We develop a fitted value iteration (FVI) method to compute bicausal optimal transport (OT) where couplings have an adapted structure. Based on the dynamic programming formulation, FVI adopts a function class to approximate the value functions in bicausal OT. Under the concentrability condition and approximate completeness assumption, we prove the sample complexity using (local) Rademacher complexity. Furthermore, we demonstrate that multilayer neural networks with appropriate structures satisfy the crucial assumptions required in sample complexity proofs. Numerical experiments reveal that FVI outperforms linear programming and adapted Sinkhorn methods in scalability as the time horizon increases, while still maintaining acceptable accuracy.

翻译：本文提出了一种拟合值迭代（FVI）方法，用于计算具有适应结构的耦合的双因果最优传输（OT）问题。基于动态规划框架，FVI采用函数类来近似双因果OT中的值函数。在可集中性条件和近似完备性假设下，我们利用（局部）Rademacher复杂度证明了样本复杂度。此外，我们证明了具有适当结构的多层神经网络能够满足样本复杂度证明所需的关键假设。数值实验表明，随着时间跨度的增加，FVI在可扩展性方面优于线性规划和适应Sinkhorn方法，同时仍能保持可接受的精度。