# Probabilistic Rank and Reward: A Scalable Model for Slate Recommendation

arXiv: https://arxiv.org/abs/2208.06263 · HTML: https://mlsanity.com/paper/2208.06263/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 53 references that are in the map.
- First posted on arXiv 10 Aug 2022.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Top-K Off-Policy Correction for a REINFORCE Recommender System](https://mlsanity.com/paper/1812.02353/) (2018)
- [Doubly Robust Policy Evaluation and Optimization](https://mlsanity.com/paper/1503.02834/) (2015)
- [Asymmetric LSH (ALSH) for Sublinear Time Maximum Inner Product Search (MIPS)](https://mlsanity.com/paper/1405.5869/) (2014)
- [Off-policy evaluation for slate recommendation](https://mlsanity.com/paper/1605.04812/) (2016)
- [Deep Reinforcement Learning for Page-wise Recommendations](https://mlsanity.com/paper/1805.02343/) (2018)
- [Offline A/B testing for Recommender Systems](https://mlsanity.com/paper/1801.07030/) (2018)
- [Off-policy Bandits with Deficient Support](https://mlsanity.com/paper/2006.09438/) (2020)
- [Computationally Efficient Optimization of Plackett-Luce Ranking Models for Relevance and Fairness](https://mlsanity.com/paper/2105.00855/) (2021)
- [Counterfactual Evaluation of Slate Recommendations with Sequential Reward Interactions](https://mlsanity.com/paper/2007.12986/) (2020)
- [Offline Evaluation of Ranking Policies with Click Models](https://mlsanity.com/paper/1804.10488/) (2018)
- [Beyond Greedy Ranking: Slate Optimization via List-CVAE](https://mlsanity.com/paper/1803.01682/) (2018)
- [BLOB : A Probabilistic Model for Recommendation that Combines Organic and Bandit Signals](https://mlsanity.com/paper/2008.12504/) (2020)
- [Learning-to-Rank at the Speed of Sampling: Plackett-Luce Gradient Estimation With Minimal Computational Complexity](https://mlsanity.com/paper/2204.10872/) (2022)
- [Combining Reward and Rank Signals for Slate Recommendation](https://mlsanity.com/paper/2107.12455/) (2021)
- [Pessimistic Off-Policy Optimization for Learning to Rank](https://mlsanity.com/paper/2206.02593/) (2022)

## Built on by (most cited first, 8 of 8)

- [Logarithmic Smoothing for Pessimistic Off-Policy Evaluation, Selection and Learning](https://mlsanity.com/paper/2405.14335/) (2024)
- [Exponential Smoothing for Off-Policy Learning](https://mlsanity.com/paper/2305.15877/) (2023)
- [Bayesian Off-Policy Evaluation and Learning for Large Action Spaces](https://mlsanity.com/paper/2402.14664/) (2024)
- [Fast Slate Policy Optimization: Going Beyond Plackett-Luce](https://mlsanity.com/paper/2308.01566/) (2023)
- [Unified PAC-Bayesian Study of Pessimism for Offline Policy Learning with Regularized Importance Sampling](https://mlsanity.com/paper/2406.03434/) (2024)
- [Off-Policy Learning in Large Action Spaces: Optimization Matters More Than Estimation](https://mlsanity.com/paper/2509.03456/) (2025)
- [Position Paper: Why the Shooting in the Dark Method Dominates Recommender Systems Practice; A Call to Abandon Anti-Utopian Thinking](https://mlsanity.com/paper/2402.02152/) (2024)
- [On-Policy and Off-Policy Learning for Large Action Spaces](https://mlsanity.com/paper/2607.28408/) (2026)

## Abstract (arXiv)

We introduce Probabilistic Rank and Reward (PRR), a scalable probabilistic model for personalized slate recommendation. Our approach allows off-policy estimation of the reward in the scenario where the user interacts with at most one item from a slate of K items. We show that the probability of a slate being successful can be learned efficiently by combining the reward, whether the user successfully interacted with the slate, and the rank, the item that was selected within the slate. PRR outperforms existing off-policy reward optimizing methods and is far more scalable to large action spaces. Moreover, PRR allows fast delivery of recommendations powered by maximum inner product search (MIPS), making it suitable in low latency domains such as computational advertising.