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Talos: Optimizing Top-$K$ Accuracy in Recommender Systems

Shengjia Zhang, Weiqin Yang, Jiawei Chen, Peng Wu, Yuegang Sun, Gang Wang, Qihao Shi, Can Wang

TL;DR

This work addresses the challenge of directly optimizing Top-$K$ accuracy in recommender systems, where traditional full-ranking or partial-AUC losses often misalign with Practical Top-$K$ goals. Talos introduces a per-user score threshold and a fast, sampling-based quantile regression to estimate thresholds, coupled with a denominator constraint to prevent score inflation and a robust outside-temperature surrogate to handle discontinuities and distribution shifts. The authors prove that Talos tightly bounds $-\ ext{log} Precision@K$, connects to Distributionally Robust Optimization, and offers convergence guarantees, while delivering strong empirical gains across four datasets and three backbone models. Practically, Talos is concise, efficient, and plug‑in ready, making direct Top-$K$ optimization more reliable in production RS settings, with open-source code to facilitate adoption.

Abstract

Recommender systems (RS) aim to retrieve a small set of items that best match individual user preferences. Naturally, RS place primary emphasis on the quality of the Top-$K$ results rather than performance across the entire item set. However, estimating Top-$K$ accuracy (e.g., Precision@$K$, Recall@$K$) requires determining the ranking positions of items, which imposes substantial computational overhead and poses significant challenges for optimization. In addition, RS often suffer from distribution shifts due to evolving user preferences or data biases, further complicating the task. To address these issues, we propose Talos, a loss function that is specifically designed to optimize the Talos recommendation accuracy. Talos leverages a quantile technique that replaces the complex ranking-dependent operations into simpler comparisons between predicted scores and learned score thresholds. We further develop a sampling-based regression algorithm for efficient and accurate threshold estimation, and introduce a constraint term to maintain optimization stability by preventing score inflation. Additionally, we incorporate a tailored surrogate function to address discontinuity and enhance robustness against distribution shifts. Comprehensive theoretical analyzes and empirical experiments are conducted to demonstrate the effectiveness, efficiency, convergence, and distributional robustness of Talos. The code is available at https://github.com/cynthia-shengjia/WWW-2026-Talos.

Talos: Optimizing Top-$K$ Accuracy in Recommender Systems

TL;DR

This work addresses the challenge of directly optimizing Top- accuracy in recommender systems, where traditional full-ranking or partial-AUC losses often misalign with Practical Top- goals. Talos introduces a per-user score threshold and a fast, sampling-based quantile regression to estimate thresholds, coupled with a denominator constraint to prevent score inflation and a robust outside-temperature surrogate to handle discontinuities and distribution shifts. The authors prove that Talos tightly bounds , connects to Distributionally Robust Optimization, and offers convergence guarantees, while delivering strong empirical gains across four datasets and three backbone models. Practically, Talos is concise, efficient, and plug‑in ready, making direct Top- optimization more reliable in production RS settings, with open-source code to facilitate adoption.

Abstract

Recommender systems (RS) aim to retrieve a small set of items that best match individual user preferences. Naturally, RS place primary emphasis on the quality of the Top- results rather than performance across the entire item set. However, estimating Top- accuracy (e.g., Precision@, Recall@) requires determining the ranking positions of items, which imposes substantial computational overhead and poses significant challenges for optimization. In addition, RS often suffer from distribution shifts due to evolving user preferences or data biases, further complicating the task. To address these issues, we propose Talos, a loss function that is specifically designed to optimize the Talos recommendation accuracy. Talos leverages a quantile technique that replaces the complex ranking-dependent operations into simpler comparisons between predicted scores and learned score thresholds. We further develop a sampling-based regression algorithm for efficient and accurate threshold estimation, and introduce a constraint term to maintain optimization stability by preventing score inflation. Additionally, we incorporate a tailored surrogate function to address discontinuity and enhance robustness against distribution shifts. Comprehensive theoretical analyzes and empirical experiments are conducted to demonstrate the effectiveness, efficiency, convergence, and distributional robustness of Talos. The code is available at https://github.com/cynthia-shengjia/WWW-2026-Talos.
Paper Structure (31 sections, 3 theorems, 50 equations, 2 figures, 20 tables)

This paper contains 31 sections, 3 theorems, 50 equations, 2 figures, 20 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Task Formulation
  4. Top-$K$ Accuracy in RS
  5. Analyses on Existing Loss Functions
  6. Methodology
  7. Loss Function for Top-$K$ Accuracy
  8. Analyses on Talos
  9. Experiments
  10. Experimental Setup
  11. Analysis on Experiment Details
  12. Related Work
  13. Conclusion and Future Works
  14. Theoretical Proofs
  15. Proof of Theorem \ref{['theorem:the-upper-bound-property']}
  16. ...and 16 more sections

Key Result

Theorem 3.1

For a proper $\tau$, satisfying $\tau \in [\frac{\log\left((e^2+2)\text{sigmoid}(-2)/2\right)}{\log\epsilon},\frac{\log(1/2)}{\log\epsilon}]$, we have the following bound relations: where $C = \log (1+e^2/2)^{1/\tau}$ is a constant.

Figures (2)

  • Figure 1: (Left). Illustration of the inconsistency between LLPAUC/AUC/NDCG and Top-$K$ accuracy (Precision@$K$ and Recall@$K$) for two difference ranking schemes of ten items, where ranking scheme 2 achieves better AUC/LLPAUC and NDCG, while worse on Top-$K$ accuracy; (Right). The relationship among Talos, LLPAUC, SL, and BPR.
  • Figure 2: Sensitivity analysis of Talos on $\tau$, where - - - denotes the performance of SL with optimal hyperparameter.

Theorems & Definitions (3)

  • Theorem 3.1: serves as a tight surrogate for Precisio-n@$K$
  • Theorem 3.2: Distributional robustness
  • Theorem 3.3: Convergence guarantee