# Offline Minimax Soft-Q-learning Under Realizability and Partial Coverage

arXiv: https://arxiv.org/abs/2302.02392 · HTML: https://mlsanity.com/paper/2302.02392/

## Key facts

- Cited by 10 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 42 of its 54 references that are in the map.
- First posted on arXiv 5 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 42)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [MOPO: Model-based Offline Policy Optimization](https://mlsanity.com/paper/2005.13239/) (2020)
- [MOReL : Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2005.05951/) (2020)
- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [A Theory of Regularized Markov Decision Processes](https://mlsanity.com/paper/1901.11275/) (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)
- [A unified view of entropy-regularized Markov decision processes](https://mlsanity.com/paper/1705.07798/) (2017)
- [Equivalence Between Policy Gradients and Soft Q-Learning](https://mlsanity.com/paper/1704.06440/) (2017)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [Taming the Noise in Reinforcement Learning via Soft Updates](https://mlsanity.com/paper/1512.08562/) (2015)
- [Pessimistic Bootstrapping for Uncertainty-Driven Offline Reinforcement Learning](https://mlsanity.com/paper/2202.11566/) (2022)
- [Offline Reinforcement Learning with Realizability and Single-policy Concentrability](https://mlsanity.com/paper/2202.04634/) (2022)
- [Non-Asymptotic Gap-Dependent Regret Bounds for Tabular MDPs](https://mlsanity.com/paper/1905.03814/) (2019)
- [Reinforcement Learning via Fenchel-Rockafellar Duality](https://mlsanity.com/paper/2001.01866/) (2020)
- [Off-Policy Evaluation via the Regularized Lagrangian](https://mlsanity.com/paper/2007.03438/) (2020)
- [Pessimistic Q-Learning for Offline Reinforcement Learning: Towards Optimal Sample Complexity](https://mlsanity.com/paper/2202.13890/) (2022)
- [Towards Instance-Optimal Offline Reinforcement Learning with Pessimism](https://mlsanity.com/paper/2110.08695/) (2021)
- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [Statistical Inference of the Value Function for Reinforcement Learning in Infinite Horizon Settings](https://mlsanity.com/paper/2001.04515/) (2020)
- [Finite Sample Analysis of Minimax Offline Reinforcement Learning: Completeness, Fast Rates and First-Order Efficiency](https://mlsanity.com/paper/2102.02981/) (2021)
- [Corruption-Robust Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06630/) (2021)
- [Fast Rates for Contextual Linear Optimization](https://mlsanity.com/paper/2011.03030/) (2020)
- [Offline Reinforcement Learning Under Value and Density-Ratio Realizability: The Power of Gaps](https://mlsanity.com/paper/2203.13935/) (2022)
- [On Well-posedness and Minimax Optimal Rates of Nonparametric Q-function Estimation in Off-policy Evaluation](https://mlsanity.com/paper/2201.06169/) (2022)
- [Optimal Conservative Offline RL with General Function Approximation via Augmented Lagrangian](https://mlsanity.com/paper/2211.00716/) (2022)

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

- [Qsharp: Provably Optimal Distributional RL for LLM Post-Training](https://mlsanity.com/paper/2502.20548/) (2025)
- [Federated Offline Reinforcement Learning: Collaborative Single-Policy Coverage Suffices](https://mlsanity.com/paper/2402.05876/) (2024)
- [Inverse Reinforcement Learning with Just Classification and a Few Regressions](https://mlsanity.com/paper/2509.21172/) (2025)
- [Adversarially Trained Weighted Actor-Critic for Safe Offline Reinforcement Learning](https://mlsanity.com/paper/2401.00629/) (2024)
- [The Role of Inherent Bellman Error in Offline Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2406.11686/) (2024)
- [Bellman Calibration for V-Learning in Offline Reinforcement Learning](https://mlsanity.com/paper/2512.23694/) (2025)
- [Towards Optimal Offline Reinforcement Learning](https://mlsanity.com/paper/2503.12283/) (2025)
- [Fitted Q-Evaluation without Bellman Completeness via Occupancy Weighting](https://mlsanity.com/paper/2512.23805/) (2025)
- [On the Complexity of Offline Reinforcement Learning with Q^star-Approximation and Partial Coverage](https://mlsanity.com/paper/2602.12107/) (2026)
- [Fast Rates for Offline Q-Learning with KL Regularization](https://mlsanity.com/paper/2610.18839/) (2026)

## Abstract (arXiv)

In offline reinforcement learning (RL) we have no opportunity to explore so we must make assumptions that the data is sufficient to guide picking a good policy, taking the form of assuming some coverage, realizability, Bellman completeness, and/or hard margin (gap). In this work we propose value-based algorithms for offline RL with PAC guarantees under just partial coverage, specifically, coverage of just a single comparator policy, and realizability of soft (entropy-regularized) Q-function of the single policy and a related function defined as a saddle point of certain minimax optimization problem. This offers refined and generally more lax conditions for offline RL. We further show an analogous result for vanilla Q-functions under a soft margin condition. To attain these guarantees, we leverage novel minimax learning algorithms to accurately estimate soft or vanilla Q-functions with L2-convergence guarantees. Our algorithms' loss functions arise from casting the estimation problems as nonlinear convex optimization problems and Lagrangifying.