# Learning Potentials for Dynamic Matching and Application to Heart Transplantation

arXiv: https://arxiv.org/abs/2602.08878 · HTML: https://mlsanity.com/paper/2602.08878/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 60 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [Reinforcement Learning in Healthcare: A Survey](https://mlsanity.com/paper/1908.08796/) (2019)
- [Secretary and Online Matching Problems with Machine Learned Advice](https://mlsanity.com/paper/2006.01026/) (2020)
- [Dual Mirror Descent for Online Allocation Problems](https://mlsanity.com/paper/2002.10421/) (2020)
- [Regularized Online Allocation Problems: Fairness and Beyond](https://mlsanity.com/paper/2007.00514/) (2020)
- [Deep Policies for Online Bipartite Matching: A Reinforcement Learning Approach](https://mlsanity.com/paper/2109.10380/) (2021)
- [Position-Indexed Formulations for Kidney Exchange](https://mlsanity.com/paper/1606.01623/) (2016)
- [Learning for Edge-Weighted Online Bipartite Matching with Robustness Guarantees](https://mlsanity.com/paper/2306.00172/) (2023)
- [Policy Optimization for Dynamic Heart Transplant Allocation](https://mlsanity.com/paper/2512.12497/) (2025)
- [Incentive-Compatible Kidney Exchange in a Slightly Semi-Random Model](https://mlsanity.com/paper/2106.11387/) (2021)
- [Near-Optimal Dynamic Matching via Coarsening with Application to Heart Transplantation](https://mlsanity.com/paper/2602.04989/) (2026)
- [Position: Machine Learning for Heart Transplant Allocation Policy Optimization Should Account for Incentives](https://mlsanity.com/paper/2602.04990/) (2026)
- [Online Matching: A Brief Survey](https://mlsanity.com/paper/2407.05381/) (2024)
- [Learning-Based Planning for Improving Science Return of Earth Observation Satellites](https://mlsanity.com/paper/2509.07997/) (2025)

## Built on by (most cited first, 3 of 3)

- [Aligning Data-Driven Predictors with Allocation: A Decision-Focused Approach to Survival Analysis](https://mlsanity.com/paper/2606.02671/) (2026)
- [Preference Elicitation for Policy Optimization and Application to Aligning Heart Transplantation with Human Values](https://mlsanity.com/paper/2608.28620/) (2026)
- [Efficient Learning of Survival Analysis Models Under Outcome-Dependent Truncation and Censoring](https://mlsanity.com/paper/2610.12538/) (2026)

## Abstract (arXiv)

Each year, thousands of patients in need of heart transplants face life-threatening wait times due to organ scarcity. While allocation policies aim to maximize population-level outcomes, current approaches often fail to account for the dynamic arrival of organs and the composition of waitlisted candidates, thereby hampering efficiency. The United States is transitioning from rigid, rule-based allocation to more flexible data-driven models. In this paper, we propose a novel framework for non-myopic policy optimization in general online matching relying on potentials, a concept originally introduced for kidney exchange. We develop scalable and accurate ways of learning potentials that are higher-dimensional and more expressive than prior approaches. Our approach is a form of self-supervised imitation learning: the potentials are trained to mimic an omniscient algorithm that has perfect foresight. We focus on the application of heart transplant allocation and demonstrate, using real historical data, that our policies significantly outperform prior approaches -- including the current US status quo policy and the proposed continuous distribution framework -- in optimizing for population-level outcomes. Our analysis and methods come at a pivotal moment in US policy, as the current heart transplant allocation system is under review. We propose a scalable and theoretically grounded path toward more effective organ allocation.