# Statistical Tractability of Off-policy Evaluation of History-dependent Policies in POMDPs

arXiv: https://arxiv.org/abs/2503.01134 · HTML: https://mlsanity.com/paper/2503.01134/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 47 of its 69 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 30 of 47)

- [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)
- [Contextual Decision Processes with Low Bellman Rank are PAC-Learnable](https://mlsanity.com/paper/1610.09512/) (2016)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1604.00923/) (2016)
- [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)
- [Provably efficient RL with Rich Observations via Latent State Decoding](https://mlsanity.com/paper/1901.09018/) (2019)
- [Minimax Weight and Q-Function Learning for Off-Policy Evaluation](https://mlsanity.com/paper/1910.12809/) (2019)
- [More Robust Doubly Robust Off-policy Evaluation](https://mlsanity.com/paper/1802.03493/) (2018)
- [Empirical Study of Off-Policy Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1911.06854/) (2019)
- [Towards Optimal Off-Policy Evaluation for Reinforcement Learning with Marginalized Importance Sampling](https://mlsanity.com/paper/1906.03393/) (2019)
- [Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes](https://mlsanity.com/paper/1908.08526/) (2019)
- [When Is Partially Observable Reinforcement Learning Not Scary?](https://mlsanity.com/paper/2204.08967/) (2022)
- [Off-Dynamics Reinforcement Learning: Training for Transfer with Domain Classifiers](https://mlsanity.com/paper/2006.13916/) (2020)
- [A Review of Off-Policy Evaluation in Reinforcement Learning](https://mlsanity.com/paper/2212.06355/) (2022)
- [RL for Latent MDPs: Regret Guarantees and a Lower Bound](https://mlsanity.com/paper/2102.04939/) (2021)
- [Off-Policy Evaluation in Partially Observable Environments](https://mlsanity.com/paper/1909.03739/) (2019)
- [Sample-Efficient Reinforcement Learning of Undercomplete POMDPs](https://mlsanity.com/paper/2006.12484/) (2020)
- [Off-policy Policy Evaluation For Sequential Decisions Under Unobserved Confounding](https://mlsanity.com/paper/2003.05623/) (2020)
- [Nearly Minimax Optimal Offline Reinforcement Learning with Linear Function Approximation: Single-Agent MDP and Markov Game](https://mlsanity.com/paper/2205.15512/) (2022)
- [Reinforcement Learning of POMDPs using Spectral Methods](https://mlsanity.com/paper/1602.07764/) (2016)
- [Proximal Reinforcement Learning: Efficient Off-Policy Evaluation in Partially Observed Markov Decision Processes](https://mlsanity.com/paper/2110.15332/) (2021)
- [Provable Reinforcement Learning with a Short-Term Memory](https://mlsanity.com/paper/2202.03983/) (2022)
- [A PAC RL Algorithm for Episodic POMDPs](https://mlsanity.com/paper/1605.08062/) (2016)
- [A Minimax Learning Approach to Off-Policy Evaluation in Confounded Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2111.06784/) (2021)
- [Provably Efficient Reinforcement Learning in Partially Observable Dynamical Systems](https://mlsanity.com/paper/2206.12020/) (2022)
- [Learning in Observable POMDPs, without Computationally Intractable Oracles](https://mlsanity.com/paper/2206.03446/) (2022)
- [Sample-Efficient Reinforcement Learning of Partially Observable Markov Games](https://mlsanity.com/paper/2206.01315/) (2022)

## Built on by (most cited first, 8 of 8)

- [To Distill or Decide? Understanding the Algorithmic Trade-off in Partially Observable Reinforcement Learning](https://mlsanity.com/paper/2510.03207/) (2025)
- [A Covering Framework for Offline POMDPs Learning using Belief Space Metric](https://mlsanity.com/paper/2603.03191/) (2026)
- [Design Experiments to Compare Multi-armed Bandit Algorithms](https://mlsanity.com/paper/2603.05919/) (2026)
- [Exponential Hardness of Off-Policy Evaluation under History-Dependent Logging](https://mlsanity.com/paper/2609.19135/) (2026)
- [Selecting Belief-State Approximations in Simulators with Latent States](https://mlsanity.com/paper/2511.20870/) (2025)
- [Minimax Optimal Strategy for Delayed Observations in Online Reinforcement Learning](https://mlsanity.com/paper/2603.03480/) (2026)
- [Off-Policy Evaluation for Missingness-Aware Policies in MDPs with Rewards Missing Not at Random](https://mlsanity.com/paper/2606.20206/) (2026)
- [Revealing After Overwriting: An Exponential POMDP OPE Lower Bound under History-Dependent Logging](https://mlsanity.com/paper/2610.05063/) (2026)

## Abstract (arXiv)

We investigate off-policy evaluation (OPE), a central and fundamental problem in reinforcement learning (RL), in the challenging setting of Partially Observable Markov Decision Processes (POMDPs) with large observation spaces. Recent works of Uehara et al. (2023a); Zhang & Jiang (2024) developed a model-free framework and identified important coverage assumptions (called belief and outcome coverage) that enable accurate OPE of memoryless policies with polynomial sample complexities, but handling more general target policies that depend on the entire observable history remained an open problem. In this work, we prove information-theoretic hardness for model-free OPE of history-dependent policies in several settings, characterized by additional assumptions imposed on the behavior policy (memoryless vs. history-dependent) and/or the state-revealing property of the POMDP (single-step vs. multi-step revealing). We further show that some hardness can be circumvented by a natural model-based algorithm -- whose analysis has surprisingly eluded the literature despite the algorithm's simplicity -- demonstrating provable separation between model-free and model-based OPE in POMDPs.