Although advancements in deep learning have significantly enhanced the recommendation accuracy of deep recommendation models, these methods still suffer from low recommendation efficiency. Recently proposed tree-based deep recommendation models alleviate the problem by directly learning tree structure and representations under the guidance of recommendation objectives. To guarantee the effectiveness of beam search for recommendation accuracy, these models strive to ensure that the tree adheres to the max-heap assumption, where a parent node's preference should be the maximum among its children's preferences. However, they employ a one-versus-all strategy, framing the training task as a series of independent binary classification objectives for each node, which limits their ability to fully satisfy the max-heap assumption. To this end, we propose a Deep Tree-based Retriever (DTR for short) for efficient recommendation. DTR frames the training task as a softmax-based multi-class classification over tree nodes at the same level, enabling explicit horizontal competition and more discriminative top-k selection among them, which mimics the beam search behavior during training. To mitigate the suboptimality induced by the labeling of non-leaf nodes, we propose a rectification method for the loss function, which further aligns with the max-heap assumption in expectation. As the number of tree nodes grows exponentially with the levels, we employ sampled softmax to approximate optimization and thereby enhance efficiency. Furthermore, we propose a tree-based sampling method to reduce the bias inherent in sampled softmax. Theoretical results reveal DTR's generalization capability, and both the rectification method and tree-based sampling contribute to improved generalization. The experiments are conducted on four real-world datasets, validating the effectiveness of the proposed method.

翻译：尽管深度学习的发展显著提升了深度推荐模型的推荐准确性，但这些方法仍面临推荐效率低下的问题。近期提出的基于树的深度推荐模型通过在推荐目标指导下直接学习树结构与表征，缓解了这一问题。为保证束搜索对推荐准确性的有效性，这些模型致力于确保树结构满足最大堆假设，即父节点的偏好应为其所有子节点偏好中的最大值。然而，它们采用一对多策略，将训练任务构建为每个节点的一系列独立二分类目标，这限制了其完全满足最大堆假设的能力。为此，我们提出一种基于深度树检索器（简称DTR）的高效推荐方法。DTR将训练任务构建为同层树节点上基于softmax的多类别分类，实现了节点间的显式横向竞争和更具区分度的top-k选择，从而在训练过程中模拟束搜索行为。为缓解非叶节点标注导致的次优性，我们提出一种损失函数的校正方法，该方法在期望意义上进一步贴合最大堆假设。由于树节点数量随层数呈指数增长，我们采用采样softmax来近似优化以提升效率。此外，我们提出一种基于树的采样方法以减少采样softmax固有的偏差。理论分析揭示了DTR的泛化能力，且校正方法与基于树的采样均有助于提升泛化性能。在四个真实数据集上进行的实验验证了所提方法的有效性。