论文标题
通过动态编程，马尔可夫链的bicausal最佳运输
Bicausal Optimal Transport for Markov Chains via Dynamic Programming
论文作者
论文摘要
在本文中，我们研究了马尔可夫链的BICAUSAL最佳运输问题，Markov链是一种适合随机过程的最佳传输配方，随着时间的发展，信息的积累。我们的分析基于运输问题与马尔可夫决策过程理论之间的关系。这样，我们就可以得出在运输问题中最佳的必要条件，以及迭代算法，即价值迭代，以计算运输成本。此外，我们与马尔可夫连锁店的耦合的经典理论联系起来，尤其是忠实耦合的概念。最后，我们说明了运输成本如何自然出现在马尔可夫链的量度集中。
In this paper we study the bicausal optimal transport problem for Markov chains, an optimal transport formulation suitable for stochastic processes which takes into consideration the accumulation of information as time evolves. Our analysis is based on a relation between the transport problem and the theory of Markov decision processes. This way we are able to derive necessary and sufficient conditions for optimality in the transport problem, as well as an iterative algorithm, namely the value iteration, for the calculation of the transportation cost. Additionally, we draw the connection with the classic theory on couplings for Markov chains, and in particular with the notion of faithful couplings. Finally, we illustrate how the transportation cost appears naturally in the study of concentration of measure for Markov chains.
