The Unified Non-Convex Framework for Robust Causal Inference: Overcoming the Gaussian Barrier and Optimization Fragility

The contemporary enterprise of Causal Inference stands at a critical juncture, balancing precariously between the demands of high-dimensional statistical efficiency and the chaotic, uncurated reality of modern data streams. For the better part of the last decade, the dominant paradigm in this field has been Double Machine Learning (DML), a sophisticated methodological framework introduced by Chernozhukov et al. (2018). This framework leverages the geometric concept of Neyman orthogonality to immunize estimates of treatment effects against the inevitable errors that arise during the estimation of nuisance parameters. While DML is theoretically elegant and has revolutionized the application of machine learning to econometrics, it possesses a fundamental Achilles' heel: it relies almost exclusively on convex loss functions--typically the squared error for regression or the logistic loss for classification. As established in the foundational robustness literature by Hampel et al. (1986), convex loss functions are inextricably linked to unbounded influence functions.