Robust Optimization in Causal Models and G-Causal Normalizing Flows

ArXiv ID: 2510.15458 “View on arXiv”

Authors: Gabriele Visentin, Patrick Cheridito

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.

Keywords: Causal Wasserstein distance, Normalizing flow, Interventionally robust optimization, Causal factor models, Data augmentation, Portfolio Optimization

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper is heavily theoretical with dense mathematical proofs (e.g., continuity under G-causal Wasserstein distance, universal approximation properties), warranting a high math score. It provides empirical validation in finance (causal regression, portfolio optimization) with clear comparisons to baselines, but the implementation details and data specifics are less emphasized than the theoretical framework.

  flowchart TD
    A["Research Goal:<br>Robust Optimization in Causal Models"] --> B["Key Methodology:<br>Interventionally Robust Optimization<br>via G-Causal Wasserstein Distance"]
    B --> C["Computational Process:<br>Proposed G-Causal Normalizing Flow<br>for Efficient Training"]
    C --> D["Data Input:<br>Causal Factor Models &<br>Interventional Data"]
    D --> E["Comparative Analysis:<br>Standard vs. Causal<br>Generative Models"]
    E --> F["Key Findings:<br>1. Robustness continuous under G-Causal Wasserstein<br>2. Outperforms non-causal models in<br>causal regression & portfolio optimization"]