# Fair and Welfare-Efficient Constrained Multi-matchings under Uncertainty

arXiv: https://arxiv.org/abs/2411.02654 · HTML: https://mlsanity.com/paper/2411.02654/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 59 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 25 of 25)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Large-Scale Methods for Distributionally Robust Optimization](https://mlsanity.com/paper/2010.05893/) (2020)
- [The Complexity of Constrained Min-Max Optimization](https://mlsanity.com/paper/2009.09623/) (2020)
- [Fair Decision Making using Privacy-Protected Data](https://mlsanity.com/paper/1905.12744/) (2019)
- [Mitigating Manipulation in Peer Review via Randomized Reviewer Assignments](https://mlsanity.com/paper/2006.16437/) (2020)
- [Improved Algorithms for Convex-Concave Minimax Optimization](https://mlsanity.com/paper/2006.06359/) (2020)
- [PeerReview4All: Fair and Accurate Reviewer Assignment in Peer Review](https://mlsanity.com/paper/1806.06237/) (2018)
- [Paper Matching with Local Fairness Constraints](https://mlsanity.com/paper/1905.11924/) (2019)
- [An Axiomatic Theory of Provably-Fair Welfare-Centric Machine Learning](https://mlsanity.com/paper/2104.14504/) (2021)
- [Matching Papers and Reviewers at Large Conferences](https://mlsanity.com/paper/2202.12273/) (2022)
- [A Practical Guide to Robust Optimization](https://mlsanity.com/paper/1501.02634/) (2015)
- [Fairness and Utilization in Allocating Resources with Uncertain Demand](https://mlsanity.com/paper/1906.09050/) (2019)
- [Fair Decision-making Under Uncertainty](https://mlsanity.com/paper/2301.12364/) (2023)
- [I Will Have Order! Optimizing Orders for Fair Reviewer Assignment](https://mlsanity.com/paper/2108.02126/) (2021)
- [Convex-Concave Min-Max Stackelberg Games](https://mlsanity.com/paper/2110.05192/) (2021)
- [Learning Resource Allocation Policies from Observational Data with an Application to Homeless Services Delivery](https://mlsanity.com/paper/2201.10053/) (2022)
- [Fairness in Matching under Uncertainty](https://mlsanity.com/paper/2302.03810/) (2023)
- [Group Fairness in Peer Review](https://mlsanity.com/paper/2410.03474/) (2024)
- [Online Resource Allocation with Samples](https://mlsanity.com/paper/2210.04774/) (2022)
- [Efficient Black-Box Importance Sampling for VaR and CVaR Estimation](https://mlsanity.com/paper/2106.10236/) (2021)
- [Prioritizing municipal lead mitigation projects as a relaxed knapsack optimization: a method and case study](https://mlsanity.com/paper/2201.09372/) (2022)
- [Robust and fair work allocation](https://mlsanity.com/paper/2202.05194/) (2022)
- [Program Targeting with Machine Learning and Mobile Phone Data: Evidence from an Anti-Poverty Intervention in Afghanistan](https://mlsanity.com/paper/2206.11400/) (2022)
- [Into the Unknown: Assigning Reviewers to Papers with Uncertain Affinities](https://mlsanity.com/paper/2301.10816/) (2023)

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

- [Optimal Transport under Group Fairness Constraints](https://mlsanity.com/paper/2601.07144/) (2026)

## Abstract (arXiv)

We study fair allocation of constrained resources, where a market designer optimizes overall welfare while maintaining group fairness. In many large-scale settings, utilities are not known in advance, but are instead observed after realizing the allocation. We therefore estimate agent utilities using machine learning. Optimizing over estimates requires trading-off between mean utilities and their predictive variances. We discuss these trade-offs under two paradigms for preference modeling -- in the stochastic optimization regime, the market designer has access to a probability distribution over utilities, and in the robust optimization regime they have access to an uncertainty set containing the true utilities with high probability. We discuss utilitarian and egalitarian welfare objectives, and we explore how to optimize for them under stochastic and robust paradigms. We demonstrate the efficacy of our approaches on three publicly available conference reviewer assignment datasets. The approaches presented enable scalable constrained resource allocation under uncertainty for many combinations of objectives and preference models.