Towards Optimizing Top-$K$ Ranking Metrics in Recommender Systems

Weiqin Yang, Jiawei Chen, Shengjia Zhang, Peng Wu, Yan Feng, Chun Chen, Can Wang

Keywords: Recommender Systems, Surrogate Loss, Top-K Recommendation, NDCG@K

TL;DR: This paper proposes a novel recommendation loss in the form of weighted SL, which directly optimizes Top-$K$ ranking metrics such as NDCG@$K$.

Abstract:

In the realm of recommender systems (RS), Top-$K$ metrics such as NDCG@$K$ are the gold standard for evaluating performance. Nonetheless, during the training of recommendation models, optimizing NDCG@$K$ poses significant challenges due to its inherent discontinuous nature and the intricacies of the Top-K truncation mechanism. Recent efforts to optimize NDCG@$K$ have either neglected the Top-$K$ truncation or suffered from low computational efficiency. To overcome these limitations, we propose SoftmaxLoss@$K$ (SL@$K$), a new loss function designed as a surrogate for optimizing NDCG@$K$ in RS. SL@$K$ integrates a quantile-based technique to handle the complex truncation term; and derives a smooth approximation of NDCG@$K$ to address discontinuity. Our theoretical analysis confirms the close bounded relationship between NDCG@$K$ and SL@$K$.
Besides, SL@$K$ also exhibits several desirable properties including concise formulation, computational efficiency, and noisy robustness. Extensive experiments on four real-world datasets and three recommendation backbones demonstrate that SL@$K$ outperforms existing loss functions with a notable average improvement of 6.19\%.

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 10372