# Scaling up Ranking under Constraints for Live Recommendations by Replacing Optimization with Prediction

arXiv: https://arxiv.org/abs/2202.07088 · HTML: https://mlsanity.com/paper/2202.07088/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 62 references that are in the map.
- First posted on arXiv 14 Feb 2022.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Fairness of Exposure in Rankings](https://mlsanity.com/paper/1802.07281/) (2018)
- [Equity of Attention: Amortizing Individual Fairness in Rankings](https://mlsanity.com/paper/1805.01788/) (2018)
- [FA*IR: A Fair Top-k Ranking Algorithm](https://mlsanity.com/paper/1706.06368/) (2017)
- [Measuring Fairness in Ranked Outputs](https://mlsanity.com/paper/1610.08559/) (2016)
- [Ranking with Fairness Constraints](https://mlsanity.com/paper/1704.06840/) (2017)
- [Designing Fair Ranking Schemes](https://mlsanity.com/paper/1712.09752/) (2017)
- [Estimation of Monge Matrices](https://mlsanity.com/paper/1904.03136/) (2019)
- [Online Ranking with Constraints: A Primal-Dual Algorithm and Applications to Web Traffic-Shaping](https://mlsanity.com/paper/1702.06971/) (2017)

## Abstract (arXiv)

Many important multiple-objective decision problems can be cast within the framework of ranking under constraints and solved via a weighted bipartite matching linear program. Some of these optimization problems, such as personalized content recommendations, may need to be solved in real time and thus must comply with strict time requirements to prevent the perception of latency by consumers. Classical linear programming is too computationally inefficient for such settings. We propose a novel approach to scale up ranking under constraints by replacing the weighted bipartite matching optimization with a prediction problem in the algorithm deployment stage. We show empirically that the proposed approximate solution to the ranking problem leads to a major reduction in required computing resources without much sacrifice in constraint compliance and achieved utility, allowing us to solve larger constrained ranking problems real-time, within the required 50 milliseconds, than previously reported.