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Advancing Loss Functions in Recommender Systems: A Comparative Study with a Rényi Divergence-Based Solution
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Analyzes Softmax Loss and Cosine Contrastive Loss as DRO-enhanced losses with different divergences, and proposes DrRL, a Rényi-divergence-constrained DRO loss that generalizes both for recommendation.
Problem
Softmax Loss (SL) is sensitive to false negatives and Cosine Contrastive Loss (CCL) discards most negatives via truncation, so recommender loss functions have robustness and data-utilization limitations.
Approach
Shows SL (KL-constrained DRO) and CCL (worst-case regret-constrained DRO) are both DRO on the negative distribution; replaces their divergences with the Rényi (Cressie-Read) divergence, yielding a closed-form loss with polynomial weighting, a learnable personalized truncation margin, and generalization of SL (gamma→1) and CCL (gamma→∞).
Key results
- On MF backbone Gowalla, DrRL reaches Recall@20 0.1785 vs 0.1652 for the best baseline CCL (+8.06%).
- DrRL improves over the best baseline on all datasets and backbones, with statistically significant gains (p<0.05) reported.
- Under temporal shift on AmazonKitchen, DrRL achieves Recall@20 0.02077 vs 0.02053 for CCL, the next best.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DrRL instead of the strongest baseline loss | MF · Gowalla | Recall@20: +8.06% | Helped |
| Use DrRL instead of the strongest baseline loss | MF · Gowalla | NDCG@20: +11.98% | Helped |
| Use DrRL instead of the strongest baseline loss | MF · AmazonKitchen | Recall@20: +5.04% | Helped |
| Use DrRL instead of the strongest baseline loss | MF · AmazonKitchen | NDCG@20: +3.05% | Helped |
| Use DrRL instead of the strongest baseline loss | MF · AmazonElectronics | Recall@20: +2.92% | Helped |
| Use DrRL instead of the strongest baseline loss | MF · AmazonElectronics | NDCG@20: +2.10% | Helped |
| Use DrRL instead of the strongest baseline loss | MF · AmazonBeauty | Recall@20: +3.13% | Helped |
| Use DrRL instead of the strongest baseline loss | MF · AmazonBeauty | NDCG@20: +1.61% | Helped |
| Add the learnable margin strategy (ablation) | DrRL · AmazonKitchen | Recall@20: 0.0482 -> 0.0501 | Helped |
| Add the learnable margin strategy (ablation) | DrRL · AmazonBeauty | Recall@20: 0.1582 -> 0.1645 | Helped |
| Add the personalized margin strategy (ablation) | DrRL · AmazonKitchen | Recall@20: 0.0477 -> 0.0501 | Helped |
| Add the personalized margin strategy (ablation) | DrRL · AmazonBeauty | Recall@20: 0.1579 -> 0.1645 | Helped |
Surprising findings
- CCL filters out over 90% of negative instances at the optimal truncation threshold.
- SL assigns noisy false-negative items weights often over 20 times larger than average.
Limitations
- Gains on some settings are small (e.g., +1.0% NDCG on Gowalla with LightGCN, +0.02 pt on temporal shift).
- Performance is concave in gamma, requiring tuning of gamma and c_gamma(eta) across settings.
- Analysis restricted to cosine similarity and basic SL, not the SL variants.
Experimental setup
Datasets: Gowalla AmazonKitchen AmazonElectronics AmazonBeauty
Benchmarks: Gowalla AmazonKitchen AmazonElectronics AmazonBeauty
Metrics: Recall@20 NDCG@20
Baselines: MSE BCE BPR CCL SL BSL AdvInfoNCE LLPAUC
Builds on: Softmax Loss Cosine Contrastive Loss Distributionally Robust Optimization BSL
Closest papers by meaning
- PSL: Rethinking and Improving Softmax Loss from Pairwise Perspective for Recommendation (NeurIPS 2024 · similarity 0.91)
- On Softmax Direct Preference Optimization for Recommendation (NeurIPS 2024 · similarity 0.88)
- Learning-Efficient Yet Generalizable Collaborative Filtering for Item Recommendation (ICML 2024 · similarity 0.88)
- From Pairwise to Ranking: Climbing the Ladder to Ideal Collaborative Filtering with Pseudo-Ranking (AAAI 2025 · similarity 0.86)
- Preference Diffusion for Recommendation (ICLR 2025 · similarity 0.85)
- Temporally and Distributionally Robust Optimization for Cold-Start Recommendation (AAAI 2024 · similarity 0.84)
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