# Distributionally robust risk evaluation with a causality constraint and structural information

arXiv: https://arxiv.org/abs/2203.10571 · HTML: https://mlsanity.com/paper/2203.10571/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 71 references that are in the map.
- First posted on arXiv 20 Mar 2022.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Data-dependent Sample Complexity of Deep Neural Networks via Lipschitz Augmentation](https://mlsanity.com/paper/1905.03684/) (2019)
- [COT-GAN: Generating Sequential Data via Causal Optimal Transport](https://mlsanity.com/paper/2006.08571/) (2020)
- [Optimal Transport Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes](https://mlsanity.com/paper/1810.02403/) (2018)
- [Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances](https://mlsanity.com/paper/1802.04885/) (2018)
- [Causal transport in discrete time and applications](https://mlsanity.com/paper/1606.04062/) (2016)
- [Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization](https://mlsanity.com/paper/1611.02610/) (2016)
- [Computational aspects of robust optimized certainty equivalents and option pricing](https://mlsanity.com/paper/1706.10186/) (2017)
- [Computational Methods for Martingale Optimal Transport problems](https://mlsanity.com/paper/1710.07911/) (2017)
- [Robust risk aggregation with neural networks](https://mlsanity.com/paper/1811.00304/) (2018)
- [Deep Empirical Risk Minimization in finance: looking into the future](https://mlsanity.com/paper/2011.09349/) (2020)
- [Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix *](https://mlsanity.com/paper/1610.06805/) (2016)
- [Cournot-Nash equilibrium and optimal transport in a dynamic setting](https://mlsanity.com/paper/2002.08786/) (2020)
- [Conditional COT-GAN for Video Prediction with Kernel Smoothing](https://mlsanity.com/paper/2106.05658/) (2021)
- [Distributionally Robust Martingale Optimal Transport](https://mlsanity.com/paper/2106.07191/) (2021)

## Built on by (most cited first, 1 of 1)

- [Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairness](https://mlsanity.com/paper/2509.26275/) (2025)

## Abstract (arXiv)

This work studies the distributionally robust evaluation of expected values over temporal data. A set of alternative measures is characterized by the causal optimal transport. We prove the strong duality and recast the causality constraint as minimization over an infinite-dimensional test function space. We approximate test functions by neural networks and prove the sample complexity with Rademacher complexity. An example is given to validate the feasibility of technical assumptions. Moreover, when structural information is available to further restrict the ambiguity set, we prove the dual formulation and provide efficient optimization methods. Our framework outperforms the classic counterparts in the distributionally robust portfolio selection problem. The connection with the naive strategy is also investigated numerically.