Robust Optimization in Causal Models and G-Causal Normalizing Flows
This addresses the need for robust optimization in causal inference applications, though it appears incremental by extending normalizing flows to incorporate causal structure.
The paper tackles the problem of interventionally robust optimization in causal models by showing these problems are continuous under the G-causal Wasserstein distance but discontinuous under standard Wasserstein distance, and proposes a causal normalizing flow architecture that outperforms non-causal generative models in data augmentation tasks like causal regression and portfolio optimization.
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.