  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.
