# Off-Policy Evaluation for Missingness-Aware Policies in MDPs with Rewards Missing Not at Random

arXiv: https://arxiv.org/abs/2606.20206 · HTML: https://mlsanity.com/paper/2606.20206/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Offline RL algorithms, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 44 of its 80 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Placed in

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

## Builds on (most cited first, 30 of 44)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Batch Policy Learning under Constraints](https://mlsanity.com/paper/1903.08738/) (2019)
- [Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation](https://mlsanity.com/paper/1810.12429/) (2018)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Offline Reinforcement Learning with Realizability and Single-policy Concentrability](https://mlsanity.com/paper/2202.04634/) (2022)
- [Empirical Study of Off-Policy Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1911.06854/) (2019)
- [Minimax-Optimal Off-Policy Evaluation with Linear Function Approximation](https://mlsanity.com/paper/2002.09516/) (2020)
- [Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes](https://mlsanity.com/paper/1908.08526/) (2019)
- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [A Review of Off-Policy Evaluation in Reinforcement Learning](https://mlsanity.com/paper/2212.06355/) (2022)
- [Pessimistic Q-Learning for Offline Reinforcement Learning: Towards Optimal Sample Complexity](https://mlsanity.com/paper/2202.13890/) (2022)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Deep Reinforcement Learning for Sepsis Treatment](https://mlsanity.com/paper/1711.09602/) (2017)
- [Off-Policy Evaluation in Partially Observable Environments](https://mlsanity.com/paper/1909.03739/) (2019)
- [Asymptotically Efficient Off-Policy Evaluation for Tabular Reinforcement Learning](https://mlsanity.com/paper/2001.10742/) (2020)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Graphical Models for Processing Missing Data](https://mlsanity.com/paper/1801.03583/) (2018)
- [Confounding-Robust Policy Evaluation in Infinite-Horizon Reinforcement Learning](https://mlsanity.com/paper/2002.04518/) (2020)
- [Risk Bounds and Rademacher Complexity in Batch Reinforcement Learning](https://mlsanity.com/paper/2103.13883/) (2021)
- [Off-policy Evaluation in Infinite-Horizon Reinforcement Learning with Latent Confounders](https://mlsanity.com/paper/2007.13893/) (2020)
- [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)
- [Semi-Supervised Offline Reinforcement Learning with Action-Free Trajectories](https://mlsanity.com/paper/2210.06518/) (2022)

## Abstract (arXiv)

In offline Reinforcement Learning, immediate rewards in logged batch data are often unobserved due to sparse or irregular record-keeping, or censored beyond certain reward values. This issue arises in practical settings, including health care and marketing. We investigate off-policy evaluation (OPE) in finite-horizon Markov decision processes when rewards are missing not at random (MNAR), which breaks ignorability and induces selection bias even after conditioning on states and actions. To address this, we formalize a reward-dependent propensity model and use future states as shadow variables to identify the full-data conditional mean reward. We further introduce a bridge function that recovers the conditional mean reward without explicitly modeling the MNAR mechanism, and estimate it via a min-max procedure to avoid double sampling. Building upon these identification results, we propose an Fitted-Q-Evaluation-style estimator that propagates the recovered rewards while allowing target policies to depend on past missingness indicators. Finally, we establish consistency and finite-sample error bounds for our OPE estimator, and show through experiments the strong performance of our method compared to existing methods on simulated and MIMIC-III Sepsis data.