# Confounding-Robust Policy Evaluation in Infinite-Horizon Reinforcement Learning

arXiv: https://arxiv.org/abs/2002.04518 · HTML: https://mlsanity.com/paper/2002.04518/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- Placed in Offline RL algorithms, one of 13 directions in Offline RL and imitation learning from data.
- First posted on arXiv 11 Feb 2020.

## Placed in

- Offline RL and imitation learning from data / [Offline RL algorithms](https://mlsanity.com/offlinerl/offline-rl-algorithms/)

## Built on by (most cited first, 30 of 57)

- [A Review of Off-Policy Evaluation in Reinforcement Learning](https://mlsanity.com/paper/2212.06355/) (2022)
- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [A Survey on Causal Reinforcement Learning](https://mlsanity.com/paper/2302.05209/) (2023)
- [Universal Off-Policy Evaluation](https://mlsanity.com/paper/2104.12820/) (2021)
- [Proximal Reinforcement Learning: Efficient Off-Policy Evaluation in Partially Observed Markov Decision Processes](https://mlsanity.com/paper/2110.15332/) (2021)
- [A Minimax Learning Approach to Off-Policy Evaluation in Confounded Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2111.06784/) (2021)
- [Instrumental Variable Value Iteration for Causal Offline Reinforcement Learning](https://mlsanity.com/paper/2102.09907/) (2021)
- [Off-Policy Confidence Interval Estimation with Confounded Markov Decision Process](https://mlsanity.com/paper/2202.10589/) (2022)
- [Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding](https://mlsanity.com/paper/2112.11449/) (2021)
- [Pessimism in the Face of Confounders: Provably Efficient Offline Reinforcement Learning in Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2205.13589/) (2022)
- [Stochastic Causal Programming for Bounding Treatment Effects](https://mlsanity.com/paper/2202.10806/) (2022)
- [Future-Dependent Value-Based Off-Policy Evaluation in POMDPs](https://mlsanity.com/paper/2207.13081/) (2022)
- [An Instrumental Variable Approach to Confounded Off-Policy Evaluation](https://mlsanity.com/paper/2212.14468/) (2022)
- [Off-Policy Evaluation for Episodic Partially Observable Markov Decision Processes under Non-Parametric Models](https://mlsanity.com/paper/2209.10064/) (2022)
- [Invariant Policy Learning: A Causal Perspective](https://mlsanity.com/paper/2106.00808/) (2021)
- [On Covariate Shift of Latent Confounders in Imitation and Reinforcement Learning](https://mlsanity.com/paper/2110.06539/) (2021)
- [Regularizing a Model-based Policy Stationary Distribution to Stabilize Offline Reinforcement Learning](https://mlsanity.com/paper/2206.07166/) (2022)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Estimating and Improving Dynamic Treatment Regimes With a Time-Varying Instrumental Variable](https://mlsanity.com/paper/2104.07822/) (2021)
- [Robust Fitted-Q-Evaluation and Iteration under Sequentially Exogenous Unobserved Confounders](https://mlsanity.com/paper/2302.00662/) (2023)
- [Model-Free and Model-Based Policy Evaluation when Causality is Uncertain](https://mlsanity.com/paper/2204.00956/) (2022)
- [Offline Policy Evaluation and Optimization under Confounding](https://mlsanity.com/paper/2211.16583/) (2022)
- [A Behavior Regularized Implicit Policy for Offline Reinforcement Learning](https://mlsanity.com/paper/2202.09673/) (2022)
- [Instrumental Variables in Causal Inference and Machine Learning: A Survey](https://mlsanity.com/paper/2212.05778/) (2022)
- [Offline Reinforcement Learning in Large State Spaces: Algorithms and Guarantees](https://mlsanity.com/paper/2510.04088/) (2025)
- [Strategic Decision-Making in the Presence of Information Asymmetry: Provably Efficient RL with Algorithmic Instruments](https://mlsanity.com/paper/2208.11040/) (2022)
- [Delphic Offline Reinforcement Learning under Nonidentifiable Hidden Confounding](https://mlsanity.com/paper/2306.01157/) (2023)
- [Confounding Robust Deep Reinforcement Learning: A Causal Approach](https://mlsanity.com/paper/2510.21110/) (2025)
- [Ambiguous Dynamic Treatment Regimes: A Reinforcement Learning Approach](https://mlsanity.com/paper/2112.04571/) (2021)
- [Efficient and Sharp Off-Policy Learning under Unobserved Confounding](https://mlsanity.com/paper/2502.13022/) (2025)

## Abstract (arXiv)

Off-policy evaluation of sequential decision policies from observational data is necessary in applications of batch reinforcement learning such as education and healthcare. In such settings, however, unobserved variables confound observed actions, rendering exact evaluation of new policies impossible, i.e., unidentifiable. We develop a robust approach that estimates sharp bounds on the (unidentifiable) value of a given policy in an infinite-horizon problem given data from another policy with unobserved confounding, subject to a sensitivity model. We consider stationary or baseline unobserved confounding and compute bounds by optimizing over the set of all stationary state-occupancy ratios that agree with a new partially identified estimating equation and the sensitivity model. We prove convergence to the sharp bounds as we collect more confounded data. Although checking set membership is a linear program, the support function is given by a difficult nonconvex optimization problem. We develop approximations based on nonconvex projected gradient descent and demonstrate the resulting bounds empirically.