# Three Routes to One Answer: Reconciling AIPW, TMLE, and Double Machine Learning for Applied Researchers

arXiv: https://arxiv.org/abs/2609.26142 · HTML: https://mlsanity.com/paper/2609.26142/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 46 references that are in the map.
- First posted on arXiv 8 Aug 2026.

## Builds on (most cited first, 8 of 8)

- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Using simulation studies to evaluate statistical methods](https://mlsanity.com/paper/1712.03198/) (2017)
- [DoubleML -- An Object-Oriented Implementation of Double Machine Learning in R](https://mlsanity.com/paper/2103.09603/) (2021)
- [Machine learning for causal inference: on the use of cross-fit estimators](https://mlsanity.com/paper/2004.10337/) (2020)
- [Practical considerations for specifying a super learner](https://mlsanity.com/paper/2204.06139/) (2022)
- [Challenges in Obtaining Valid Causal Effect Estimates with Machine Learning Algorithms](https://mlsanity.com/paper/1711.07137/) (2017)
- [Estimation of time-specific intervention effects on continuously distributed time-to-event outcomes by targeted maximum likelihood estimation](https://mlsanity.com/paper/2106.11009/) (2021)
- [Non-Plug-In Estimators Could Outperform Plug-In Estimators: a Cautionary Note and a Diagnosis](https://mlsanity.com/paper/2408.10091/) (2024)

## Built on by (most cited first, 1 of 1)

- [When Sample-Splitting Choices Matter in TMLE and AIPW: Cross-Fitting, Targeting, and Repetition](https://mlsanity.com/paper/2610.16192/) (2026)

## Abstract (arXiv)

Augmented inverse-probability weighting (AIPW), targeted maximum likelihood estimation (TMLE), and double/debiased machine learning (DML) are three routes to the same efficient influence function for the average treatment effect --- settled theory we treat as background. This tutorial's contribution is its worked, shared-nuisance reconciliation on real data: what a practitioner must actually match for the routes, and the software packages, to agree. Working the effect of smoking cessation on weight change in the open NHEFS data (n=1566) with one shared Super Learner library and identical cross-fitting folds, we build all three estimators by hand from one influence function, in full-sample, cross-fit, and double-cross-fit variants; the six resulting doubly-robust estimates span only 3.32--3.42 kg, consistent with the established benchmark. We then reconcile the same estimand across our engine and the tmle, AIPW, DoubleML, and tmle3 packages. At their defaults the estimates span 3.32--3.49 kg. Once the library and folds are matched and single-split noise is averaged out, the three library-sharing implementations agree to within 0.01 kg --- so the residual spread traces to the nuisance library, folds, and repetitions, not to the estimator label. Because the estimators share one influence function, they agree under good overlap; under a positivity violation the pooled ATE is not identified without additional extrapolation assumptions, and their finite-sample estimates can then diverge sharply. We therefore place a positivity diagnosis ahead of estimator choice, illustrate the failure on a no-overlap example, and close with a reporting checklist. Open-source R code reproduces every number.