# Causal Imitation Learning Under Measurement Error and Distribution Shift

arXiv: https://arxiv.org/abs/2601.22206 · HTML: https://mlsanity.com/paper/2601.22206/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 22 of its 34 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Placed in

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

## Builds on (most cited first, 22 of 22)

- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Causal Confusion in Imitation Learning](https://mlsanity.com/paper/1905.11979/) (2019)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Reinforcement and Imitation Learning via Interactive No-Regret Learning](https://mlsanity.com/paper/1406.5979/) (2014)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Of Moments and Matching: A Game-Theoretic Framework for Closing the Imitation Gap](https://mlsanity.com/paper/2103.03236/) (2021)
- [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)
- [Off-Policy Evaluation in Partially Observable Environments](https://mlsanity.com/paper/1909.03739/) (2019)
- [Shaking the foundations: delusions in sequence models for interaction and control](https://mlsanity.com/paper/2110.10819/) (2021)
- [Proximal Reinforcement Learning: Efficient Off-Policy Evaluation in Partially Observed Markov Decision Processes](https://mlsanity.com/paper/2110.15332/) (2021)
- [Causal Imitation Learning with Unobserved Confounders](https://mlsanity.com/paper/2208.06267/) (2022)
- [A Minimax Learning Approach to Off-Policy Evaluation in Confounded Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2111.06784/) (2021)
- [Sequence Model Imitation Learning with Unobserved Contexts](https://mlsanity.com/paper/2208.02225/) (2022)
- [Off-Policy Confidence Interval Estimation with Confounded Markov Decision Process](https://mlsanity.com/paper/2202.10589/) (2022)
- [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)
- [Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference](https://mlsanity.com/paper/2104.02929/) (2021)
- [Off-Policy Evaluation for Episodic Partially Observable Markov Decision Processes under Non-Parametric Models](https://mlsanity.com/paper/2209.10064/) (2022)
- [Proximal Causal Inference for Complex Longitudinal Studies](https://mlsanity.com/paper/2109.07030/) (2021)
- [Initial State Interventions for Deconfounded Imitation Learning](https://mlsanity.com/paper/2307.15980/) (2023)

## Abstract (arXiv)

We study offline imitation learning (IL) when part of the decision-relevant state is observed only through noisy measurements and the distribution may change between training and deployment. Such settings induce spurious state-action correlations, so standard behavioral cloning (BC) -- whether conditioning on raw measurements or ignoring them -- can converge to systematically biased policies under distribution shift. We propose a general framework for IL under measurement error, inspired by explicitly modeling the causal relationships among the variables, yielding a target that retains a causal interpretation and is robust to distribution shift. Building on ideas from proximal causal inference, we introduce textttCausIL, which treats noisy state observations as proxy variables, and we provide identification conditions under which the target policy is recoverable from demonstrations without rewards or interactive expert queries. We develop estimators for both discrete and continuous state spaces; for continuous settings, we use an adversarial procedure over RKHS function classes to learn the required parameters. We evaluate textttCausIL on semi-simulated longitudinal data from the PhysioNet/Computing in Cardiology Challenge 2019 cohort and demonstrate improved robustness to distribution shift compared to BC baselines.