# Take It or Leave It: Intent-Controlled Partial Optimal Transport

arXiv: https://arxiv.org/abs/2605.20030 · HTML: https://mlsanity.com/paper/2605.20030/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 17 of 17)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Universal Domain Adaptation through Self Supervision](https://mlsanity.com/paper/2002.07953/) (2020)
- [Style Transfer by Relaxed Optimal Transport and Self-Similarity](https://mlsanity.com/paper/1904.12785/) (2019)
- [Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures](https://mlsanity.com/paper/1508.07941/) (2015)
- [OVANet: One-vs-All Network for Universal Domain Adaptation](https://mlsanity.com/paper/2104.03344/) (2021)
- [Smooth and Sparse Optimal Transport](https://mlsanity.com/paper/1710.06276/) (2017)
- [Unified Optimal Transport Framework for Universal Domain Adaptation](https://mlsanity.com/paper/2210.17067/) (2022)
- [Improving Mini-batch Optimal Transport via Partial Transportation](https://mlsanity.com/paper/2108.09645/) (2021)
- [Sparsity-Constrained Optimal Transport](https://mlsanity.com/paper/2209.15466/) (2022)
- [P2OT: Progressive Partial Optimal Transport for Deep Imbalanced Clustering](https://mlsanity.com/paper/2401.09266/) (2024)
- [Universal Domain Adaptation from Foundation Models: A Baseline Study](https://mlsanity.com/paper/2305.11092/) (2023)
- [Block-coordinate Frank-Wolfe algorithm and convergence analysis for semi-relaxed optimal transport problem](https://mlsanity.com/paper/2205.13766/) (2022)
- [Insights into capacity constrained optimal transport](https://mlsanity.com/paper/1304.6456/) (2013)
- [Training-Free Label Space Alignment for Universal Domain Adaptation](https://mlsanity.com/paper/2509.17452/) (2025)

## Abstract (arXiv)

While optimal transport (OT) enforces a rigid constraint by requiring two measures to be matched exactly, partial optimal transport relaxes this requirement by allowing mass to remain unmatched through a global budget, scalar rebate, or uniform rejection rule. However, many applications call for more structured, pointwise rejection mechanisms, where the decision to leave mass unmatched depends on side-specific reliability, support geometry, or external information about which components should participate in the comparison. We introduce intent-controlled partial optimal transport (IC-POT), a targeted generalization of partial transport that replaces the global rejection paradigm with pointwise rejection costs over both measures. We show that the resulting optimization problem admits a dual interpretation in terms of local acceptance thresholds and can be solved by recasting it as a balanced Kantorovich OT problem on an augmented support. Beyond theoretical analysis, we demonstrate the practical relevance of IC-POT in settings where rejection is driven by side information. In positive-unlabeled learning and open-partial domain adaptation, incorporating pointwise rejection rules that encode statistical structure improves fixed baseline pipelines. Finally, we motivate the use of IC-POT with a geophysical practical case: multi-modal satellite ocean measurements, for which physical and sensors priors naturally inform the rejection mechanism and define the retrieved comparable signal information.