Title: Putting BPR in a Box: Bounding the Score Space in Bayesian Personalized Ranking
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: BPR, optimization, recommendation

Abstract: Bayesian Personalized Ranking (BPR) has been widely adopted for recommendation by optimizing pairwise score objectives. However, existing BPR-based methods typically focus on enlarging pairwise score differences, which often leads to excessive separation or clustering of pairwise data—an issue that can result in suboptimal performance. In this work, we propose BoxBPR, a novel framework that introduces explicit box constraints into the pairwise score space of BPR. Specifically, we present the motivation and formulation of both lower and upper bounds, derive a simple yet effective constraint based on the relationships among pairwise data, and directly integrate it into the BPR objective. We then introduce the optimization criteria of BoxBPR and describe the corresponding training process. From both lower- and upper-bound perspectives, we demonstrate that BoxBPR establishes a stronger connection to key top-$K$ evaluation metrics than BPR in recommendation tasks. Extensive experiments on three real-world datasets validate the effectiveness of BoxBPR, and comprehensive analyses further highlight the critical role of lower- and upper-bound constraints in BoxBPR.