# A Spectral Approach to Off-Policy Evaluation for POMDPs

arXiv: https://arxiv.org/abs/2109.10502 · HTML: https://mlsanity.com/paper/2109.10502/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 22 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [Doubly Robust Off-policy Value Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1511.03722/) (2015)
- [Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1604.00923/) (2016)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Counterfactual Off-Policy Evaluation with Gumbel-Max Structural Causal Models](https://mlsanity.com/paper/1905.05824/) (2019)
- [Off-Policy Evaluation in Partially Observable Environments](https://mlsanity.com/paper/1909.03739/) (2019)
- [Off-policy Evaluation in Infinite-Horizon Reinforcement Learning with Latent Confounders](https://mlsanity.com/paper/2007.13893/) (2020)

## Built on by (most cited first, 21 of 21)

- [A Survey on Causal Reinforcement Learning](https://mlsanity.com/paper/2302.05209/) (2023)
- [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)
- [Off-Policy Confidence Interval Estimation with Confounded Markov Decision Process](https://mlsanity.com/paper/2202.10589/) (2022)
- [Off-Policy Evaluation in Partially Observed Markov Decision Processes under Sequential Ignorability](https://mlsanity.com/paper/2110.12343/) (2021)
- [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)
- [Reinforcement Learning from Partial Observation: Linear Function Approximation with Provable Sample Efficiency](https://mlsanity.com/paper/2204.09787/) (2022)
- [Offline Policy Evaluation and Optimization under Confounding](https://mlsanity.com/paper/2211.16583/) (2022)
- [On the Curses of Future and History in Future-dependent Value Functions for Off-policy Evaluation](https://mlsanity.com/paper/2402.14703/) (2024)
- [Statistical Tractability of Off-policy Evaluation of History-dependent Policies in POMDPs](https://mlsanity.com/paper/2503.01134/) (2025)
- [A Policy Gradient Method for Confounded POMDPs](https://mlsanity.com/paper/2305.17083/) (2023)
- [Two-way Deconfounder for Off-policy Evaluation in Causal Reinforcement Learning](https://mlsanity.com/paper/2412.05783/) (2024)
- [Blessing from Human-AI Interaction: Super Reinforcement Learning in Confounded Environments](https://mlsanity.com/paper/2209.15448/) (2022)
- [Causal Deep Reinforcement Learning Using Observational Data](https://mlsanity.com/paper/2211.15355/) (2022)
- [OPERA: Automatic Offline Policy Evaluation with Re-weighted Aggregates of Multiple Estimators](https://mlsanity.com/paper/2405.17708/) (2024)
- [A Unified Framework of Policy Learning for Contextual Bandit with Confounding Bias and Missing Observations](https://mlsanity.com/paper/2303.11187/) (2023)
- [Demystifying the Paradox of Importance Sampling with an Estimated History-Dependent Behavior Policy in Off-Policy Evaluation](https://mlsanity.com/paper/2505.22492/) (2025)
- [The Sample Complexity of Online Strategic Decision Making with Information Asymmetry and Knowledge Transportability](https://mlsanity.com/paper/2506.09940/) (2025)
- [Revealing After Overwriting: An Exponential POMDP OPE Lower Bound under History-Dependent Logging](https://mlsanity.com/paper/2610.05063/) (2026)

## Abstract (arXiv)

We consider off-policy evaluation (OPE) in Partially Observable Markov Decision Processes, where the evaluation policy depends only on observable variables but the behavior policy depends on latent states (Tennenholtz et al. (2020a)). Prior work on this problem uses a causal identification strategy based on one-step observable proxies of the hidden state, which relies on the invertibility of certain one-step moment matrices. In this work, we relax this requirement by using spectral methods and extending one-step proxies both into the past and future. We empirically compare our OPE methods to existing ones and demonstrate their improved prediction accuracy and greater generality. Lastly, we derive a separate Importance Sampling (IS) algorithm which relies on rank, distinctness, and positivity conditions, and not on the strict sufficiency conditions of observable trajectories with respect to the reward and hidden-state structure required by Tennenholtz et al. (2020a).