# StochasticRank: Global Optimization of Scale-Free Discrete Functions

arXiv: https://arxiv.org/abs/2003.02122 · HTML: https://mlsanity.com/paper/2003.02122/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2020.

## Built on by (most cited first, 13 of 13)

- [Doubly-Robust Estimation for Correcting Position-Bias in Click Feedback for Unbiased Learning to Rank](https://mlsanity.com/paper/2203.17118/) (2022)
- [Learning-to-Rank at the Speed of Sampling: Plackett-Luce Gradient Estimation With Minimal Computational Complexity](https://mlsanity.com/paper/2204.10872/) (2022)
- [On (Normalised) Discounted Cumulative Gain as an Off-Policy Evaluation Metric for Top-n Recommendation](https://mlsanity.com/paper/2307.15053/) (2023)
- [Practical and Robust Safety Guarantees for Advanced Counterfactual Learning to Rank](https://mlsanity.com/paper/2407.19943/) (2024)
- [Learning Metrics that Maximise Power for Accelerated A/B-Tests](https://mlsanity.com/paper/2402.03915/) (2024)
- [Which Tricks Are Important for Learning to Rank?](https://mlsanity.com/paper/2204.01500/) (2022)
- [Inference-time Stochastic Ranking with Risk Control](https://mlsanity.com/paper/2306.07188/) (2023)
- [Newton Losses: Using Curvature Information for Learning with Differentiable Algorithms](https://mlsanity.com/paper/2410.19055/) (2024)
- [Gradient Boosting Reinforcement Learning](https://mlsanity.com/paper/2407.08250/) (2024)
- [Proximal Ranking Policy Optimization for Practical Safety in Counterfactual Learning to Rank](https://mlsanity.com/paper/2409.09881/) (2024)
- [Estimating the Hessian Matrix of Ranking Objectives for Stochastic Learning to Rank with Gradient Boosted Trees](https://mlsanity.com/paper/2404.12190/) (2024)
- [Learning to Rank with Variable Result Presentation Lengths](https://mlsanity.com/paper/2506.23319/) (2025)
- [Exposure-Based Reinforcement Learning to Rank](https://mlsanity.com/paper/2607.18689/) (2026)

## Abstract (arXiv)

In this paper, we introduce a powerful and efficient framework for direct optimization of ranking metrics. The problem is ill-posed due to the discrete structure of the loss, and to deal with that, we introduce two important techniques: stochastic smoothing and novel gradient estimate based on partial integration. We show that classic smoothing approaches may introduce bias and present a universal solution for a proper debiasing. Importantly, we can guarantee global convergence of our method by adopting a recently proposed Stochastic Gradient Langevin Boosting algorithm. Our algorithm is implemented as a part of the CatBoost gradient boosting library and outperforms the existing approaches on several learning-to-rank datasets. In addition to ranking metrics, our framework applies to any scale-free discrete loss function.