# Minimax Weight and Q-Function Learning for Off-Policy Evaluation

arXiv: https://arxiv.org/abs/1910.12809 · HTML: https://mlsanity.com/paper/1910.12809/

## Key facts

- Cited by 150 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2019.

## Built on by (most cited first, 30 of 150)

- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [What are the Statistical Limits of Offline RL with Linear Function Approximation?](https://mlsanity.com/paper/2010.11895/) (2020)
- [Offline Reinforcement Learning with Realizability and Single-policy Concentrability](https://mlsanity.com/paper/2202.04634/) (2022)
- [Hyperparameter Selection for Offline Reinforcement Learning](https://mlsanity.com/paper/2007.09055/) (2020)
- [Provable Benefits of Actor-Critic Methods for Offline Reinforcement Learning](https://mlsanity.com/paper/2108.08812/) (2021)
- [A Review of Off-Policy Evaluation in Reinforcement Learning](https://mlsanity.com/paper/2212.06355/) (2022)
- [Offline Reinforcement Learning: Fundamental Barriers for Value Function Approximation](https://mlsanity.com/paper/2111.10919/) (2021)
- [Model Selection for Offline Reinforcement Learning: Practical Considerations for Healthcare Settings](https://mlsanity.com/paper/2107.11003/) (2021)
- [Near-Optimal Offline Reinforcement Learning via Double Variance Reduction](https://mlsanity.com/paper/2102.01748/) (2021)
- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [Universal Off-Policy Evaluation](https://mlsanity.com/paper/2104.12820/) (2021)
- [Risk Bounds and Rademacher Complexity in Batch Reinforcement Learning](https://mlsanity.com/paper/2103.13883/) (2021)
- [DARA: Dynamics-Aware Reward Augmentation in Offline Reinforcement Learning](https://mlsanity.com/paper/2203.06662/) (2022)
- [Bootstrapping Fitted Q-Evaluation for Off-Policy Inference](https://mlsanity.com/paper/2102.03607/) (2021)
- [Instabilities of Offline RL with Pre-Trained Neural Representation](https://mlsanity.com/paper/2103.04947/) (2021)
- [Nearly Horizon-Free Offline Reinforcement Learning](https://mlsanity.com/paper/2103.14077/) (2021)
- [Deeply-Debiased Off-Policy Interval Estimation](https://mlsanity.com/paper/2105.04646/) (2021)
- [A Minimax Learning Approach to Off-Policy Evaluation in Confounded Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2111.06784/) (2021)
- [Offline Reinforcement Learning Under Value and Density-Ratio Realizability: The Power of Gaps](https://mlsanity.com/paper/2203.13935/) (2022)
- [Autoregressive Dynamics Models for Offline Policy Evaluation and Optimization](https://mlsanity.com/paper/2104.13877/) (2021)
- [On Well-posedness and Minimax Optimal Rates of Nonparametric Q-function Estimation in Off-policy Evaluation](https://mlsanity.com/paper/2201.06169/) (2022)
- [Towards Hyperparameter-free Policy Selection for Offline Reinforcement Learning](https://mlsanity.com/paper/2110.14000/) (2021)
- [Policy learning "without" overlap: Pessimism and generalized empirical Bernstein's inequality](https://mlsanity.com/paper/2212.09900/) (2022)
- [Average-Reward Off-Policy Policy Evaluation with Function Approximation](https://mlsanity.com/paper/2101.02808/) (2021)
- [Off-Policy Confidence Interval Estimation with Confounded Markov Decision Process](https://mlsanity.com/paper/2202.10589/) (2022)
- [A Statistical Analysis of Polyak-Ruppert Averaged Q-learning](https://mlsanity.com/paper/2112.14582/) (2021)
- [Optimal Conservative Offline RL with General Function Approximation via Augmented Lagrangian](https://mlsanity.com/paper/2211.00716/) (2022)

## Abstract (arXiv)

We provide theoretical investigations into off-policy evaluation in reinforcement learning using function approximators for (marginalized) importance weights and value functions. Our contributions include: (1) A new estimator, MWL, that directly estimates importance ratios over the state-action distributions, removing the reliance on knowledge of the behavior policy as in prior work (Liu et al., 2018). (2) Another new estimator, MQL, obtained by swapping the roles of importance weights and value-functions in MWL. MQL has an intuitive interpretation of minimizing average Bellman errors and can be combined with MWL in a doubly robust manner. (3) Several additional results that offer further insights into these methods, including the sample complexity analyses of MWL and MQL, their asymptotic optimality in the tabular setting, how the learned importance weights depend the choice of the discriminator class, and how our methods provide a unified view of some old and new algorithms in RL.