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We develop a fitted value iteration (FVI) method to compute bicausal optimaltransport (OT) where couplings have an adapted structure. Based on the dynamicprogramming formulation, FVI adopts a function class to approximate the valuefunctions in bicausal OT. Under the concentrability condition and approximatecompleteness assumption, we prove the sample complexity using (local)Rademacher complexity. Furthermore, we demonstrate that multilayer neuralnetworks with appropriate structures satisfy the crucial assumptions requiredin sample complexity proofs. Numerical experiments reveal that FVI outperformslinear programming and adapted Sinkhorn methods in scalability as the timehorizon increases, while still maintaining acceptable accuracy.

Fitted Value Iteration Methods for Bicausal Optimal Transport