# Combining T-learning and DR-learning: a framework for oracle-efficient estimation of causal contrasts

arXiv: https://arxiv.org/abs/2402.01972 · HTML: https://mlsanity.com/paper/2402.01972/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2024.

## Built on by (most cited first, 18 of 18)

- [Model-agnostic meta-learners for estimating heterogeneous treatment effects over time](https://mlsanity.com/paper/2407.05287/) (2024)
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- [Debiased Front-Door Learners for Heterogeneous Effects](https://mlsanity.com/paper/2509.22531/) (2025)
- [Causal machine learning for heterogeneous treatment effects in the presence of missing outcome data](https://mlsanity.com/paper/2412.19711/) (2024)
- [Meta-Router: Bridging Gold-standard and Preference-based Evaluations in Large Language Model Routing](https://mlsanity.com/paper/2509.25535/) (2025)
- [Targeted Regularization for Causal Effect Estimation with Exponential Dispersion Family Outcomes](https://mlsanity.com/paper/2502.07295/) (2025)
- [Domain Adaptation Under MNAR Missingness](https://mlsanity.com/paper/2504.00322/) (2025)
- [Statistical Learning for Heterogeneous Treatment Effects: Pretraining, Prognosis, and Prediction](https://mlsanity.com/paper/2505.00310/) (2025)
- [Learning density ratios in causal inference using Bregman-Riesz regression](https://mlsanity.com/paper/2510.16127/) (2025)
- [Targeted learning of heterogeneous treatment effect curves for right censored or left truncated time-to-event data](https://mlsanity.com/paper/2603.26502/) (2026)
- [Orthogonal machine learning for conditional odds and risk ratios](https://mlsanity.com/paper/2604.10412/) (2026)
- [Targeted Highly Adaptive Lasso Minimum Loss Estimation of Target Functions](https://mlsanity.com/paper/2607.03824/) (2026)
- [Estimating Treatment Effects for Depression in Longitudinal Therapy Switching Settings](https://mlsanity.com/paper/2607.27214/) (2026)

## Abstract (arXiv)

We introduce efficient plug-in (EP) learning, a novel framework for the estimation of heterogeneous causal contrasts, such as the conditional average treatment effect and conditional relative risk. The EP-learning framework enjoys the same oracle efficiency as Neyman-orthogonal learning strategies, such as DR-learning and R-learning, while addressing some of their primary drawbacks: (i) their practical applicability can be hindered by non-convex loss functions; and (ii) they may suffer from poor performance and instability due to inverse probability weighting and pseudo-outcomes that violate bounds. To overcome these issues, the EP-learner leverages an efficient plug-in estimator of the population risk function for the causal contrast. In doing so, it inherits the stability of plug-in strategies such as T-learning, while improving on their efficiency. Under reasonable conditions, EP-learners based on empirical risk minimization are oracle-efficient, exhibiting asymptotic equivalence to the minimizer of an oracle-efficient one-step debiased estimator of the population risk function. In simulation experiments, we show that EP-learners of the conditional average treatment effect and conditional relative risk outperform state-of-the-art competitors, including the T-learner, R-learner, and DR-learner. Open-source implementations of the proposed methods are available in our textttR package texttthte3.