# Fitted value iteration methods for bicausal optimal transport

arXiv: https://arxiv.org/abs/2306.12658 · HTML: https://mlsanity.com/paper/2306.12658/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 61 references that are in the map.
- First posted on arXiv 22 Jun 2023.

## Builds on (most cited first, 27 of 27)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [A Theoretical Analysis of Deep Q-Learning](https://mlsanity.com/paper/1901.00137/) (2019)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality](https://mlsanity.com/paper/1810.08033/) (2018)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021)
- [COT-GAN: Generating Sequential Data via Causal Optimal Transport](https://mlsanity.com/paper/2006.08571/) (2020)
- [Risk Bounds and Rademacher Complexity in Batch Reinforcement Learning](https://mlsanity.com/paper/2103.13883/) (2021)
- [On the Efficiency of Entropic Regularized Algorithms for Optimal Transport](https://mlsanity.com/paper/1906.01437/) (2019)
- [Quantitative Stability of Regularized Optimal Transport and Convergence of Sinkhorn's Algorithm](https://mlsanity.com/paper/2110.06798/) (2021)
- [Causal transport in discrete time and applications](https://mlsanity.com/paper/1606.04062/) (2016)
- [Approximating smooth functions by deep neural networks with sigmoid activation function](https://mlsanity.com/paper/2010.04596/) (2020)
- [Computational methods for adapted optimal transport](https://mlsanity.com/paper/2203.05005/) (2022)
- [Convergence Rates for Regularized Optimal Transport via Quantization](https://mlsanity.com/paper/2208.14391/) (2022)
- [Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization](https://mlsanity.com/paper/1611.02610/) (2016)
- [Local Rademacher Complexity Bounds based on Covering Numbers](https://mlsanity.com/paper/1510.01463/) (2015)
- [Extended Mean Field Control Problems: stochastic maximum principle and transport perspective](https://mlsanity.com/paper/1802.05754/) (2018)
- [Computation of optimal transport and related hedging problems via penalization and neural networks](https://mlsanity.com/paper/1802.08539/) (2018)
- [Marginal and dependence uncertainty: bounds, optimal transport, and sharpness](https://mlsanity.com/paper/1709.00641/) (2017)
- [Stability and Sample Complexity of Divergence Regularized Optimal Transport](https://mlsanity.com/paper/2212.00367/) (2022)
- [Cournot-Nash equilibrium and optimal transport in a dynamic setting](https://mlsanity.com/paper/2002.08786/) (2020)
- [Distributionally robust Kalman filtering with volatility uncertainty](https://mlsanity.com/paper/2302.05993/) (2023)
- [Transport plans with domain constraints](https://mlsanity.com/paper/1804.04283/) (2018)

## Built on by (most cited first, 2 of 2)

- [Bisimulation Metrics are Optimal Transport Distances, and Can be Computed Efficiently](https://mlsanity.com/paper/2406.04056/) (2024)
- [Nested Optimal Transport Distances](https://mlsanity.com/paper/2509.06702/) (2025)

## Abstract (arXiv)

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.