# On the Curses of Future and History in Future-dependent Value Functions for Off-policy Evaluation

arXiv: https://arxiv.org/abs/2402.14703 · HTML: https://mlsanity.com/paper/2402.14703/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 73 references that are in the map.
- First posted on arXiv 22 Feb 2024.

## Builds on (most cited first, 30 of 46)

- [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)
- [DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections](https://mlsanity.com/paper/1906.04733/) (2019)
- [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)
- [Hybrid RL: Using Both Offline and Online Data Can Make RL Efficient](https://mlsanity.com/paper/2210.06718/) (2022)
- [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)
- [Offline Reinforcement Learning with Realizability and Single-policy Concentrability](https://mlsanity.com/paper/2202.04634/) (2022)
- [Minimax-Optimal Off-Policy Evaluation with Linear Function Approximation](https://mlsanity.com/paper/2002.09516/) (2020)
- [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)
- [Provable Benefits of Actor-Critic Methods for Offline Reinforcement Learning](https://mlsanity.com/paper/2108.08812/) (2021)
- [Batch Value-function Approximation with Only Realizability](https://mlsanity.com/paper/2008.04990/) (2020)
- [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)
- [Improper Learning for Non-Stochastic Control](https://mlsanity.com/paper/2001.09254/) (2020)
- [Towards Instance-Optimal Offline Reinforcement Learning with Pessimism](https://mlsanity.com/paper/2110.08695/) (2021)
- [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)
- [Near-optimal Offline Reinforcement Learning with Linear Representation: Leveraging Variance Information with Pessimism](https://mlsanity.com/paper/2203.05804/) (2022)
- [Off-policy Policy Evaluation For Sequential Decisions Under Unobserved Confounding](https://mlsanity.com/paper/2003.05623/) (2020)
- [Reinforcement Learning of POMDPs using Spectral Methods](https://mlsanity.com/paper/1602.07764/) (2016)
- [PAC Reinforcement Learning for Predictive State Representations](https://mlsanity.com/paper/2207.05738/) (2022)
- [Provable Reinforcement Learning with a Short-Term Memory](https://mlsanity.com/paper/2202.03983/) (2022)

## Built on by (most cited first, 10 of 10)

- [Offline Reinforcement Learning in Large State Spaces: Algorithms and Guarantees](https://mlsanity.com/paper/2510.04088/) (2025)
- [Statistical Tractability of Off-policy Evaluation of History-dependent Policies in POMDPs](https://mlsanity.com/paper/2503.01134/) (2025)
- [RL in Latent MDPs is Tractable: Online Guarantees via Off-Policy Evaluation](https://mlsanity.com/paper/2406.01389/) (2024)
- [Reinforcement Learning with Continuous Actions Under Unmeasured Confounding](https://mlsanity.com/paper/2505.00304/) (2025)
- [A Unifying View of Coverage in Linear Off-Policy Evaluation](https://mlsanity.com/paper/2601.19030/) (2026)
- [A Covering Framework for Offline POMDPs Learning using Belief Space Metric](https://mlsanity.com/paper/2603.03191/) (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)
- [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 study off-policy evaluation (OPE) in partially observable environments with complex observations, with the goal of developing estimators whose guarantee avoids exponential dependence on the horizon. While such estimators exist for MDPs and POMDPs can be converted to history-based MDPs, their estimation errors depend on the state-density ratio for MDPs which becomes history ratios after conversion, an exponential object. Recently, Uehara et al. [2022a] proposed future-dependent value functions as a promising framework to address this issue, where the guarantee for memoryless policies depends on the density ratio over the latent state space. However, it also depends on the boundedness of the future-dependent value function and other related quantities, which we show could be exponential-in-length and thus erasing the advantage of the method. In this paper, we discover novel coverage assumptions tailored to the structure of POMDPs, such as outcome coverage and belief coverage, which enable polynomial bounds on the aforementioned quantities. As a side product, our analyses also lead to the discovery of new algorithms with complementary properties.