# Lower-Left Partial AUC: An Effective and Efficient Optimization Metric for Recommendation

arXiv: https://arxiv.org/abs/2403.00844 · HTML: https://mlsanity.com/paper/2403.00844/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 47 references that are in the map.
- First posted on arXiv 29 Feb 2024.

## Builds on (most cited first, 21 of 21)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Ups and Downs: Modeling the Visual Evolution of Fashion Trends with One-Class Collaborative Filtering](https://mlsanity.com/paper/1602.01585/) (2016)
- [Denoising Implicit Feedback for Recommendation](https://mlsanity.com/paper/2006.04153/) (2020)
- [SimpleX: A Simple and Strong Baseline for Collaborative Filtering](https://mlsanity.com/paper/2109.12613/) (2021)
- [A Survey on Accuracy-oriented Neural Recommendation: From Collaborative Filtering to Information-rich Recommendation](https://mlsanity.com/paper/2104.13030/) (2021)
- [Learning with Average Top-k Loss](https://mlsanity.com/paper/1705.08826/) (2017)
- [Recall@k Surrogate Loss with Large Batches and Similarity Mixup](https://mlsanity.com/paper/2108.11179/) (2021)
- [Alleviating Structural Distribution Shift in Graph Anomaly Detection](https://mlsanity.com/paper/2401.14155/) (2024)
- [When AUC meets DRO: Optimizing Partial AUC for Deep Learning with Non-Convex Convergence Guarantee](https://mlsanity.com/paper/2203.00176/) (2022)
- [Large-scale Stochastic Optimization of NDCG Surrogates for Deep Learning with Provable Convergence](https://mlsanity.com/paper/2202.12183/) (2022)
- [On the Theories Behind Hard Negative Sampling for Recommendation](https://mlsanity.com/paper/2302.03472/) (2023)
- [Large-scale Optimization of Partial AUC in a Range of False Positive Rates](https://mlsanity.com/paper/2203.01505/) (2022)
- [Rumor Detection with Self-supervised Learning on Texts and Social Graph](https://mlsanity.com/paper/2204.08838/) (2022)
- [Support Vector Algorithms for Optimizing the Partial Area Under the ROC Curve](https://mlsanity.com/paper/1605.04337/) (2016)
- [Two-Way Partial AUC and Its Properties](https://mlsanity.com/paper/1508.00298/) (2015)
- [Implicit Rate-Constrained Optimization of Non-decomposable Objectives](https://mlsanity.com/paper/2107.10960/) (2021)
- [Asymptotically Unbiased Instance-wise Regularized Partial AUC Optimization: Theory and Algorithm](https://mlsanity.com/paper/2210.03967/) (2022)
- [CROLoss: Towards a Customizable Loss for Retrieval Models in Recommender Systems](https://mlsanity.com/paper/2208.02971/) (2022)
- [Rich-Item Recommendations for Rich-Users: Exploiting Dynamic and Static Side Information](https://mlsanity.com/paper/2001.10495/) (2020)

## Built on by (most cited first, 9 of 9)

- [ROC-n-reroll: How verifier imperfection affects test-time scaling](https://mlsanity.com/paper/2507.12399/) (2025)
- [PSL: Rethinking and Improving Softmax Loss from Pairwise Perspective for Recommendation](https://mlsanity.com/paper/2411.00163/) (2024)
- [Breaking the Top-K Barrier: Advancing Top-K Ranking Metrics Optimization in Recommender Systems](https://mlsanity.com/paper/2508.05673/) (2025)
- [Advancing Loss Functions in Recommender Systems: A Comparative Study with a R'enyi Divergence-Based Solution](https://mlsanity.com/paper/2506.15120/) (2025)
- [Talos: Optimizing Top-K Accuracy in Recommender Systems](https://mlsanity.com/paper/2601.19276/) (2026)
- [FairPOT: Balancing AUC Performance and Fairness with Proportional Optimal Transport](https://mlsanity.com/paper/2508.03940/) (2025)
- [Correct and Weight: A Simple Yet Effective Loss for Implicit Feedback Recommendation](https://mlsanity.com/paper/2601.04291/) (2026)
- [DSL: Understanding and Improving Softmax Recommender Systems with Competition-Aware Scaling](https://mlsanity.com/paper/2602.07206/) (2026)
- [SeedER: Seed-Expand-Retrieve for Efficient Knowledge Graph Retrieval](https://mlsanity.com/paper/2605.23753/) (2026)

## Abstract (arXiv)

Optimization metrics are crucial for building recommendation systems at scale. However, an effective and efficient metric for practical use remains elusive. While Top-K ranking metrics are the gold standard for optimization, they suffer from significant computational overhead. Alternatively, the more efficient accuracy and AUC metrics often fall short of capturing the true targets of recommendation tasks, leading to suboptimal performance. To overcome this dilemma, we propose a new optimization metric, Lower-Left Partial AUC (LLPAUC), which is computationally efficient like AUC but strongly correlates with Top-K ranking metrics. Compared to AUC, LLPAUC considers only the partial area under the ROC curve in the Lower-Left corner to push the optimization focus on Top-K. We provide theoretical validation of the correlation between LLPAUC and Top-K ranking metrics and demonstrate its robustness to noisy user feedback. We further design an efficient point-wise recommendation loss to maximize LLPAUC and evaluate it on three datasets, validating its effectiveness and robustness.