用新损失函数缓解推荐系统对热门商品的偏倚，提升公平性。

Recommender systems based on graph neural networks (GNNs) have been proved to perform well on user-item interactions. However, they commonly suffer from popularity bias -- the tendency to over-recommend popular items -- resulting in less personalization, unfair exposure and lower recommendation diversity. Current solutions address popularity bias through different stages of the recommendation pipeline, including pre-processing methods that may distort data distributions, in-processing approaches which can complicate optimization, and post-processing techniques that are limited in correcting bias already embedded in the learned representations. To address these limitations, we propose PBiLoss, a novel regularization-based loss function designed to explicitly counteract popularity bias in graph-based recommenders. PBiLoss augments traditional training objectives by penalizing the model's inclination toward popular items, thereby encouraging the recommendation of less popular but potentially more personalized content. We introduce two sampling strategies -- Popular Positive (PopPos) and Popular Negative (PopNeg) -- and explore two methods to distinguish popular items -- one based on a fixed popularity threshold and another without any threshold -- making the approach flexible and adaptive. Our proposed method is model-agnostic and can be seamlessly integrated into state-of-the-art graph-based frameworks such as LightGCN and its variants. Extensive experiments carried out on datasets including Epinions, iFashion, and MovieLens highlight the advantages of the PBiLoss for enhancing fairness in recommendations, decreasing PRU and PRI by up to 10\%, compared to other baseline models, while maintaining accuracy and other standard metrics intact in the process.