发表机构
Yau Mathematical Sciences Center, Tsinghua University; Department of Applied Mathematics, The Hong Kong Polytechnic University（清华大学丘成桐数学科学中心; 香港理工大学应用数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对经典逆最优传输仅从单一观测推断代价函数易受噪声影响的问题，提出多观测逆最优传输框架，通过凸规划重构与带外推的块坐标下降算法，从多个传输计划中学习通用代价函数，显著降低恢复误差并提取稳健结构模式。
AI 中文摘要
经典逆最优传输（IOT）通常从单个观测到的传输计划中推断代价函数，这在实践中可能对噪声和观测偏差敏感。为解决这一局限，我们提出了多观测逆最优传输（M-IOT）框架，该框架从多个传输计划中学习通用代价函数。我们将由此产生的双层优化问题重新表述为可处理的单层凸规划，并刻画了最优解集的存在性与几何结构。此外，我们提出了一种带安德森型外推的块坐标下降（BCDwAE）算法，并建立了其Q线性收敛性。在合成数据、城市出行流量和电子商务推荐上的大量实验表明，与单观测基线相比，M-IOT降低了恢复误差，并从含噪多视图数据中提取出稳健的结构模式。
英文摘要
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.
