# Probably Correct Optimal Stable Matching for Two-Sided Markets Under Uncertainty

arXiv: https://arxiv.org/abs/2501.03018 · HTML: https://mlsanity.com/paper/2501.03018/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 31 references that are in the map.
- First posted on arXiv 6 Jan 2025.

## Builds on (most cited first, 4 of 4)

- [Competing Bandits in Matching Markets](https://mlsanity.com/paper/1906.05363/) (2019)
- [Bandit Learning in Decentralized Matching Markets](https://mlsanity.com/paper/2012.07348/) (2020)
- [Beyond log2(T) Regret for Decentralized Bandits in Matching Markets](https://mlsanity.com/paper/2103.07501/) (2021)
- [Regret, stability & fairness in matching markets with bandit learners](https://mlsanity.com/paper/2102.06246/) (2021)

## Built on by (most cited first, 5 of 5)

- [Probably Correct Optimal Stable Matching under Two-Sided Uncertainty](https://mlsanity.com/paper/2607.04824/) (2026)
- [Learning in Matching Games with Bandit Feedback](https://mlsanity.com/paper/2506.03802/) (2025)
- [Learn to Match: Two-Sided Matching with Temporally Extended Feedback](https://mlsanity.com/paper/2606.06744/) (2026)
- [Exact Regret Frontiers and Externality Scheduling in Centralized Serial-Dictatorship Bandits](https://mlsanity.com/paper/2609.19963/) (2026)
- [DataCupid: Stable Matching Repair for Training Data Acquisition with Delayed Feedback](https://mlsanity.com/paper/2610.12960/) (2026)

## Abstract (arXiv)

We consider a learning problem for the stable marriage model under unknown preferences for the left side of the market. We focus on the centralized case, where at each time step, an online platform matches the agents, and obtains a noisy evaluation reflecting their preferences. Our aim is to quickly identify the stable matching that is left-side optimal, rendering this a pure exploration problem with bandit feedback. We specifically aim to find Probably Correct Optimal Stable Matchings and present several bandit algorithms to do so. Our findings provide a foundational understanding of how to efficiently gather and utilize preference information to identify the optimal stable matching in two-sided markets under uncertainty. An experimental analysis on synthetic data complements theoretical results on sample complexities for the proposed methods.