# Causal Imitation Learning under Expert-Observable and Expert-Unobservable Confounding

arXiv: https://arxiv.org/abs/2502.07656 · HTML: https://mlsanity.com/paper/2502.07656/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 29 of its 56 references that are in the map.
- First posted on arXiv 11 Feb 2025.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 29 of 29)

- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [ChauffeurNet: Learning to Drive by Imitating the Best and Synthesizing the Worst](https://mlsanity.com/paper/1812.03079/) (2018)
- [Learning by Cheating](https://mlsanity.com/paper/1912.12294/) (2019)
- [Exploring the Limitations of Behavior Cloning for Autonomous Driving](https://mlsanity.com/paper/1904.08980/) (2019)
- [Causal Confusion in Imitation Learning](https://mlsanity.com/paper/1905.11979/) (2019)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Imitating Driver Behavior with Generative Adversarial Networks](https://mlsanity.com/paper/1701.06699/) (2017)
- [Algorithmic Stability for Adaptive Data Analysis](https://mlsanity.com/paper/1511.02513/) (2015)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Fighting Copycat Agents in Behavioral Cloning from Observation Histories](https://mlsanity.com/paper/2010.14876/) (2020)
- [Feedback in Imitation Learning: The Three Regimes of Covariate Shift](https://mlsanity.com/paper/2102.02872/) (2021)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Learning Deep Features in Instrumental Variable Regression](https://mlsanity.com/paper/2010.07154/) (2020)
- [Shaking the foundations: delusions in sequence models for interaction and control](https://mlsanity.com/paper/2110.10819/) (2021)
- [Causal Imitation Learning with Unobserved Confounders](https://mlsanity.com/paper/2208.06267/) (2022)
- [Data-driven Planning via Imitation Learning](https://mlsanity.com/paper/1711.06391/) (2017)
- [Sequence Model Imitation Learning with Unobserved Contexts](https://mlsanity.com/paper/2208.02225/) (2022)
- [Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach](https://mlsanity.com/paper/2007.01290/) (2020)
- [Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression](https://mlsanity.com/paper/1508.03365/) (2015)
- [Causal Imitation Learning under Temporally Correlated Noise](https://mlsanity.com/paper/2202.01312/) (2022)
- [Sequential Causal Imitation Learning with Unobserved Confounders](https://mlsanity.com/paper/2208.06276/) (2022)
- [Valid Causal Inference with (Some) Invalid Instruments](https://mlsanity.com/paper/2006.11386/) (2020)
- [Auto IV: Counterfactual Prediction via Automatic Instrumental Variable Decomposition](https://mlsanity.com/paper/2107.05884/) (2021)
- [Ivy: Instrumental Variable Synthesis for Causal Inference](https://mlsanity.com/paper/2004.05316/) (2020)
- [Invariant Causal Imitation Learning for Generalizable Policies](https://mlsanity.com/paper/2311.01489/) (2023)
- [Causal Imitability Under Context-Specific Independence Relations](https://mlsanity.com/paper/2306.00585/) (2023)
- [Learning Decision Policies with Instrumental Variables through Double Machine Learning](https://mlsanity.com/paper/2405.08498/) (2024)
- [Initial State Interventions for Deconfounded Imitation Learning](https://mlsanity.com/paper/2307.15980/) (2023)

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

- [Learning Long-Context Diffusion Policies via Past-Token Prediction](https://mlsanity.com/paper/2505.09561/) (2025)

## Abstract (arXiv)

We propose a general framework for causal Imitation Learning (IL) with hidden confounders, which subsumes several existing settings. Our framework accounts for two types of hidden confounders: (a) variables observed by the expert but not by the imitator, and (b) confounding noise hidden from both. By leveraging trajectory histories as instruments, we reformulate causal IL in our framework into a Conditional Moment Restriction (CMR) problem. We propose DML-IL, an algorithm that solves this CMR problem via instrumental variable regression, and upper bound its imitation gap. Empirical evaluation on continuous state-action environments, including Mujoco tasks, demonstrates that DML-IL outperforms existing causal IL baselines.