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：我们提出了一种拟合值迭代（FVI）方法来计算耦合具有适应结构的双因果最优输运（OT）。基于动态规划形式，FVI采用函数类逼近双因果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）拉德马赫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在可扩展性上优于线性规划和适应Sinkhorn方法，同时仍保持可接受的精度。