Robust Optimization in Causal Models and G-Causal Normalizing Flows
Gabriele Visentin, Patrick Cheridito
TL;DR
The paper analyzes data augmentation for downstream causal tasks under distributional shifts, proving that causal optimization is continuous under the $G$-causal Wasserstein distance and that solutions are interventionally robust. It then introduces $G$-causal normalizing flows—an invertible, hypernetwork-conditioned, $G$-compatible architecture with a universal approximation property for SCMs—and shows that likelihood training minimizes the $W_G$ distance. The authors provide theoretical guarantees linking KL training to $W_G$ convergence and validate the approach with experiments on causal regression and mean-variance portfolio optimization, demonstrating superior performance to non-causal generative models when augmenting data for causal tasks. This work offers a principled framework for causal-aware data augmentation with practical impact on robust decision-making under distribution shifts.
Abstract
In this paper, we show that interventionally robust optimization problems in causal models are continuous under the $G$-causal Wasserstein distance, but may be discontinuous under the standard Wasserstein distance. This highlights the importance of using generative models that respect the causal structure when augmenting data for such tasks. To this end, we propose a new normalizing flow architecture that satisfies a universal approximation property for causal structural models and can be efficiently trained to minimize the $G$-causal Wasserstein distance. Empirically, we demonstrate that our model outperforms standard (non-causal) generative models in data augmentation for causal regression and mean-variance portfolio optimization in causal factor models.