# Robust Fitted-Q-Evaluation and Iteration under Sequentially Exogenous Unobserved Confounders

arXiv: https://arxiv.org/abs/2302.00662 · HTML: https://mlsanity.com/paper/2302.00662/

## Key facts

- Cited by 13 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.
- Builds on 60 of its 127 references that are in the map.
- First posted on arXiv 1 Feb 2023.

## 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 60)

- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Doubly Robust Off-policy Value Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1511.03722/) (2015)
- [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)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (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)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [Hybrid RL: Using Both Offline and Online Data Can Make RL Efficient](https://mlsanity.com/paper/2210.06718/) (2022)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Policy Finetuning: Bridging Sample-Efficient Offline and Online Reinforcement Learning](https://mlsanity.com/paper/2106.04895/) (2021)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes](https://mlsanity.com/paper/1908.08526/) (2019)
- [Generalization and Exploration via Randomized Value Functions](https://mlsanity.com/paper/1402.0635/) (2014)
- [Robust Reinforcement Learning using Offline Data](https://mlsanity.com/paper/2208.05129/) (2022)
- [Benchmarks for Deep Off-Policy Evaluation](https://mlsanity.com/paper/2103.16596/) (2021)
- [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)
- [Off-policy Policy Evaluation For Sequential Decisions Under Unobserved Confounding](https://mlsanity.com/paper/2003.05623/) (2020)
- [Confounding-Robust Policy Evaluation in Infinite-Horizon Reinforcement Learning](https://mlsanity.com/paper/2002.04518/) (2020)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [Doubly Robust Bias Reduction in Infinite Horizon Off-Policy Estimation](https://mlsanity.com/paper/1910.07186/) (2019)
- [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)
- [Provably Efficient Causal Reinforcement Learning with Confounded Observational Data](https://mlsanity.com/paper/2006.12311/) (2020)
- [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)
- [An Off-policy Policy Gradient Theorem Using Emphatic Weightings](https://mlsanity.com/paper/1811.09013/) (2018)

## Built on by (most cited first, 13 of 13)

- [Offline Reinforcement Learning in Large State Spaces: Algorithms and Guarantees](https://mlsanity.com/paper/2510.04088/) (2025)
- [Confounding Robust Deep Reinforcement Learning: A Causal Approach](https://mlsanity.com/paper/2510.21110/) (2025)
- [A Policy Gradient Method for Confounded POMDPs](https://mlsanity.com/paper/2305.17083/) (2023)
- [Efficient and Sharp Off-Policy Learning under Unobserved Confounding](https://mlsanity.com/paper/2502.13022/) (2025)
- [A Natural Extension To Online Algorithms For Hybrid RL With Limited Coverage](https://mlsanity.com/paper/2403.09701/) (2024)
- [Two-way Deconfounder for Off-policy Evaluation in Causal Reinforcement Learning](https://mlsanity.com/paper/2412.05783/) (2024)
- [Model-Free Robust φ-Divergence Reinforcement Learning Using Both Offline and Online Data](https://mlsanity.com/paper/2405.05468/) (2024)
- [Efficient and Sharp Off-Policy Evaluation in Robust Markov Decision Processes](https://mlsanity.com/paper/2404.00099/) (2024)
- [Causal Deepsets for Off-policy Evaluation under Spatial or Spatio-temporal Interferences](https://mlsanity.com/paper/2407.17910/) (2024)
- [Demystifying the Paradox of Importance Sampling with an Estimated History-Dependent Behavior Policy in Off-Policy Evaluation](https://mlsanity.com/paper/2505.22492/) (2025)
- [Pessimistic Causal Reinforcement Learning with Mediators for Confounded Offline Data](https://mlsanity.com/paper/2403.11841/) (2024)
- [Robust Counterfactual Policy Optimisation via Nondeterministic Causal Models](https://mlsanity.com/paper/2608.02893/) (2026)
- [Risk-Aware Quantile Learning for Personalized Dynamic Treatment Regimes](https://mlsanity.com/paper/2608.05434/) (2026)

## Abstract (arXiv)

Offline reinforcement learning is important in domains such as medicine, economics, and e-commerce where online experimentation is costly, dangerous or unethical, and where the true model is unknown. However, most methods assume all covariates used in the behavior policy's action decisions are observed. Though this assumption, sequential ignorability/unconfoundedness, likely does not hold in observational data, most of the data that accounts for selection into treatment may be observed, motivating sensitivity analysis. We study robust policy evaluation and policy optimization in the presence of sequentially-exogenous unobserved confounders under a sensitivity model. We propose and analyze orthogonalized robust fitted-Q-iteration that uses closed-form solutions of the robust Bellman operator to derive a loss minimization problem for the robust Q function, and adds a bias-correction to quantile estimation. Our algorithm enjoys the computational ease of fitted-Q-iteration and statistical improvements (reduced dependence on quantile estimation error) from orthogonalization. We provide sample complexity bounds, insights, and show effectiveness both in simulations and on real-world longitudinal healthcare data of treating sepsis. In particular, our model of sequential unobserved confounders yields an online Markov decision process, rather than partially observed Markov decision process: we illustrate how this can enable warm-starting optimistic reinforcement learning algorithms with valid robust bounds from observational data.