Optimal transportation plans with escort entropy regularization
Optimal transportation plans with escort entropy regularization
复制标题
护航熵正则化的最优运输计划
DOI：
10.1007/s41884-021-00058-2
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Amari Shun-ichi
中科院分区：
文献类型：
--
作者：
Kurose Takashi;Yoshizawa Shintaro;Amari Shun-ichi
熵正则化的Wasserstein输运问题对于解决各种应用中的许多问题都是有用的。研究了包括q-护送正则化在内的变形护送熵正则化，证明了最优运输方案的逆护送分布族构成一个具有双平面信息几何结构的变形指数族。这阐明了伴游变换及其逆变换在变形指数族理论中的作用。进一步证明了正则化代价函数给出了平面流形的对偶势。在正则化代价的基础上，导出了概率单纯形中两个概率分布之间的新的散度函数和相关的黎曼度量。
The entropy-regularized Wasserstein transportation problem is useful for solving lots of problems in various applications. We study the deformed escort entropy regularization including theq-escort regularization and prove that the family of the inverse escort distributions of the optimal transportation plans forms a deformed exponential family, which has dually flat information-geometric structure. This elucidates the role of the escort transformation and its inverse in the theory of deformed exponential families. We further prove that the regularized cost function gives the dual potential of the flat manifold. We derive a new divergence function between two probability distributions in a probability simplex and a related Riemannian metric based on the regularized cost.