Improved Debiased Machine Learning through Optimization and Calibration

In this exam, I present two projects. The first addresses estimation of heterogeneous treatment effects, a central problem for understanding effect modification and guiding individualized decision-making. It develops efficient plug-in learning, a novel oracle-efficient optimization framework that overcomes key limitations of Neyman-orthogonal learning. The second focuses on debiased estimation and inference for average treatment effects and, more generally, linear functionals of regression functions. It introduces calibration—traditionally a machine learning tool for prediction—into causal inference, showing how it achieves higher-order debiasing and enables doubly robust inference within doubly robust estimation procedures.


Part I: Efficient Plug-in Learning.
Efficient plug-in (EP) learning is a framework for estimating heterogeneous causal contrasts such as the conditional average treatment effect and conditional relative risk. EP-learning achieves oracle efficiency, like DR- and R-learning, while addressing two major drawbacks of those methods: (i) non-convex loss functions that limit practical applicability, and (ii) instability from inverse probability weighting and pseudo-outcomes that can violate natural bounds. EP-learner instead constructs a plug-in estimator of the population risk, inheriting the stability of methods like T-learning. Under mild conditions, empirical risk minimization with EP-learning is oracle-efficient and asymptotically equivalent to a one-step debiased estimator. Simulation studies show that EP-learners for conditional treatment effect and relative risk outperform state-of-the-art competitors including T-, R-, and DR-learners.

Part II: Doubly Robust Inference via Calibration.
Doubly robust estimators are widely used for linear functionals such as average treatment effects. While consistency requires only one nuisance function to be consistently estimated, asymptotic normality typically requires both to converge sufficiently fast. We correct this mismatch by calibrating nuisance estimators within the doubly robust procedure, yielding doubly robust asymptotic normality. Our framework, calibrated debiased machine learning (calibrated DML), augments standard DML with an isotonic regression adjustment. We show that calibrated DML remains asymptotically normal if either the regression or the Riesz representer is estimated well, allowing the other to converge arbitrarily slowly or even inconsistently. A simple bootstrap method provides valid confidence intervals without additional nuisance estimation. Across semi-synthetic benchmarks, calibrated DML reduces bias and improves coverage relative to standard DML, and can be integrated into existing pipelines with only minor code modifications.