Learning Universal Costs via Multi-Observation Inverse Optimal Transport
Abstract
Classical Inverse Optimal Transport (IOT) typically infers a cost function from a single observed transport plan, which may be sensitive to noise and observational biases in practice. To address this limitation, we propose the Multi-Observation Inverse Optimal Transport (M-IOT) framework, which learns a universal cost function from multiple transport plans. We reformulate the resulting bilevel optimization problem into a tractable single-level convex program and characterize the existence and geometric structure of the optimal solution set. Moreover, we propose a Block Coordinate Descent with Anderson-type Extrapolation (BCDwAE) algorithm and establish its Q-linear convergence. Extensive experiments on synthetic data, urban mobility flows, and e-commerce recommendations demonstrate that M-IOT reduces recovery error compared to single-observation baselines and extracts robust structural patterns from noisy multi-view data.
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BibTeX
@misc{bao2026learning,
title = {{Learning Universal Costs via Multi-Observation Inverse Optimal Transport}},
author = {Chenglong Bao and Zanyu Li and Defeng Sun},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37291},
eprint = {2609.37291},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37291},
}
RIS
TY - UNPB
TI - Learning Universal Costs via Multi-Observation Inverse Optimal Transport
AU - Chenglong Bao
AU - Zanyu Li
AU - Defeng Sun
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37291
UR - https://arxiv.org/abs/2609.37291
AB - Classical Inverse Optimal Transport (IOT) typically infers a cost function from a single observed transport plan, which may be sensitive to noise and observational biases in practice. To address this limitation, we propose the Multi-Observation Inverse Optimal Transport (M-IOT) framework, which learns a universal cost function from multiple transport plans. We reformulate the resulting bilevel optimization problem into a tractable single-level convex program and characterize the existence and geometric structure of the optimal solution set. Moreover, we propose a Block Coordinate Descent with Anderson-type Extrapolation (BCDwAE) algorithm and establish its Q-linear convergence. Extensive experiments on synthetic data, urban mobility flows, and e-commerce recommendations demonstrate that M-IOT reduces recovery error compared to single-observation baselines and extracts robust structural patterns from noisy multi-view data.
ER -