正则化最优传输逆问题的精确快速解法
An exact and fast solution of the inverse Regularized Optimal Transport problem
- Enrico Fermi Research Center（恩里科·费米研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对正则化最优传输的逆问题，提出通过双中心化操作精确求解的闭式方法，可联合估计温度参数并扩展至更广泛的传输模型类。
AI中文摘要：
最优传输描述了在给定位置间传输质量的代价矩阵时，在两个分布间移动质量的最有效方式。通过Sinkhorn算法求解的熵正则化最优传输是该问题的广泛使用的正则化版本。其逆问题提出了相反的问题：给定观测到的传输计划，是什么代价矩阵产生了它？这一问题难以解决，因为代价仅在附加规范自由度下可识别。本文表明，该自由度可通过对观测计划应用单次双中心化操作精确固定，以闭式解得到真实代价矩阵，无需迭代优化。当已知少量真实代价项时，相同方法可让我们联合估计控制熵正则化的温度参数，以及该估计可靠性的诊断指标。我们进一步表明，该方法并非特定于熵正则化最优传输，而是可扩展到由代价与计划间可逆关系定义的更广泛的传输模型类。
英文摘要：
Optimal transport describes the most efficient way to move mass between two distributions, given a cost matrix for moving mass between each pair of locations. Entropic optimal transport, solved via the Sinkhorn algorithm, is a widely used regularized version of this problem. Its inverse problem asks the opposite question: given an observed transport plan, what cost matrix produced it? This is difficult because the cost is identifiable only up to an additive gauge freedom. Here we show that this freedom can be fixed exactly by a single double-centering operation applied to the observed plan, yielding the true cost matrix in closed form, with no iterative optimization required. When a modest number of true cost entries are known, the same approach lets us jointly estimate the temperature parameter controlling the entropic regularization, together with a diagnostic for the reliability of this estimate. We further show that the method is not specific to the entropic optimal transport, but extends to a broader class of transport models defined by an invertible relation between cost and plan.
