# Computationally Efficient Optimization of Plackett-Luce Ranking Models for Relevance and Fairness

arXiv: https://arxiv.org/abs/2105.00855 · HTML: https://mlsanity.com/paper/2105.00855/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2021.

## Built on by (most cited first, 30 of 36)

- [Joint Multisided Exposure Fairness for Recommendation](https://mlsanity.com/paper/2205.00048/) (2022)
- [Doubly-Robust Estimation for Correcting Position-Bias in Click Feedback for Unbiased Learning to Rank](https://mlsanity.com/paper/2203.17118/) (2022)
- [Towards Fair RAG: On the Impact of Fair Ranking in Retrieval-Augmented Generation](https://mlsanity.com/paper/2409.11598/) (2024)
- [Learning-to-Rank at the Speed of Sampling: Plackett-Luce Gradient Estimation With Minimal Computational Complexity](https://mlsanity.com/paper/2204.10872/) (2022)
- [Fair Ranking as Fair Division: Impact-Based Individual Fairness in Ranking](https://mlsanity.com/paper/2206.07247/) (2022)
- [Introducing the Expohedron for Efficient Pareto-optimal Fairness-Utility Amortizations in Repeated Rankings](https://mlsanity.com/paper/2202.03237/) (2022)
- [Safe Deployment for Counterfactual Learning to Rank with Exposure-Based Risk Minimization](https://mlsanity.com/paper/2305.01522/) (2023)
- [Probabilistic Rank and Reward: A Scalable Model for Slate Recommendation](https://mlsanity.com/paper/2208.06263/) (2022)
- [Effective Controllable Bias Mitigation for Classification and Retrieval using Gate Adapters](https://mlsanity.com/paper/2401.16457/) (2024)
- [Practical and Robust Safety Guarantees for Advanced Counterfactual Learning to Rank](https://mlsanity.com/paper/2407.19943/) (2024)
- [Policy-Gradient Training of Language Models for Ranking](https://mlsanity.com/paper/2310.04407/) (2023)
- [Probabilistic Permutation Graph Search: Black-Box Optimization for Fairness in Ranking](https://mlsanity.com/paper/2204.13765/) (2022)
- [LTRR: Learning To Rank Retrievers for LLMs](https://mlsanity.com/paper/2506.13743/) (2025)
- [Inference-time Stochastic Ranking with Risk Control](https://mlsanity.com/paper/2306.07188/) (2023)
- [Sampling Individually-Fair Rankings that are Always Group Fair](https://mlsanity.com/paper/2306.11964/) (2023)
- [Ranking Across Different Content Types: The Robust Beauty of Multinomial Blending](https://mlsanity.com/paper/2408.09168/) (2024)
- [HPS: Hard Preference Sampling for Human Preference Alignment](https://mlsanity.com/paper/2502.14400/) (2025)
- [Low-variance estimation in the Plackett-Luce model via quasi-Monte Carlo sampling](https://mlsanity.com/paper/2205.06024/) (2022)
- [Debias the Black-box: A Fair Ranking Framework via Knowledge Distillation](https://mlsanity.com/paper/2208.11628/) (2022)
- [Optimizing Group-Fair Plackett-Luce Ranking Models for Relevance and Ex-Post Fairness](https://mlsanity.com/paper/2308.13242/) (2023)
- [Proximal Ranking Policy Optimization for Practical Safety in Counterfactual Learning to Rank](https://mlsanity.com/paper/2409.09881/) (2024)
- [PMAT: Optimizing Action Generation Order in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2502.16496/) (2025)
- [Optimizing Compound Retrieval Systems](https://mlsanity.com/paper/2504.12063/) (2025)
- [Learning to Re-rank with Constrained Meta-Optimal Transport](https://mlsanity.com/paper/2305.00319/) (2023)
- [Estimating the Hessian Matrix of Ranking Objectives for Stochastic Learning to Rank with Gradient Boosted Trees](https://mlsanity.com/paper/2404.12190/) (2024)
- [Do Not Wait: Learning Re-Ranking Model Without User Feedback At Serving Time in E-Commerce](https://mlsanity.com/paper/2406.14004/) (2024)
- [Off-Policy Evaluation of Ranking Policies via Embedding-Space User Behavior Modeling](https://mlsanity.com/paper/2506.00446/) (2025)
- [Learning to Rank with Variable Result Presentation Lengths](https://mlsanity.com/paper/2506.23319/) (2025)
- [RewardRank: Optimizing True Learning-to-Rank Utility](https://mlsanity.com/paper/2508.14180/) (2025)
- [Credit-assigned Policy Gradient for Early Stage Retrieval in Two-stage Ranking](https://mlsanity.com/paper/2605.26385/) (2026)

## Abstract (arXiv)

Recent work has proposed stochastic Plackett-Luce (PL) ranking models as a robust choice for optimizing relevance and fairness metrics. Unlike their deterministic counterparts that require heuristic optimization algorithms, PL models are fully differentiable. Theoretically, they can be used to optimize ranking metrics via stochastic gradient descent. However, in practice, the computation of the gradient is infeasible because it requires one to iterate over all possible permutations of items. Consequently, actual applications rely on approximating the gradient via sampling techniques. In this paper, we introduce a novel algorithm: PL-Rank, that estimates the gradient of a PL ranking model w.r.t. both relevance and fairness metrics. Unlike existing approaches that are based on policy gradients, PL-Rank makes use of the specific structure of PL models and ranking metrics. Our experimental analysis shows that PL-Rank has a greater sample-efficiency and is computationally less costly than existing policy gradients, resulting in faster convergence at higher performance. PL-Rank further enables the industry to apply PL models for more relevant and fairer real-world ranking systems.