang et al., 4 Jul 2025). It is a model-agnostic residual diffusion wrapper that denoises item-level bundle embeddings produced by a backbone BR model, with the explicit goal of repairing embeddings under perturbed bundle–item affiliations (Zhang et al., 4 Jul 2025). This setting differs from classic cold-start: the bundle identity persists, but the affiliated items are no longer static.

A domain-specific extension appears in multi-round service bundle recommendation. DLISR models iterative mashup development, where a developer progressively selects services and the recommender updates the next-service suggestion conditioned on the target mashup, the already selected services, and the candidate service (Ma et al., 2021). Although developed in service-oriented computing rather than retail BR, it exemplifies a broader expansion of bundle recommendation toward interactive and sequential settings (Ma et al., 2021).

4. Data resources, evaluation, and empirical practice

The BR literature uses a broad set of public benchmarks. The survey lists music playlists such as NetEase Cloud Music, Spotify, and AOTM; book lists such as Youshu and Goodreads; fashion datasets such as iFashion and Clothing–Amazon; game bundles such as Steam; meal datasets such as MealRec and MealRec$\mathcal B$5; travel-package and trajectory datasets; service-package data from ProgrammableWeb; and additional domains including Zhihu answer lists and retail baskets (Sun et al., 2024). Among these, Youshu, NetEase, and iFashion recur as standard discriminative BR benchmarks in CrossCBR, MIDGN, MultiCBR, HED, BunCa, DisCo, EpicCBR, and fairness studies (Ma et al., 2022).

Evaluation is dominated by top-$\mathcal B$6 ranking metrics. The survey identifies Precision@K, Recall@K, F1@K, NDCG@K, MAP, MRR, and AUC as common accuracy and ranking measures, and also catalogs diversity, coverage, entropy, novelty, and fairness or exposure metrics (Sun et al., 2024). In discriminative BR reproducibility experiments, the survey reports Recall@20/40 and NDCG@20/40 for methods including CrossCBR, MultiCBR, BundleGT, MIDGN, BGCN, and HyperMBR, and observes that cooperative multi-view methods outperform single-view or unified-view baselines, while graph-based models outperform classic collaborative filtering baselines (Sun et al., 2024).

Empirical practice also includes online deployment. BundleNet was deployed for more than one year in a popular NetEase game, using a workflow of daily data collection and preprocessing, model fine-tuning from the previous checkpoint, bulk forward inference over user–bundle pairs, and top-$\mathcal B$7 retrieval stored in online cache (Deng et al., 2021). The reported online gains were more than $\mathcal B$8 improvement on bundle conversion rate and more than $\mathcal B$9 relative improvement on gross merchandise volume (Deng et al., 2021). GPCL likewise reports deployment on a real-world e-commerce platform with substantial improvements, although the abstract does not give numerical details (Liu et al., 2023).

5. Fairness, sparsity, uncertainty, and robustness

Sparsity is a structural property of BR rather than an incidental nuisance. CLBR characterizes the problem as severe on both the user side, where each user interacts with few bundles, and the creator side, where the combinatorial space of possible bundles makes bundle–item affiliations sparse as well (Zhu et al., 2022). To mitigate this, it proposes counterfactual data augmentation and a counterfactual constraint, generating counterfactual graph views through a heuristic sampler and constraining representation consistency between factual and counterfactual graphs (Zhu et al., 2022). This line of work frames sparsity not only as missing data but also as insufficient graph signal for GNN propagation.

Uncertainty and false negatives are additional issues in contrastive BR. GPCL argues that existing successful solutions ignore the uncertainty issue, which has significant impact because highly sparse or diverse settings lack discriminative information, and that instancewise contrastive learning fails to distinguish semantically similar negatives, producing a sampling bias issue (Liu et al., 2023). Its Gaussian embeddings and prototypical contrastive learning are targeted responses to those two failure modes (Liu et al., 2023). A plausible implication is that BR representation learning increasingly treats uncertainty estimation and negative-sample quality as first-class modeling problems rather than secondary regularization details.

Fairness introduces a multi-layered complication because exposure is generated at the bundle level but inherited by items inside the recommended bundle. A reproducibility study of product-side fairness in BR analyzes exposure disparities at both the bundle and item levels using six metrics: Exposed Utility Ratio, Realized Utility Ratio, Expected Exposure Loss, Expected Exposure Relevance, Expected Exposure Disparity, and Demographic Parity (Nguyen et al., 18 Jul 2025). The study finds that exposure patterns differ notably between bundles and items, that fairness assessments vary considerably depending on the metric used, and that bundle-level fairness does not imply item-level fairness (Nguyen et al., 18 Jul 2025). It also reports that when users interact more frequently with bundles than with individual items, BR systems tend to yield fairer exposure distributions across both levels (Nguyen et al., 18 Jul 2025).

Robustness must also account for changing bundle composition. RDiffBR shows that mainstream BR models can fluctuate or decline when bundle–item affiliations vary at inference time, and proposes residual diffusion to repair item-level bundle embeddings under such perturbations (Zhang et al., 4 Jul 2025). Together with fairness work, this suggests that BR cannot be evaluated only by static top-$X$0 accuracy on fixed bundle catalogs.

6. Open challenges and emerging directions

The survey highlights four persistent challenges. First, representation learning in non-Euclidean spaces remains open because user–bundle–item interactions may form tree-like or hierarchical structures; existing hyperbolic models are early attempts, but future work is directed toward native hyperbolic or adaptive Riemannian GNNs (Sun et al., 2024). Second, data sparsity and cold-start remain central, especially for new bundles with zero interaction history; promising directions include multimodal side information and LLM or vision–LLM support for zero-shot or few-shot bundle embedding (Sun et al., 2024).

Third, user intent and dynamic generation are increasingly important in generative BR. The survey notes that high-quality bundles reflect a coherent underlying intent, while many generative models do not model intent explicitly (Sun et al., 2024). MIDGN’s intent disentanglement, BRIDGE’s instruction-driven generation, and diffusion-based cold-start models such as DisCo indicate three distinct attempts to formalize intent: latent intent chunks, generated instructions, and personalized distribution-space generation (Zhao et al., 2022). This suggests a convergence between discriminative intent modeling and generative bundle construction.

Fourth, responsible BR extends beyond popularity bias. The survey identifies fairness and exposure as emerging concerns and points toward causal or counterfactual frameworks for diagnosing systemic bias dynamically (Sun et al., 2024). The fairness reproducibility study sharpens that agenda by recommending multi-objective training with both bundle-level and item-level fairness constraints, group definitions beyond popularity, causal approaches to distinguish model bias from low utility, and online evaluation of fairness–accuracy–business trade-offs (Nguyen et al., 18 Jul 2025).

Across these directions, BR is no longer only a ranking problem over a fixed bundle catalog. It is now simultaneously a heterogeneous graph learning problem, a multi-view and contrastive representation problem, a generative modeling problem, and an evaluation problem involving fairness, robustness, and deployment constraints (Sun et al., 2024).