Two-stage recommender systems play a crucial role in efficiently identifying relevant items and personalizing recommendations from a vast array of options. This paper, based on an error decomposition framework, analyzes the generalization error for two-stage recommender systems with a tree structure, which consist of an efficient tree-based retriever and a more precise yet time-consuming ranker. We use the Rademacher complexity to establish the generalization upper bound for various tree-based retrievers using beam search, as well as for different ranker models under a shifted training distribution. Both theoretical insights and practical experiments on real-world datasets indicate that increasing the branches in tree-based retrievers and harmonizing distributions across stages can enhance the generalization performance of two-stage recommender systems.

Two-stage recommender systems play a crucial role in efficiently identifying relevant items and personalizing recommendations from a vast array of options.

Thanks to their scalability, two-stage recommenders are used by many of today's

Two-stage recommender systems play a crucial role in efficiently identifying relevant items and personalizing recommendations from a vast array of options. This paper, based on an error decomposition framework, analyzes the generalization error for two-stage recommender systems with a tree structure, which consist of an efficient tree-based retriever and a more precise yet time-consuming ranker. We use the Rademacher complexity to establish the generalization upper bound for various tree-based retrievers using beam search, as well as for different ranker models under a shifted training distribution. Both theoretical insights and practical experiments on real-world datasets indicate that increasing the branches in tree-based retrievers and harmonizing distributions across stages can enhance the generalization performance of two-stage recommender systems.

Thanks to their scalability, two-stage recommenders are used by many of today's largest online platforms, including YouTube, LinkedIn, and Pinterest. These systems produce recommendations in two steps: (i) multiple nominators--tuned for low prediction latency--preselect a small subset of candidates from the whole item pool; (ii) a slower but more accurate ranker further narrows down the nominated items, and serves to the user. Despite their popularity, the literature on two-stage recommenders is relatively scarce, and the algorithms are often treated as mere sums of their parts. Such treatment presupposes that the two-stage performance is explained by the behavior of the individual components in isolation. This is not the case: using synthetic and real-world data, we demonstrate that interactions between the ranker and the nominators substantially affect the overall performance.

Thanks to their scalability, two-stage recommenders are used by many of today's largest online platforms, including YouTube, LinkedIn, and Pinterest. These systems produce recommendations in two steps: (i) multiple nominators--tuned for low prediction latency--preselect a small subset of candidates from the whole item pool; (ii) a slower but more accurate ranker further narrows down the nominated items, and serves to the user. Despite their popularity, the literature on two-stage recommenders is relatively scarce, and the algorithms are often treated as mere sums of their parts. Such treatment presupposes that the two-stage performance is explained by the behavior of the individual components in isolation. This is not the case: using synthetic and real-world data, we demonstrate that interactions between the ranker and the nominators substantially affect the overall performance.

Production-grade recommender systems rely heavily on a large-scale corpus used by online media services, including Netflix, Pinterest, and Amazon. These systems enrich recommendations by learning users' and items' embeddings projected in a low-dimensional space with two-stage models (two deep neural networks), which facilitate their embedding constructs to predict users' feedback associated with items. Despite its popularity for recommendations, its theoretical behaviors remain comprehensively unexplored. We study the asymptotic behaviors of the two-stage recommender that entail a strong convergence to the optimal recommender system. We establish certain theoretical properties and statistical assurance of the two-stage recommender. In addition to asymptotic behaviors, we demonstrate that the two-stage recommender system attains faster convergence by relying on the intrinsic dimensions of the input features. Finally, we show numerically that the two-stage recommender enables encapsulating the impacts of items' and users' attributes on ratings, resulting in better performance compared to existing methods conducted using synthetic and real-world data experiments.

Two-stage recommender systems are widely adopted in industry due to their scalability and maintainability. These systems produce recommendations in two steps: (i) multiple nominators preselect a small number of items from a large pool using cheap-to-compute item embeddings; (ii) with a richer set of features, a ranker rearranges the nominated items and serves them to the user. A key challenge of this setup is that optimal performance of each stage in isolation does not imply optimal global performance. In response to this issue, Ma et al. (2020) proposed a nominator training objective importance weighted by the ranker's probability of recommending each item. In this work, we focus on the complementary issue of exploration. Modeled as a contextual bandit problem, we find LinUCB (a near optimal exploration strategy for single-stage systems) may lead to linear regret when deployed in two-stage recommenders. We therefore propose a method of synchronising the exploration strategies between the ranker and the nominators. Our algorithm only relies on quantities already computed by standard LinUCB at each stage and can be implemented in three lines of additional code. We end by demonstrating the effectiveness of our algorithm experimentally.