# Post-hoc Selection of Pareto-Optimal Solutions in Search and Recommendation

arXiv: https://arxiv.org/abs/2306.12165 · HTML: https://mlsanity.com/paper/2306.12165/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 60 references that are in the map.
- First posted on arXiv 21 Jun 2023.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Introducing LETOR 4.0 Datasets](https://mlsanity.com/paper/1306.2597/) (2013)
- [Embarrassingly Shallow Autoencoders for Sparse Data](https://mlsanity.com/paper/1905.03375/) (2019)
- [Managing Popularity Bias in Recommender Systems with Personalized Re-ranking](https://mlsanity.com/paper/1901.07555/) (2019)
- [Fine-Grained Spoiler Detection from Large-Scale Review Corpora](https://mlsanity.com/paper/1905.13416/) (2019)
- [NeuralNDCG: Direct Optimisation of a Ranking Metric via Differentiable Relaxation of Sorting](https://mlsanity.com/paper/2102.07831/) (2021)
- [Toward Pareto Efficient Fairness-Utility Trade-off inRecommendation through Reinforcement Learning](https://mlsanity.com/paper/2201.00140/) (2022)
- [CPFair: Personalized Consumer and Producer Fairness Re-ranking for Recommender Systems](https://mlsanity.com/paper/2204.08085/) (2022)
- [Multi-FR: A Multi-objective Optimization Framework for Multi-stakeholder Fairness-aware Recommendation](https://mlsanity.com/paper/2105.02951/) (2021)
- [On Application of Learning to Rank for E-Commerce Search](https://mlsanity.com/paper/1903.04263/) (2019)
- [Choosing the Best of Both Worlds: Diverse and Novel Recommendations through Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2110.15097/) (2021)
- [Top-N Recommendation Algorithms: A Quest for the State-of-the-Art](https://mlsanity.com/paper/2203.01155/) (2022)
- [Distilled Neural Networks for Efficient Learning to Rank](https://mlsanity.com/paper/2202.10728/) (2022)

## Built on by (most cited first, 1 of 1)

- [Exploring Diversity, Novelty, and Popularity Bias in ChatGPT's Recommendations](https://mlsanity.com/paper/2601.01997/) (2026)

## Abstract (arXiv)

Information Retrieval (IR) and Recommender Systems (RS) tasks are moving from computing a ranking of final results based on a single metric to multi-objective problems. Solving these problems leads to a set of Pareto-optimal solutions, known as Pareto frontier, in which no objective can be further improved without hurting the others. In principle, all the points on the Pareto frontier are potential candidates to represent the best model selected with respect to the combination of two, or more, metrics. To our knowledge, there are no well-recognized strategies to decide which point should be selected on the frontier. In this paper, we propose a novel, post-hoc, theoretically-justified technique, named "Population Distance from Utopia" (PDU), to identify and select the one-best Pareto-optimal solution from the frontier. In detail, PDU analyzes the distribution of the points by investigating how far each point is from its utopia point (the ideal performance for the objectives). The possibility of considering fine-grained utopia points allows PDU to select solutions tailored to individual user preferences, a novel feature we call "calibration". We compare PDU against existing state-of-the-art strategies through extensive experiments on tasks from both IR and RS. Experimental results show that PDU and combined with calibration notably impact the solution selection. Furthermore, the results show that the proposed framework selects a solution in a principled way, irrespective of its position on the frontier, thus overcoming the limits of other strategies.