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arXiv · 2605.20030

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

Salil Parth Tripathi·Bertrand Chapron·Fabrice Collard·Nicolas Courty·Ronan Fablet
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Abstract

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 \emph{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.

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Salil Parth Tripathi, Bertrand Chapron, Fabrice Collard, Nicolas Courty, Ronan Fablet. 2026-05-19. Take It or Leave It: Intent-Controlled Partial Optimal Transport. https://arxiv.org/abs/2605.20030

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