The prosperous development of e-commerce has spawned diverse recommendation scenarios (e.g., promotion scenario), and accompanied a new recommendation paradigm, comb-K recommendation. In the promotion scenario, the recommender system first selects K promotional items with lightning deals or limited-time discounts and then dispenses them to each user, encouraging the purchase desire of users and maximizing the total revenue of K items on all users. Significantly different from traditional top-K recommendation, when selecting a combination of K items, comb-K recommendation needs to fully consider the preferences of all users, rather than the preference of a single user. Considering the fact that each user only views a small part of selected items (a.k.a., dispensation window phenomenon), when selecting K items, we need to consider how many items are validly dispensed to each user and indeed generate revenue. To maximize the total revenue of K items, comb-K recommendation needs to address the following questions: (1) How to seamlessly integrating the item selection and item dispensation? (2) How to fully consider the preferences of all users in a productive way? Thus, we take the first step to formula comb-K recommendation as a combinatorial optimization problem with the crucial constraint of the dispensation window. Specifically, we model the promotion scenario as a heterogeneous graph and leverage a heterogeneous graph neural network to estimate user-item preferences, serving as the basis of comb-K recommendation in the user-level. However, for large-scale promotion scenario, the comb-K recommendation will be combination explosion and becomes unsolvable. To handle large-scale promotion scenario, we design a novel heterogeneous graph pooling model to cluster massive users into limited crowds and estimate crowd-item preference, so the large-scale comb-K recommendation becomes solvable in the crowd-level. Then, considering the “long tail” phenomenon in e-commerce, we design a fast strategy called restricted neighbor heuristic search to further accelerate the solving process of large-scale comb-K recommendation. Extensive experiments on four datasets demonstrate the superiority of comb-K recommendation over top-K recommendation. On billion-scale datasets, the proposed comb-K recommendation significantly improves the Total Click and Hit Ratio by 9.35% and 7.14%, respectively.

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